Payback Method | Payback Period Formula

The payback period is the time required for the amount invested in an asset to be repaid by the net cash outflow generated by the asset. It is a simple way to evaluate the risk associated with a proposed project.

The payback period is expressed in years and fractions of years. For example, if a company invests $300,000 in a new production line, and the production line then produces cash flow of $100,000 per year, then the payback period is 3.0 years ($300,000 initial investment / $100,000 annual payback). An investment with a shorter payback period is considered to be better, since the investor's initial outlay is at risk for a shorter period of time. The calculation used to derive the payback period is called the payback method.

The formula for the payback method is simplistic: Divide the cash outlay (which is assumed to occur entirely at the beginning of the project) by the amount of net cash flow generated by the project per year (which is assumed to be the same in every year).

Payback Period Example

Alaskan Lumber is considering the purchase of a band saw that costs $50,000 and which will generate $10,000 per year of net cash flow. The payback period for this capital investment is 5.0 years. Alaskan is also considering the purchase of a conveyor system for $36,000, which will reduce saw mill transport costs by $12,000 per year. The payback period for this capital investment is 3.0 years. If Alaskan only has sufficient funds to invest in one of these projects, and if it were only using the payback method as the basis for its investment decision, it would buy the conveyor system, since it has a shorter payback period.

Payback Method Advantages and Disadvantages

The payback period is useful from a risk analysis perspective, since it gives a quick picture of the amount of time that the initial investment will be at risk. If you were to analyze a prospective investment using the payback method, you would tend to accept those investments having rapid payback periods, and reject those having longer ones. It tends to be more useful in industries where investments become obsolete very quickly, and where a full return of the initial investment is therefore a serious concern. Though the payback method is widely used due to its simplicity, it suffers from the following problems:

1. Asset life span. If an asset’s useful life expires immediately after it pays back the initial investment, then there is no opportunity to generate additional cash flows. The payback method does not incorporate any assumption regarding asset life span.

2. Additional cash flows. The concept does not consider the presence of any additional cash flows that may arise from an investment in the periods after full payback has been achieved.

3. Cash flow complexity. The formula is too simplistic to account for the multitude of cash flows that actually arise with a capital investment. For example, cash investments may be required at several stages, such as cash outlays for periodic upgrades. Also, cash outflows may change significantly over time, varying with customer demand and the amount of competition.

4. Profitability. The payback method focuses solely upon the time required to pay back the initial investment; it does not track the ultimate profitability of a project at all. Thus, the method may indicate that a project having a short payback but with no overall profitability is a better investment than a project requiring a long-term payback but having substantial long-term profitability.

5. Time value of money. The method does not take into account the time value of money, where cash generated in later periods is work less than cash earned in the current period. A variation on the payback period formula, known as the discounted payback formula, eliminates this concern by incorporating the time value of money into the calculation.

6. Individual asset orientation. Many fixed asset purchases are designed to improve the efficiency of a single operation, which is completely useless if there is a process bottleneck located downstream from that operation that restricts the ability of the business to generate more output. The payback period formula does not account for the output of the entire system, only a specific operation. Thus, its use is more at the tactical level than at the strategic level.

7. Incorrect averaging. The denominator of the calculation is based on the average cash flows from the project over several years - but if the forecasted cash flows are mostly in the part of the forecast furthest in the future, the calculation will incorrectly yield a payback period that is too soon. The following example illustrates the problem.

Payback Method Example #2

ABC International has received a proposal from a manager, asking to spend $1,500,000 on equipment that will result in cash inflows in accordance with the following table:

Year Cash Flow1 +$150,0002 +150,0003 +200,0004 +600,0005 +900,000

The total cash flows over the five-year period are projected to be $2,000,000, which is an average of $400,000 per year. When divided into the $1,500,000 original investment, this results in a payback period of 3.75 years. However, the briefest perusal of the projected cash flows

reveals that the flows are heavily weighted toward the far end of the time period, so the results of this calculation cannot be correct.

Instead, the company's financial analyst runs the calculation year by year, deducting the cash flows in each successive year from the remaining investment. The results of this calculation are:

Year Cash Flow Net Invested Cash

0   -$1,500,000

1 +$150,000 -1,350,000

2 +150,000 -1,200,000

3 +200,000 -1,000,000

4 +600,000 -400,000

5 +900,000 0

The table indicates that the real payback period is located somewhere between Year 4 and Year 5. There is $400,000 of investment yet to be paid back at the end of Year 4, and there is $900,000 of cash flow projected for Year 5. The analyst assumes the same monthly amount of cash flow in Year 5, which means that he can estimate final payback as being just short of 4.5 years.

Summary

The payback method should not be used as the sole criterion for approval of a capital investment. Instead, consider using the net present value or internal rate of return methods to incorporate the time value of money and more complex cash flows, and use throughput analysis to see if the investment will actually boost overall corporate profitability. There are also other considerations in a capital investment decision, such as whether the same asset model should be purchased in volume to reduce maintenance costs, and whether lower-cost and lower-capacity units would make more sense than an expensive "monument" asset.

Similar Terms

The payback period formula is also known as the payback method.

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How do you calculate the payback period?The payback period is calculated by counting the number of years it will take to recover the cash invested in a project.

Let's assume that a company invests $400,000 in more efficient equipment. The cash savings from the new equipment is expected to be $100,000 per year for 10 years. The payback period is 4 years ($400,000 divided by $100,000 per year).

A second project requires an investment of $200,000 and it generates cash as follows: $20,000 in Year 1; $60,000 in Year 2; $80,000 in Year 3; $100,000 in Year 4; $70,000 in Year 5. The payback period is 3.4 years ($20,000 + $60,000 + $80,000 = $160,000 in the first three years + $40,000 of the $100,000 occurring in Year 4).

Note that the payback calculation uses cash flows, not net income. Also, the payback calculation does not address a project's total profitability. Rather, the payback period simply computes how fast a company will recover its cash investment.

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Home > Managerial Accounting > Capital Budgeting > Payback Period

Payback PeriodPayback period is the time in which the initial cash outflow of an investment is expected to be recovered from the cash inflows generated by the investment. It is one of the simplest investment appraisal techniques.

Formula

The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. In case they are even, the formula to calculate payback period is:

Payback Period = Initial Investment

Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

Payback Period = A +B

C

In the above formula,A is the last period with a negative cumulative cash flow;B is the absolute value of cumulative cash flow at the end of the period A;C is the total cash flow during the period after A

Both of the above situations are applied in the following examples.

Decision Rule

Accept the project only if its payback period is LESS than the target payback period.

Examples

Example 1: Even Cash FlowsCompany C is planning to undertake a project requiring initial investment of $105 million. The project is expected to generate $25 million per year for 7 years. Calculate the payback period of the project.

SolutionPayback Period = Initial Investment ÷ Annual Cash Flow = $105M ÷ $25M = 4.2 years

Example 2: Uneven Cash FlowsCompany C is planning to undertake another project requiring initial investment of $50 million and is expected to generate $10 million in Year 1, $13 million in Year 2, $16 million in year 3, $19 million in Year 4 and $22 million in Year 5. Calculate the payback value of the project.

Solution

(cash flows in millions) CumulativeCash FlowYear Cash Flow

0 (50) (50)

1 10 (40)

2 13 (27)

3 16 (11)

4 19 8

5 22 30

Payback Period= 3 + (|-$11M| ÷ $19M)= 3 + ($11M ÷ $19M)≈ 3 + 0.58≈ 3.58 years

Advantages and Disadvantages

Advantages of payback period are:

1. Payback period is very simple to calculate.2. It can be a measure of risk inherent in a project. Since cash flows that occur later in a project's

life are considered more uncertain, payback period provides an indication of how certain the project cash inflows are.

3. For companies facing liquidity problems, it provides a good ranking of projects that would return money early.

Disadvantages of payback period are:

1. Payback period does not take into account the time value of money which is a serious drawback since it can lead to wrong decisions. A variation of payback method that attempts to remove this drawback is called discounted payback period method.

2. It does not take into account, the cash flows that occur after the payback period.

Written by Irfanullah Jan

The Payback Period represents the amount of time that it takes for a Capital Budgeting project to recover its initial cost. The use of the Payback Period as a Capital Budgeting decision rule specifies that all independent projects with a Payback Period less than a specified number of years should be accepted. When choosing among mutually exclusive projects, the project with the quickest payback is preferred.

The calculation of the Payback Period is best illustrated with an example. Consider Capital Budgeting project A which yields the following cash flows over its five year life.

YearCash Flow

0 -1000

1 500

2 400

3 200

4 200

5 100

To begin the calculation of the Payback Period for project A let's add an additional column to the above table which represents the Net Cash Flow (NCF) for the project in each year.

YearCash Flow

Net Cash Flow

0 -1000 -1000

1 500 -500

2 400 -100

3 200 100

4 200 300

5 100 400

Notice that after two years the Net Cash Flow is negative (-1000 + 500 + 400 = -100) while after three years the Net Cash Flow is positive (-1000 + 500 + 400 + 200 = 100). Thus the Payback Period, or breakeven point, occurs sometime during the third year. If we assume that the cash flows occur regularly over the course of the year, the Payback Period can be computed using the following equation:

Thus, the Payback Period for project A can be computed as follows:

Payback Period

Payback Period = 2 + (100)/(200) = 2.5 years

Thus, the project will recoup its initial investment in 2.5 years.

As a decision rule, the Payback Period suffers from several flaws. For instance, it ignores the Time Value of Money, does not consider all of the project's cash flows, and the accept/reject criterion is arbitrary.

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Example Problems

Find the Payback Period for the project with the

following cash flows.

Year   Cash Flow  

0 $  

1 $  

2 $  

3 $  

4 $  

5 $  

Payback:   years

   

 

Net Present Value

The Net Present Value (NPV) of a Capital Budgeting project indicates the expected impact of the project on the value of the firm. Projects with a positive NPV are expected to increase the value of the firm. Thus, the NPV decision rule specifies that all independent projects with a positive NPV should be accepted. When choosing among mutually exclusive projects, the project with the largest (positive) NPV should be selected.

The NPV is calculated as the present value of the project's cash inflows minus the present value of the project's cash outflows. This relationship is expressed by the following formula:

where

CFt = the cash flow at time t and r = the cost of capital.

The example below illustrates the calculation of Net Present Value. Consider Capital Budgeting projects A and B which yield the following cash flows over their five year lives. The cost of capital for the project is 10%.

  Project A Project B

YearCash Flow

Cash Flow

0 $-1000 $-1000

1 500 100

2 400 200

3 200 200

4 200 400

5 100 700

Net Present Value

Project A:

Project B:

Thus, if Projects A and B are independent projects then both projects should be accepted. On the other hand, if they are mutually exclusive projects then Project A should be chosen since it has the larger NPV.

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Example Problems

Find the NPV for the following Capital Budgeting project.

Year   Cash Flow  

0 $  

1 $  

2 $  

3 $  

4 $  

5 $  

Cost of Capital:   %

NPV: $  

   

 

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Internal Rate of Return

The Internal Rate of Return (IRR) of a Capital Budgeting project is the discount rate at which the Net Present Value (NPV) of a project equals zero. The IRR decision rule specifies that all independent projects with an IRR greater than the cost of capital should be accepted. When choosing among mutually exclusive projects, the project with the highest IRR should be selected (as long as the IRR is greater than the cost of capital).

where

CFt = the cash flow at time t and

The determination of the IRR for a project, generally, involves trial and error or a numerical technique. Fortunately, financial calculators greatly simplify this process.

The example below illustrates the determination of IRR. Consider Capital Budgeting projects A and B which yield the following cash flows over their five year lives. The cost of capital for both projects is 10%.

  Project A Project B

YearCash Flow

Cash Flow

0 $-1000 $-1000

1 500 100

2 400 200

3 200 200

4 200 400

5 100 700

Internal Rate of Return

Project A:

Project B:

Thus, if Projects A snd B are independent projects then both projects should be accepted since their IRRs are greater than the cost of capital. On the other hand, if they are mutually exclusive projects then Project A should be chosen since it has the higher IRR.

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Example Problems

Find the IRR for the following Capital Budgeting project.

Year   Cash Flow  

0 $  

1 $  

2 $  

3 $  

4 $  

5 $  

IRR:   %

   

Investment Appraisal

Purpose

All businesses require capital equipment (fixed assets) such as machinery, premises and vehicles. The purchase of such assets is known as capital investment and is undertaken for the following reasons:

1. To replace existing equipment which is out-of-date or obsolete2. To expand the productive capacity of the business

3. To reduce the production costs per unit (i.e. to achieve economies of scale)

4. To produce new products and, therefore, break into new markets

Capital investment, like all other business activities, involves an element of uncertainty, because expenditure is incurred today in order to produce some benefit in the future. Investment appraisal techniques are designed to aid decision-making regarding such investment projects.

There are 3 methods which can be used to appraise any investment project:

1. The Payback method2. The Average Rate of Return (A.R.R) method

3. The Net Present Value (N.P.V) method.

Payback Method

This is the simplest method of investment appraisal and is usually preferred by small businesses because of its simplicity. Larger businesses may use it as a screening process before embarking on one of the more complicated techniques.

The payback period is the time taken for the equipment, (machinery etc.), to generate sufficient net cash flow to pay for itself.

For example:

A manufacturing firm is considering investing £ 500,000 in new machinery. The equipment is expected increase the firm's cashflow by £ 150,000 per year. How long is the payback period ?

After 1 year, the cashflow will be £ 150,000.

After 2 years, the cashflow will be £ 300,000.

After 3 years, the cashflow will be £ 450,000.

The firm will need £ 50,000 (or one third) of the cashflow from year 4 in order to reach the payback point.

Therefore, the payback period is 3 1/3 years (or 3 years, 4 months).

Firms can use this technique in one of two ways:

Firstly, a firm could set an upper limit on the time allowed for payback, and any project which is not expected to payback within this period is rejected.

Secondly, when faced with a choice of projects, the payback method can be used to rank projects according to the speed at which they payback.

However, the payback method ignores the following two important factors:

1. The total return on the investment project (i.e. the earnings after payback).

2. The timing of the return prior to payback.

The payback method clearly discriminates against projects which produce a slow but substantial return, resulting in the danger that highly profitable projects will be rejected because of the delay in producing a return (yield).

Example:

Each of the three alternative projects below involve an initial cost of £ 1 million, and produce net cash flow as shown:

PROJECT YEAR 1 YEAR 2 YEAR 3 YEAR 4 YEAR 5

A £ 0m £ 0.5m £ 0.5m £ 0.5m £ 0.5m

B £ 0.5m £ 0.5m £ 0.5m £ 0m £ 0m

C £ 0m £ 0m £ 0.5m £ 1m £ 1m

Project A pays back in 3 years (£ 0 in year 1 + £ 0.5m in year 2 + £ 0.5m in year 3).

Project B pays back in 2 years (£ 0.5m in year 1 + £ 0.5m in year 2).

Project C pays back in 3 1/2 years (£ 0 in year 1 + £ 0 in year 2 + £ 0.5m in year 3 + half of the £ 1m in year 4).

Using 'The Pay-back Method' to decide between these projects, project B would be selected. But if you looked at the total revenue over the full life of each project, project C actually brings more cash into the business and would be the better project to select.

Average Rate of Return (A.R.R.) Method

This method takes the total return (yield) over the whole life of the asset into account and therefore overcomes one of the defects of the payback method.

In order to understand the arithmetic, consider an item of capital (e.g. a machine) which will cost £ 1 million to purchase, is expected to last 5 years, and will produce an annual net cash flow of £ 0.5 million.

The total return (yield) is: 5 x £ 0.5 million = £ 2.5 million

If we now deduct the initial cost of investment (£ 1 million) we are left with a total return (yield), net of the initial capital outlay, of £ 1.5 million.

Annually, this works out at:

When we express this annual figure as a percentage of the original capital outlay we get the Average Rate of Return for the project:

To recap, the 4 steps for calculating the A.R.R. are:

1. Add up the total forecasted net cash flow2. Deduct the capital outlay from this

3. Divide the resulting figure by the expected life (in years) of the capital

4. Express this annual figure as a percentage of the capital outlay

As with the Payback method, we can use the A.R.R. in two ways. Firstly, the firm might set a predetermined level and reject any project which has an expected A.R.R. less than this percentage. Secondly, when faced with a choice of alternative projects, then the projects can be ranked by their A.R.R.

Further examples. A firm is considering three alternative investment projects. The maximum life of each asset is three years and the capital outlay is £ 100,000 in each case. The table below depicts net cash flow in each of the three years:

PROJECT YEAR 1 YEAR 2 YEAR 3

A £ 50,000 £ 50,000 £ 50,000

B £ 100,000 £ 20,000 £ 0

C £ 0 £ 50,000 £ 140,000

Project A:

Total forecasted net cash flow = £ 150,000

Total forecasted net cash flow - capital outlay = £ 50,000

£ 16,666.67 (this is the amount of profit per year)

16.67%.

Project B:

Total forecasted net cash flow = £ 120,000

Total forecasted net cash flow - capital outlay = £ 20,000

£ 6,666.67 (this is the amount of profit per year)

6.67%

Project C:

Total forecasted net cash flow = £ 190,000

Total forecasted net cash flow - capital outlay = £ 90,000

£ 30,000 (this is the amount of profit per year)

30%

The great defect of the A.R.R. method of investment appraisal is that it attaches no importance to the timing of the inflows of cash. A.R.R treats all money as of equal value, irrespective of when it is received.

Hence, a project may be favoured even though it only produces a return over a long period of time.

The more sophisticated methods of investment appraisal take the timing of the cash inflows into account, as well as the size of the inflows.

A sum of money in one year's time is worth less than that same sum of money now (i.e. inflation will erode the real value of that sum of money over the year). This is where the notion of present value is used.

Net Present Value (N.P.V.) Method

The return on an investment comes in the form of a stream of earnings in the future. The N.P.V. method of investment appraisal takes into account the size of the cash inflows over the life of the equipment, but also makes adjustment for the timing of the money. A greater weighting (or importance) is given to the inflows of cash in the earlier years.

The weighting can be calculated from the following formula:

A = the actual sum of money concerned

r = the rate of discount (called the 'Discount factor')

n = the number of years

This enables us to calculate the present value of money, net of operating costs, to be received in a certain number of years. Hence, £ 1000 in two years time, at a 3% rate of discount, has a present value of:

In examinations you will usually be given the discount factor, so that you do not have to work it out!

The present value of each year's cash inflow are then aggregated (this is called the discounted cashflow, or D.C.F) and this figure is compared with the initial capital outlay. If the sum of present values (minus the capital cost) is positive, then it is worthwhile proceeding with the project. If the resulting figure is negative, then the project should not be undertaken.

Example:

In appraising a £ 300,000 investment project, a firm uses a discount rate of 5%. The equipment will produce a cash inflow (net of operating costs) of £ 75,000 per year, over a five year period. At the end of the five years, the firm expects to sell the equipment for £ 10,000. What is the Net Present Value of the project?

Year cashflow Present Value

0 -£ 300,000 -£ 300,000

1 +£ 75,000 +£ 71,428.57

2 +£ 75,000 +£ 68,027.21

3 +£ 75,000 +£ 64,787.82

4 +£ 75,000 +£ 61,702.69

5 +£ 85,000 +£ 66,599.72

Year 0 is the present day (i.e. when the initial capital outlay is spent).

The cashflow of £ 75,000 in year 1 has a present value of:

£ 71,428.57

The cashflow of £ 75,000 in year 2 has a present value of:

£ 68,027.21

The process continues for the remaining years.

The discounted cashflow is the sum of the present values for the 5 cash inflows (i.e. from year 1 to year 5).

This figure is £ 332,546.01

The net present value is found by deducting the initial capital outlay from the discounted cashflow. In other words:

£ 332,546.01 - £ 300,000 = £ 32,546.01

Since this result is positive, then it is advisable for the firm to go ahead with the investment project. If the result had been negative, then the investment project should not be undertaken.

Other Influencing Factors

There are many other factors that a business will need to take into consideration when appraising an investment project, other than the financial (quantitative) factors.

Qualitative factors such as the objectives of the business must be considered at all times, as well as the effect upon the employees of new machinery, new working practices and changes to their working conditions.

The external environment needs to be considered before any decision can be taken regarding a proposed investment project.

These factors include the state of the economy (e.g. it may be dangerous to attempt to expand during a recession, because demand for products may be falling), pressure group activity, the level of technological progress in the industry (e.g. competitors may already be using the new machinery), and any legislation (e.g. restricting the use of certain materials, components).

The effects of the actions of the business on the environment must also be taken into consideration, since any external costs (e.g. pollution) will have a detrimental effect on the image and reputation of the business.

Finally, as with any investment decision, the business will also need to consider the amount of finance that is available for expansion, and the effect that any borrowing to raise extra finance will have on the gearing ratio.

A rate of return is measure of profit as a percentage of investment.

How it works/Example:

Let's say John Doe opens a lemonade stand. He invests $500 in the venture, and the lemonade stand makes about $10 a day, or about $3,000 a year (he takes some days off).

In its simplest form, John Doe's rate of return in one year is simply the profits as a percentage of the investment, or $3,000/$500 = 600%.

There is one fundamental relationship you should be aware of when thinking about rates of return: the riskier the venture, the higher the expected rate of return.

For example, investing in a restaurant is much riskier than investing in Treasury bills. One is backed by the full faith and credit of the United States government; the other is backed by your cousin's sofa. Accordingly, the risk that you'll lose your money is much higher in the restaurant scenario, and to induce and reward you to make the investment, the anticipated returns have to be much higher than the 1% that the Treasury bill would pay. Inversely, the safer the investment, the lower the expected rate of return should be.

Why it Matters:

If only it were that simple. Rates of return often involve incorporating other factors, including the bites that inflation and taxes take out of profits, the length of time involved, and any additional capital an investor makes in the venture. If the investment is foreign, then changes in exchange rates will also affect the rate of return.

Compounded annual growth rate (CAGR) is a common rate of return measure that represents the annual growth rate of an investment for a specific period of time.The formula for CAGR is:CAGR   =   (EV/BV)1/n - 1

where:EV = The investment's ending valueBV = The investment's beginning valuen  = Years

For example, let's assume you invest $1,000 in the Company XYZ mutual fund, and over the next five years, the portfolio looks like this:

End of Year    Ending Value1                              $7502                              $1,0003                              $3,0004                              $4,0005                              $5,000

Using this information and the formula above, we can calculate that the CAGR for the investment is:

CAGR = ($5,000/$1,000)1/5 - 1 = .37972 = 37.97%

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Home > Managerial Accounting > Capital Budgeting > Accounting Rate of Return

Accounting Rate of Return (ARR)Accounting rate of return (also known as simple rate of return) is the ratio of estimated accounting profit of a project to the average investment made in the project. ARR is used in investment appraisal.

Formula

Accounting Rate of Return is calculated using the following formula:

ARR = Average Accounting Profit

Average Investment

Average accounting profit is the arithmetic mean of accounting income expected to be earned during each year of the project's life time. Average investment may be calculated as the sum of the beginning and ending book value of the project divided by 2. Another variation of ARR formula uses initial investment instead of average investment.

Decision Rule

Accept the project only if its ARR is equal to or greater than the required accounting rate of return. In case of mutually exclusive projects, accept the one with highest ARR.

Examples

Example 1: An initial investment of $130,000 is expected to generate annual cash inflow of $32,000 for 6 years. Depreciation is allowed on the straight line basis. It is estimated that the project will generate scrap value of $10,500 at end of the 6th year. Calculate its accounting rate of return assuming that there are no other expenses on the project.

SolutionAnnual Depreciation = (Initial Investment − Scrap Value) ÷ Useful Life in YearsAnnual Depreciation = ($130,000 − $10,500) ÷ 6 ≈ $19,917Average Accounting Income = $32,000 − $19,917 = $12,083Accounting Rate of Return = $12,083 ÷ $130,000 ≈ 9.3%

Example 2: Compare the following two mutually exclusive projects on the basis of ARR. Cash flows and salvage values are in thousands of dollars. Use the straight line depreciation method.

Project A:

Year 0 1 2 3

Cash Outflow -220

Cash Inflow 91 130 105

Salvage Value 10

Project B:

Year 0 1 2 3

Cash Outflow -198

Cash Inflow 87 110 84

Salvage Value 18

Solution

Project A:

Step 1: Annual Depreciation = ( 220 − 10 ) / 3 = 70

Step 2: Year 1 2 3

Cash Inflow 91 130 105

Salvage Value 10

Depreciation* -70 -70 -70

Accounting Income 21 60 45 

Step 3: Average Accounting Income = ( 21 + 60 + 45 ) / 3

= 42

Step 4: Accounting Rate of Return = 42 / 220 = 19.1%

Project B:

Step 1: Annual Depreciation = ( 198 − 18 ) / 3 = 60

Step 2: Year 1 2 3

Cash Inflow 87 110 84

Salvage Value 18

Depreciation* -60 -60 -60

Accounting Income 27 50 42 

Step 3: Average Accounting Income = ( 27 + 50 + 42 ) / 3

= 39.666

Step 4: Accounting Rate of Return = 39.666 / 198 ≈ 20.0%

Since the ARR of the project B is higher, it is more favorable than the project A.

Advantages and Disadvantages

Advantages

1. Like payback period, this method of investment appraisal is easy to calculate.2. It recognizes the profitability factor of investment.

Disadvantages

1. It ignores time value of money. Suppose, if we use ARR to compare two projects having equal initial investments. The project which has higher annual income in the latter years of its useful life may rank higher than the one having higher annual income in the beginning years, even if the present value of the income generated by the latter project is higher.

It can be calculated in different ways. Thus there is problem of consistency.

2. It uses accounting income rather than cash flow information. Thus it is not suitable for projects which having high maintenance costs because their viability also depends upon timely cash inflows.

Written by Irfanullah Jan

RATES OF RETURN : UNDERSTAND, MEASURE AND COMPARE

What do rates of returns measure and why are they important?

An example of a 'rate of return' is the interest rate quoted for a term deposit. This is the metric most used to compare different investments. It is expressed as a percent because investment opportunities come in all sizes. Absolute dollars of profit do not allow for comparison, but a percentage is 'relative'. The period of time measured is almost always presumed to be one year.

The profits from an investment can come from income received during the holding period, and also capital gains from the eventual sale. Together these are called the "total return". When comparing investments always use the total return. E.g.

Buyers of dividend paying stocks too often look only at the dividend and ignore the potential for capital loss/gain.

Before investing in foreign countries consider the capital losses that may be caused by changing Foreign Exchange (FX) rates.

Detailed instructions for measuring your own portfolio's rate of return are on the page Keep Track.

Are quoted rates of return comparable between investments? NO !

Each of the asset types in the box below has its returns normally calculated in a different way. For most uses the results are 'good enough' for comparisons. But for any fine-tuning of a decision take the time to translate the 'normally' calculated return into a 'true' economic rate of return. The IIAC (investment industry self-regulating body) has produced this document of measurement conventions for fixed income products. Conventions may differ between countries. This page is written from a Canadian's perspective.

Security Type Method of Calculation

Flat rate GIC, CD, CSB, term deposit

compound when interest payable, measured as simple interest

Credit card debt, bank line of accrue daily, compound monthly, measured as compound interest

credit, bank acc't

Bond yield compound every 6 months, measured as simple interest

Bond couponsaccrue daily, does not compound when payable, measured as simple interest

Stock index ignores cash flows, continually compounding on price alone

Stocks, total return stock index, mutual funds

continually compounding on price plus all cash flows to/from owners

Stock dividend does not compound when payable, measured as simple interest

Cdn mortgagecompound with payment schedule, measured as the simple interest derivation of 6-month compound rate

US monthly mortgage compound monthly, measured as simple interest

US weekly mortgage compound weekly, measured as simple interest

Real estate measured as cumulative interest over holding period

Gross domestic product (GDP) compound yearly, measured as a 'real' rate

Government T-Bills have their own specific rules

The 'true' rate of return is what most people's understanding of it would be. People refer to it as the Compound Annual Growth rate (CAGR), Effective Annual rate, Annual Equivalent rate, Internal Rate of Return (IRR), discount rate, geometric mean, or Annualized Compound rate.. Essentially these all refer to the same concept. Different terms are used in different contexts.

E.g. if $100 invested at the beginning of the year grows to $112 by the end of the year, then the rate of return was 12%. To be more specific;

The period used is one year. The income paid, or payable, or accrued is included in the ending value,

Any income paid early is re-invested to earn its own income for the remaining portion of the year, or considered to have done so.

That income-on-income is included in the end-of-year value.

What do those terms mean?

There are many different words used to describe the type of income measurement being used in different situations. Unfortunately different people use different words, and use the same word to mean different thing. Always clarify in your mind what is being meant, without preconceptions.

REAL vs. NOMINAL returns ANNUAL vs. CUMULATIVE returns (also called HOLDING PERIOD return)

TOTAL return

AVERAGE returns (arithmetic vs geometric)

REALIZED profits vs. PAPER profits

ACCRUED interest

TO COMPOUND (verb)

REGULAR vs. COMPOUND interest (adjective)

NOMINAL vs. EFFECTIVE rates

SIMPLE vs. COMPOUND INTEREST (methodology)

SIMPLE INTEREST (methodology)

COMPOUND INTEREST (methodology)

GOVERNMENT T-BILL rates

REAL vs. NOMINAL returns: Real rates of return are what is left after the rate of inflation has been subtracted from the nominal rate. Much analysis of historical stock returns uses real returns because all investors demand at least the rate of inflation in order to justify deferring consumption, so it is premium above inflation that matters. E.g. Long-bond yields have historically been equal to 2% plus inflation. The '2%' is the real yield. It represents the risk premium for term risk - ignoring the compensation for inflation.E.g. GDP is the yearly production of a country measured using the market value of items. Its year-to-year change is heavily influenced by the inflation increases of the transactions. So the percent change in GDP is usually reported with the rate of inflation (GDP deflator) removed.

Instead of simple subtraction, you sometimes see the calculation of the real return as:

((1+return) / (1+inflation)) - 1. E.g. ((1+5%) / (1+3%)) - 1 = 1.9% real return (not 2%). This is the technically correct math but the simple subtraction is good enough.

See also the discussion below on "Nominal vs. Effective rates".

ANNUAL vs. CUMULATIVE return (also called HOLDING PERIOD return) :

Cumulative returns measure the total increase in the value of an investment over a number of years, not just one year. For example: if you bought your home for $100,000 and sold it 10 years later for $150,000, you had a 50% cumulative return.

Sometimes this measurement is the simplest, and perfectly valid, when comparing investments with the same time frame. But most times it is used to impress you because it produces a large number. You may not be told explicitly that it is cumulative - hoping you will think it is the annual rate earned each year of the investment. Even if they tell you, they count on you not being able to quickly convert it into a yearly return (only 4.1% in that example).

Most everyone thinks of rates of return in the context of a one year period. That percentage is 'meaningful' to people. They have certain benchmarks in their mind for comparison. They know the yearly rate for term deposits or for their bank's Line Of Credit. They know the yearly inflation rate. When comparing investments, yearly rates are the most logical, because investment terms may differ.

You may hear the cumulative return referred to as a Total Return.

TOTAL return :

You hear the term Total Return used most often to clarify that both the capital gains plus all dividend and interest income is being measured in total. E.g. Stock indexes measure only the price changes of their component companies. But some indexes publish their Total Return variant that includes dividends paid and the income earned by the reinvestment of those dividends. It is the Total Return Indexes that would be used to benchmark your own portfolio returns.

The term 'total return' is also used when referring to what is called 'cumulative return' above.

AVERAGE returns (arithmetic vs geometric) :

You know how to calculate an arithmetic average. But the question is: "Do investors WANT to find an average return of a multi-year period?" Consider the example

Start with $100 Earn 100% return the first year. ($100*100%=$100 profit)

Lose 50% the second year. ($200*50%=$100 loss)

End with the same original $100

The arithmetic average return of the two years would be (100 - 50) / 2 = 25%. But over the whole period there was a 0% true return ("geometric mean"). Using arithmetic averages means that any losses will be undervalued because they are calculated on the higher amount at the year's start. The arithmetic mean will always be larger than the geometric mean.

The greater the volatility of individual year's returns, the greater the difference between the arithmetic and geometric means. The difference can be estimated by the equation: Difference = 1/2 Variance = 1/2 StandardDeviationSquaredE.g. US equities historically had a 20% standard deviation with a 10% average (geometric) return. The expected difference would be 1/2 * 0.2 * 0.2 = 2%. The expected arithmetic mean would be 10% + 2% = 12%.

Fortunately, when you hear the term 'average' used by mutual funds or others in the finance industry, it almost always refers to the geometric mean that you DO want to use to compare investments. They use the term 'average' because that is the concept everyone understands.

REALIZED profits vs. PAPER profits :

Realized profits have been converted to cash by a transaction. E.g. dividend dollars have been received, or an asset has been sold. Paper profits have had no transaction to prove their value. E.g. increases in market value have been calculated but the assets not yet sold. This distinction does not affect the method chosen to measure the rate of return.

Many investors have a preference for high dividend stocks because they feel this cash is more 'real' than paper profits. But in the accumulation phase, those realized profits must be reinvested back into paper assets, leaving the investor no more sure of his wealth gains.

ACCRUED interest :

Accrued interest is acknowledged as payable, eventually, but not yet booked (posted to your account). For example with credit cards, the interest expense for each day is calculated individually. Only at month end are they added together and posted to your account. The total accrued up to any mid-month date does not affect the calculation of interest for subsequent days. I.e. it has only accrued, not compounded.

Bank accounts and credit cards post all the daily accruals for the month, at the month end. Only then does it compound. With bonds, the accruals keep adding up for 6-months, until they equal the interest payment due. When buying a bond or debenture, you pay the transaction price plus the portion of the next interest payment that has accrued since the bond's last payment.

TO COMPOUND (verb) :

Some investments have interest that compounds. E.g. a mortgage's interest compounds. It means that any unpaid interest that is due, but not paid, is added to the balance of the principal ... so the subsequent interest is calculated on the now-bigger balance. Of course if the mortgage payment is received, nothing compounds.

Compounding reflects an activity that is factual (true or not). For example: Preferred shares have their attributes defined by the prospectus. The prospectus will state (e.g.) that the dividends are cumulative (accrue if unpaid), but none say that unpaid dividends compound (unpaid dividends never earn interest to compensate for their being paid late).

The frequency of compounding will always be at least as often as the scheduled cash flows. E.g. A monthly-pay mortgage will compound monthly and a weekly-pay mortgage will compound weekly. If it were not to compound, there would be no incentive to make the required payment - the eventual payment would be the same whether paid on time, or late. It is the compounding that creates the incentive to pay on time.

The more frequent the compounding the greater the true rate of return. This is because the income is put to work quicker, earning more of its own income.

Principal at the start (P). Interest earned in 1st compounding period = (P * i%).

Principal value then after the interest compounds = P + (P * i%) or P*(1 + i%).

Interest earned in 2nd compounding period = P*(1 + i%) * i%.

Principal value then after the 2nd period's interest compounds = P*(1 + i%)(1 + i%).

If the investment compounded monthly, then there would be twelve repeats of (1 + i%) in a year. The interest rate i% is not the yearly rate. It is the rate for only the compounding period - in this example the monthly rate. The 'true' yearly rate would be calculated from the the resulting (Principal at end) / (Principal at beginning) - 1 ... as if the interest compounding each month does not get paid.

REGULAR vs. COMPOUND interest (adjective) :

These terms are usually used to describe term deposits, GICs and CDs. They are meant to distinguish between

products that pay out the interest earned when it becomes payable (regular), and products that retain the interest and reinvest it (compound).

NOMINAL vs. EFFECTIVE rates :

The use of these terms is virtually synonymous with "simple vs. compound interest (methodology)" below. The terms are used in the context of quoting two different rates for the same product; one using simple interest methodology (nominal) and another using compounding interest methodology (effective). Warning, 'nominal' was also used above in the section "real vs. nominal returns".

SIMPLE vs. COMPOUND INTEREST (methodology) :

There are two ways to measure yearly interest, just like a distance can be measured in English or Metric. Or think of the two systems like two languages that both use the same words (interest rate), but to mean different things. When you hear the term 'compound' ask yourself first whether it is used as a verb or an adjective to indicate the measurement method.

When a product is described as "x% compounded monthly" (or weekly, etc) you know the rate is measured using simple interest methodology because none of that clarification is necessary when measuring with compound interest methodology.

The following two sections describe each in more detail.

SIMPLE INTEREST (methodology) :

To calculate the rate of return using simple interest methodology, add all the interest paid in a year is added together. NO income earned on re-invested income is included. Divided that by the investment $$ at the beginning of the year. Simple interest methodology ignores the time-value-of-money (TVM means a dollar today is worth more than a dollar tomorrow). If a $100 investment pays $1 interest each month, simple interest methodology treats all the year's $12 as if paid at the year end. It would make no difference if all the $12 was paid after the second day. The return would still be measured as $12/$100 = 12%.

Bonds pay interest twice yearly. If they are quoted to pay 12%, then 6% is paid each 6 months.

GICs and US mortgages may be paid every month. If their quoted rate is 12%, then 1% is paid/charged each month.

Stocks' dividend yields are quoted as the total of all (normally 4) payments in the

year, divided by the current stock price.

COMPOUND INTEREST (methodology) :

Compound interest takes into account the time-value-of-money. It recognizes that being paid interest before the end of the year allows you to reinvest it to earn additional income (regardless what you actually do with the money). E.g. 12% simple interest that pays 6% twice a year would be quoted as 12.36% compound interest.

Principal at the start (P = $100). Interest earned in 1st 6-month compounding period = (P * i%) = $100 * 6% = $6.

Principal value then after the interest compounds = P + (P * i%) or P*(1 + i%) = $106.

Interest earned in 2nd 6-month compounding period = P*(1 + i%) * i% = $106 * 6% = $6.36.

Principal value at year's end = P*(1 + i%)(1 + i%) = $112.36 compound interest.

It makes no difference to the measurement process whether interest is paid out or reinvested within the original product. Interest paid out is presumed used to buy another investment that earns the same return.

Stock total-return indexes are measured using compound interest. Whenever the component stocks pay dividends, the dividends are considered to be reinvested to buy more index units. The value of the investment at the end of the year includes the value of the additional units bought plus any dividends subsequently earned by those units.

GOVERNMENT T-BILL rates :

Their interest rate is measured with a specific convention. They are bought at some discount to their $100 face value. Where 'P' stands for the price paid, the interest rate = (100 - P) divided by P. Instead of normalizing it to a year, the interest is prorated by 't' the number of days: (365 / t) * 100.

Buy a financial calculator

Buying a financial calculator is the only way to deal with these inconsistencies. A $40 model will last you a lifetime and be used every day. Although not stocked most of the year, they are available during back-to-school sales in September. At other times of the year they can be found in university book stores and on line. UPDATE: there are now phone apps that do the job. Look for those with the five basic inputs below. Many have built in situation-specific modules, but you never know what assumptions they have used in the background.

The best calculator on the web is from Finance Calculator. Keep this link at the top of your Favorites list. If you want a hard-copy printout you can use these tables. These are what we used 'in the good old days'.

For a more comprehensive list of equations that derive from the time-value-of-money read this page from Wikipedia.

Time Value of Money

The three time-lines below exemplify most investments. Match the cash flow arrows of the time lines to the cash flows of your problem. Each uses 4 of the 5 variables below. You can solve for any of the variables, using a calculator, by inputting the other 3.

Variables:

1) n : The number of time periods. Each period can be a day, week, month or year, etc. The interest earned within the period will be considered to compound at the period end.

2) i% : The interest rate is applied to the principal value at the beginning of each time period. If the time periods represent months, then the interest is the '% per month', etc. The rate is the same for all the periods. If this is not the case in your particular analysis, you cannot use these functions.

3) PV : The initial investment (loan) is represented by the arrow for Present Value. The directions of the arrow represents cash going into, or coming out of the investment. The directions can be reversed with no change in the functions.

4) FV : The value of the investment at the end of the time series is represented by the arrow for Future Value. Same as for PV, the direction of the cash flow can be switched.

5) Pmt : The regular Payments of an annuity are all the same value and made at the time of compounding. You must input into the calculator whether the Payments happen at the beginning of the periods or at their end. The time lines below show both options: B) has Payments at the end of the period, C) has Payments at the beginning of the period.

A)

This time line shows the equality of cash at different times. There are no cash flows during the intervening time. Your calculator may call this function "interest", or something else. The variables for input are PV, FV, n and i%. Common uses for this timeline are

Convert a quoted rate that uses simple interest to the true rate. Find the interest rate of a pay-day-loan.

Find the price you should pay for a strip bond.

Find the capital gains you realized from owning real estate over many years.

Examples

B)

This time line shows a lump-sum investment (or loan) at the start, followed immediately be a series of equal payments that continue for a set period of time. This diagram shows the Payments happening at the end of the period. Alternately, the first payment may happen at t=0. Your calculator may call this function "loan", or something else. The variables for input are PV, Pmts, n and i%. Common uses for this timeline are

Find the payments required for a mortgage.

Find the rate of return implicit in an annuity purchased for retirement.

Find the present value of an oil well.

Examples

C)

This time line shows a series of equal payments that continue for a set period of time, until a lump-sum cash flow at the end. This diagram shows the Payments happening at the beginning of the period. Alternately, the first payment may happen at t=1. Your calculator may call this function "saving", or something else. The variables for input are FV, Pmts, n and i%. Common uses for this timeline are

Determine how much must be saved every year in order to have $$ when retire. Find the rate of return implicit in the cost of life insurance.

Examples

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Chapter One Chapter Two

Chapter Three

Chapter Four

Chapter Five

1. 3.1 Time Value Of Money

2. 3.2 Discounted Cash Flow Valuation

1. 3.2.1 Introduction To Discounted Cash Flow Valuation

2. 3.2.2 Annuities And The Future Value And Present Value Of Multiple Cash Flows

3. 3.3 Loans And Amortization

4. 3.4 Bonds

5. 3.5 Stock Valuation

3. 3.2.3 Perpetuities

4. 3.2.4 The Effect Of Compounding

Discounted Cash Flow Valuation - Introduction To Discounted Cash Flow Valuation

Discounted cash flow (DCF) is a valuation method used to estimate the attractiveness of an investment opportunity. DCF analysis uses future free cash flow projections and discounts them (most often using the weighted average cost of capital, which we'll discuss in section 13 of this walkthrough) to arrive at a present value, which is then used to evaluate the potential for investment. If the value arrived at through DCF analysis is higher than the current cost of the investment, the opportunity may be a good one.

The formula for calculating DCF is usually given something like this:

PV = CF1 / (1+k) + CF2 / (1+k)2 + … [TCF / (k - g)] / (1+k)n-1

Where:PV = present valueCFi = cash flow in year ik = discount rateTCF = the terminal year cash flowg = growth rate assumption in perpetuity beyond terminal yearn = the number of periods in the valuation model including the terminal year

There are many variations when it comes to what you can use for your cash flows and discount rate in a DCF analysis. For example, free cash flows can be calculated as operating profit + depreciation + amortization of goodwill - capital expenditures - cash taxes - change in working capital. Although the calculations are complex, the purpose of DCF analysis is simply to estimate the money you'd receive from an investment and to adjust for the time value of money.

Discounted cash flow models are powerful, but they do have shortcomings. DCF is merely a mechanical valuation tool, which makes it subject to the axiom "garbage in, garbage out." Small changes in inputs can result in large changes in the value of a company. Instead of trying to project the cash flows to infinity, terminal value techniques are often used. A simple annuity is used to estimate the terminal value past 10 years, for example. This is done because it is harder to come to a realistic estimate of the cash flows as time goes on.

At a time when financial statements are under close scrutiny, the choice of what metric to use for making company valuations has become increasingly important. Wall Street analysts are emphasizing cash flow-based analysis for making judgments about company performance.

DCF analysis is a key valuation tool at analysts' disposal. Analysts use DCF to determine a company's current value according to its estimated future cash flows. For investors keen on gaining insights on what drives share value, few tools can rival DCF analysis.

Accounting scandals and inappropriate calculation of revenues and capital expenses give DCF new importance. With heightened concerns over the quality of earnings and reliability of standard valuation metrics like P/E ratios, more investors are turning to free cash flow, which offers a more transparent metric for gauging performance than earnings. It is harder to fool the cash register. Developing a DCF model demands a lot more work than simply dividing the share price by earnings or sales. But in return for the effort, investors get a good picture of the key drivers of share value: expected growth in operating earnings, capital efficiency, balance sheet capital structure, cost of equity and debt, and expected duration of growth. An added bonus is that DCF is less likely to be manipulated by aggressive accounting practices.

DCF analysis shows that changes in long-term growth rates have the greatest impact on share valuation. Interest rate changes also make a big difference. Consider the numbers generated by a DCF model offered by Bloomberg Financial Markets. Sun Microsystems, which in 2012 traded on the market at $3.25, is valued at almost $5.50, which makes its price of $3.25 a steal. The model assumes a long-term growth rate of 13%. If we cut the growth rate assumption by 25%, Sun's share valuation falls to $3.20. If we raise the growth rate variable by 25%, the shares go up to $7.50. Similarly, raising interest rates by one percentage point pushes the share value to $3.55; a 1% fall in interest rates boosts the value to about $7.70.

Investors can also use the DCF model as a reality check. Instead of trying to come up with a target share price, they can plug in the current share price and, working backwards, calculate how fast the company would need to grow to justify the valuation. The lower the implied growth rate, the better - less growth has therefore already been "priced into" the stock.

Best of all, unlike comparative metrics like P/Es and price-to-sales ratios, DCF produces a bona fide stock value. Because it does not weigh all the inputs included in a DCF model, ratio-based valuation acts more like a beauty contest: stocks are compared to each other rather than judged on intrinsic value. If the companies used as comparisons are all over-priced, the investor can end up holding a stock with a share price ready for a fall. A well-designed DCF model should, by contrast, keep investors out of stocks that look cheap only against expensive peers.

DCF models are powerful, but they do have shortcomings. Small changes in inputs can result in large changes in the value of a company. Investors must constantly second-guess valuations; the inputs that produce these valuations are always changing and are susceptible to error.

Meaningful valuations depend on the user's ability to make solid cash flow projections. While forecasting cash flows more than a few years into the future is difficult, crafting results into eternity (which is a necessary input) is near impossible. A single, unexpected event can immediately make a DCF model obsolete. By guessing at what a decade of cash flow is worth today, most analysts limit their outlook to 10 years. Investors should watch out for DCF models that project to ridiculous lengths of time. Also, the DCF model focuses on long-range investing;

it isn't suited for short-term investments.

Investors shouldn't base a decision to buy a stock solely on discounted cash flow analysis - it is a moving target, full of challenges. If the company fails to meet financial performance expectations, if one of its big customers jumps to a competitor, or if interest rates take an unexpected turn, the model's numbers have to be re-run. Any time expectations change, the DCF-generated value is going to change.

While many finance courses espouse the gospel of DCF analysis as the preferred valuation methodology for all cash flow generating assets, in practice, DCF can be difficult to apply in the valuation of stocks. Even if one believes the gospel of DCF, other valuation approaches are useful to help generate a complete valuation picture of a stock.

Alternative MethodologiesEven if one believes that DCF is the final word in assessing the value of an equity investment, it is very useful to supplement the approach with multiple-based target price approaches. If you are going to project income and cash flows, it is easy to use the supplementary approaches. It is important to assess which trading multiples (P/E, price/cash flow, etc.) are applicable based on the company's history and its sector. Choosing a target multiple range is where it gets tricky.

While this is analogous to arbitrary discount rate selection, by using a trailing earnings number two years out and an appropriate P/E multiple to calculate a target price, this will entail far fewer assumptions to "value" the stock than under the DCF scenario. This improves the reliability of the conclusion relative to the DCF approach. Because we know what a company's P/E or price/cash flow multiple is after every trade, we have a lot of historical data from which to assess the future multiple possibilities. In contrast, the DCF model discount rate is always theoretical, and we do not really have any historical data to draw from when calculating it.

For more insight, read Discounted Cash Flow Analysis, Top 3 Pitfalls Of Discounted Cash Flow Analysis and our DCF Analysis Tutorial.

Annuities And The Future Value And Present Value Of Multiple Cash Flows

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Financial Advisors

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Stock Simulator

Complete Guide To Corporate FinanceAAA |

Chapter One Chapter Two

Chapter Three

Chapter Four

Chapter Five

1. 3.1 Time Value Of Money

2. 3.2 Discounted Cash Flow Valuation

3. 3.3 Loans And Amortization

4. 3.4 Bonds

5. 3.5 Stock Valuation

1. 3.2.1 Introduction To Discounted Cash Flow Valuation

2. 3.2.2 Annuities And The Future Value And Present Value Of Multiple Cash Flows

3. 3.2.3 Perpetuities

4. 3.2.4 The Effect Of Compounding

Discounted Cash Flow Valuation - Introduction To Discounted Cash Flow Valuation

Discounted cash flow (DCF) is a valuation method used to estimate the attractiveness of an investment opportunity. DCF analysis uses future free cash flow projections and discounts them (most often using the weighted average cost of capital, which we'll discuss in section 13 of this walkthrough) to arrive at a present value, which is then used to evaluate the potential for investment. If the value arrived at through DCF analysis is higher than the current cost of the investment, the opportunity may be a good one.

The formula for calculating DCF is usually given something like this:

PV = CF1 / (1+k) + CF2 / (1+k)2 + … [TCF / (k - g)] / (1+k)n-1

Where:PV = present valueCFi = cash flow in year ik = discount rateTCF = the terminal year cash flowg = growth rate assumption in perpetuity beyond terminal yearn = the number of periods in the valuation model including the terminal year

There are many variations when it comes to what you can use for your cash flows and discount rate in a DCF analysis. For example, free cash flows can be calculated as operating profit + depreciation + amortization of goodwill - capital expenditures - cash taxes - change in working capital. Although the calculations are complex, the purpose of DCF analysis is simply to estimate the money you'd receive from an investment and to adjust for the time value of money.

Discounted cash flow models are powerful, but they do have shortcomings. DCF is merely a mechanical valuation tool, which makes it subject to the axiom "garbage in, garbage out." Small changes in inputs can result in large changes in the value of a company. Instead of trying to project the cash flows to infinity, terminal value techniques are often used. A simple annuity is used to estimate the terminal value past 10 years, for example. This is done because it is harder to come to a realistic estimate of the cash flows as time goes on.

At a time when financial statements are under close scrutiny, the choice of what metric to use for making company valuations has become increasingly important. Wall Street analysts are emphasizing cash flow-based analysis for making judgments about company performance.

DCF analysis is a key valuation tool at analysts' disposal. Analysts use DCF to determine a company's current value according to its estimated future cash flows. For investors keen on gaining insights on what drives share value, few tools can rival DCF analysis.

Accounting scandals and inappropriate calculation of revenues and capital expenses give DCF new importance. With heightened concerns over the quality of earnings and reliability of standard valuation metrics like P/E ratios, more investors are turning to free cash flow, which offers a more transparent metric for gauging performance than earnings. It is harder to fool the cash register. Developing a DCF model demands a lot more work than simply dividing the share price by earnings or sales. But in return for the effort, investors get a good picture of the key drivers of share value: expected growth in operating earnings, capital efficiency, balance sheet capital structure, cost of equity and debt, and expected duration of growth. An added bonus is that DCF is less likely to be manipulated by aggressive accounting practices.

DCF analysis shows that changes in long-term growth rates have the greatest impact on share valuation. Interest rate changes also make a big difference. Consider the numbers generated by a DCF model offered by Bloomberg Financial Markets. Sun Microsystems, which in 2012 traded on the market at $3.25, is valued at almost $5.50, which makes its price of $3.25 a steal. The model assumes a long-term growth rate of 13%. If we cut the growth rate assumption by 25%, Sun's share valuation falls to $3.20. If we raise the growth rate variable by 25%, the shares go up to $7.50. Similarly, raising interest rates by one percentage point pushes the share value to $3.55; a 1% fall in interest rates boosts the value to about $7.70.

Investors can also use the DCF model as a reality check. Instead of trying to come up with a target share price, they can plug in the current share price and, working backwards, calculate how fast the company would need to grow to justify the valuation. The lower the implied growth rate, the better - less growth has therefore already been "priced into" the stock.

Best of all, unlike comparative metrics like P/Es and price-to-sales ratios, DCF produces a bona fide stock value. Because it does not weigh all the inputs included in a DCF model, ratio-based valuation acts more like a beauty contest: stocks are compared to each other rather than judged on intrinsic value. If the companies used as comparisons are all over-priced, the investor can end up holding a stock with a share price ready for a fall. A well-designed DCF model should, by contrast, keep investors out of stocks that look cheap only against expensive peers.

DCF models are powerful, but they do have shortcomings. Small changes in inputs can result in large changes in the value of a company. Investors must constantly second-guess valuations; the inputs that produce these valuations are always changing and are susceptible to error.

Meaningful valuations depend on the user's ability to make solid cash flow projections. While forecasting cash flows more than a few years into the future is difficult, crafting results into

eternity (which is a necessary input) is near impossible. A single, unexpected event can immediately make a DCF model obsolete. By guessing at what a decade of cash flow is worth today, most analysts limit their outlook to 10 years. Investors should watch out for DCF models that project to ridiculous lengths of time. Also, the DCF model focuses on long-range investing; it isn't suited for short-term investments.

Investors shouldn't base a decision to buy a stock solely on discounted cash flow analysis - it is a moving target, full of challenges. If the company fails to meet financial performance expectations, if one of its big customers jumps to a competitor, or if interest rates take an unexpected turn, the model's numbers have to be re-run. Any time expectations change, the DCF-generated value is going to change.

While many finance courses espouse the gospel of DCF analysis as the preferred valuation methodology for all cash flow generating assets, in practice, DCF can be difficult to apply in the valuation of stocks. Even if one believes the gospel of DCF, other valuation approaches are useful to help generate a complete valuation picture of a stock.

Alternative MethodologiesEven if one believes that DCF is the final word in assessing the value of an equity investment, it is very useful to supplement the approach with multiple-based target price approaches. If you are going to project income and cash flows, it is easy to use the supplementary approaches. It is important to assess which trading multiples (P/E, price/cash flow, etc.) are applicable based on the company's history and its sector. Choosing a target multiple range is where it gets tricky.

While this is analogous to arbitrary discount rate selection, by using a trailing earnings number two years out and an appropriate P/E multiple to calculate a target price, this will entail far fewer assumptions to "value" the stock than under the DCF scenario. This improves the reliability of the conclusion relative to the DCF approach. Because we know what a company's P/E or price/cash flow multiple is after every trade, we have a lot of historical data from which to assess the future multiple possibilities. In contrast, the DCF model discount rate is always theoretical, and we do not really have any historical data to draw from when calculating it.

For more insight, read Discounted Cash Flow Analysis, Top 3 Pitfalls Of Discounted Cash Flow Analysis and our DCF Analysis Tutorial.

Variance AnalysisDefinition

Variance Analysis, in managerial accounting, refers to the investigation of deviations in financial performance from the standards defined in organizational budgets.

Topic Contents:

1. Definition 2. Explanation

3. Types of variances

4. Basis of calculation

5. Functions & Importance

Explanation

Variance analysis typically involves the isolation of different causes for the variation in income and expenses over a given period from the budgeted standards.

So for example, if direct wages had been budgeted to cost $100,000 actually cost $200,000 during a period, variance analysis shall aim to identify how much of the increase in direct wages is attributable to:

Increase in the wage rate (adverse labor rate variance); Decline in the productivity of workforce (adverse labor efficiency variance);

Unanticipated idle time (labor idle time variance);

More wages incurred due to higher production than the budget (favorable sales volume variance).

Types of Variances

Main types of variances are as follows:

Sales Volume Variance Sales Mix Variance

Sales Quantity Variance

Sales Price Variance

Direct Material Price Variance

Direct Material Usage Variance

Direct Material Mix Variance

Direct Material Yield Variance

Direct Labor Rate Variance

Direct Labor Efficiency Variance

Direct Labor Idle Time Variance

Variable Overhead Spending Variance

Variable Overhead Efficiency Variance

Fixed Overhead Spending Variance

Fixed Overhead Volume Capacity & Efficiency Variance

Fixed Overhead Total Variance

Click on variances listed above to view their explanations, formulas, calculations & examples

Basis of Calculation

Variance analysis highlights the causes of the variation in income and expenses during a period compared to the budget.

In order to make variances meaningful, the concept of 'flexed budget' is used when calculating variances. Flexed budget acts as a bridge between the original budget (fixed budget) and the actual results.

Flexed budget is prepared in retrospect based on the actual output. Sales volume variance accounts for the difference between budgeted profit and the profit under a flexed budget. All remaining variances are calculated as the difference between actual results and the flexed budget.

Following is a graphical illustration of how variances are calculated using the flexed budget approach:

Flexed budget is prepared using actual output. As actual quantity is the 1.5 times of budgeted quantity, sales and expenses have been 'flexed' to 1.5 times of the original budget with the exception of fixed overhead which remains the same under the marginal costing basis.

Budget(Original)

Budget(Flexed)

ActualResult

Output (10,000 units) (15,000 units) (15,000 units)

Sales $1,000,000

The difference of$300,000 representsSales Price Variance

$1,500,000 $1,800,000

Direct Materials ($100,000)

The difference of$50,000 representsDirect Material Total Variance

($150,000) ($200,000)

The total variance can be analyzed intomaterial usage variance & material price variance

Direct Labor ($200,000)

The difference of$50,000 representsDirect Labor Total Variance

($300,000) ($350,000)

The total variance can be analyzed intolabor efficiency variance & labor rate variance

Variable Overheads ($300,000)

The difference of$50,000 representsVariable Overhead Total Variance

($450,000) ($500,000)

The total variance can be analyzed intovariable Overhead Rate & Efficiency variance

Fixed Overheads ($75,000)

The difference of$25,000 representsFixed Overhead Total Variance

($75,000) ($50,000)

The total variance can be analyzed intoFixed Overhead Expenditure & Volume variance

Total $325,000 $525,000 $700,000

The difference between budgeted profit and profit under flexed budget ($200,000) represents the Sales Volume Variance. Sales Volume Variance can be further analyzed into Sales Mix

Variance & Sales Quantity Variance

As you may have noticed, all variances other than the sales volume variance are basically calculated as the difference between actual and flexed income & expenses. The difference between flexed budget profit and the fixed budget profit is accounted for separately in a single variance, i.e. sales volume variance.

This approach to calculating variances facilitates comparison of like with like. Hence, we can compare the actual expenditure incurred during a period with the standard expenditure that 'should have been incurred' for the level of actual production. Similarly, actual sales revenue can be compared with the standard revenue that 'should have been earned' for the level of actual sales during a period in order to determine the effect of

Functions and Importance

Variance analysis is an important part of an organization's information system.

Functions of variance analysis include:

Planning, Standards and Benchmarks

In order to calculate variances, standards and budgetary targets have to be set in advance against which the organization's performance can be compared against. It therefore encourages forward thinking and a proactive approach towards setting performance benchmarks.

Control Mechanism

Variance analysis facilitates 'management by exception' by highlighting deviations from standards which are affecting the financial performance of an organization. If variance analysis is not performed on a regular basis, such exceptions may 'slip through' causing a delay in management action necessary in the situation.

Responsibility Accounting

Variance analysis facilitates performance measurement and control at the level of responsibility centers (e.g. a department, division, designation, etc). For example, procurement department shall be answerable in case of a substantial increase in the purchasing cost of raw materials (i.e. adverse material price variance) whereas the production department shall be held responsible with respect to an increase in the usage of raw materials (i.e. adverse material usage variance). Therefore, the performance of each responsibility centre is measured and evaluated against budgetary standards with respect to only those areas which are within their direct control

Sales Volume VarianceDefinition

Sales Volume Variance is the measure of change in profit or contribution as a result of the difference between actual and budgeted sales quantity.

Topic Contents:

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

Formula

Sales Volume Variance (where absorption costing is used):

(Actual Unit Sold - Budgeted Unit Sales)   x   = Standard Profit Per Unit

Sales Volume Variance (where marginal costing is used):

(Actual Unit Sold - Budgeted Unit Sales)   x   = Standard Contribution Per Unit

Explanation

Sales Volume Variance quantifies the effect of a change in the level of sales on the profit or contribution over the period.

Sales volume variance differs from other volume based variances such as material usage variance and labor efficiency variance in that it calculates not just the variance in sales revenue as a result of the change in activity but it quantifies the overall change in the profit or contribution.

The nature of the sales volume variance helps in forming a more meaningful analysis of other variances in the preparation of the operating statement. For example, the material usage variance needs to take into account only the difference between the actual consumption of material and the standard consumption of material for the actual number of units sold since the sales volume variance already takes into account the variation in material cost caused by the difference between budgeted and actual sales volume.

Sales volume variance should be calculated using the standard profit per unit in case of absorption costing whereas in case of marginal costing system, standard contribution per unit is to be applied.

Example

Wrangler Plc is a manufacturer of jeans trousers and jackets.

Information relating to Wrangler Plc's sales during the last period is as follows:

TrousersUnits

JacketsUnits

Budgeted 12,000 5,000

Actual 10,000 8,000

Standard costs and revenues per unit of trouser and jacket are as follows:

Trousers$

Jackets$

Revenue 20 50

Direct labor 5 10

Direct Material 6 15

Variable Overheads 4 10

Fixed Overheads 2 5

Wrangler Plc uses marginal costing to prepare its operating statement.

Sales Volume Variance shall be calculated as follows:

Step 1: Calculate the standard contribution per unit

As Wrangler Plc uses marginal costing system, we need to calculate the standard contribution per unit. Allocation of the fixed overheads may therefore be ignored.

Trousers$

Jackets$

Revenue 20 50

Direct labor (5) (10)

Direct Material (6) (15)

Variable Overheads (4) (10)

Standard contribution per unit 5 15

Step 2: Calculate the difference between actual units sold and budgeted sales

TrousersUnits

JacketsUnits

Actual 10,000 8,000

Budgeted (12,000) (5,000)

Difference (2,000) 3,000

Step 3: Calculate the variance for each product

Trousers Jackets

Standard contribution per unit (Step 1) $5 $15

Actual Units Sold - Budgeted Sales (Step 2) x (2000 units) x 3000 units

Variance $10,000 Adverse $45,000 Favorable

Step 4: Add the individual variances

Sales Volume Variance $35,000 Favorable      =   ($10,000 - $45,000)

Note: If Wrangler Plc used absorption costing, sales volume variance would be calculated based on the standard profit per unit (i.e. fixed costs per unit of output will need to be deducted from the standard contribution calculated in Step 1).

Analysis

Favorable sales volume variance suggests a higher standard profit or contribution than the budgeted profit or contribution.

Reasons for favorable sales volume variance include:

Favorable sales quantity variance (i.e. higher total number of units sold than budgeted) Favorable sales mix variance> (i.e. higher proportion of the more profitable products sold than

planned in the budget)

Adverse sales volume variance indicated a lower standard profit or contribution than the budgeted profit or contribution.

Causes for an adverse sales volume variance include:

Adverse sales quantity variance (i.e. lower total number of units sold than budgeted) Adverse sales mix variance (i.e. higher proportion of the less profitable products sold than

anticipated in the budget)

Favorable sales volume variance can be achieved in case of a favorable sales mix variance even if the total number of units of all products sold during the period are lower than the total budgeted units (and vice versa).

It is therefore important to investigate the sales volume variance by analyzing it further into sales quantity and sales mix variances in case where an organization sells more than one product.

- See more at: http://accounting-simplified.com/management/variance-analysis/sales/volume.html#sthash.U1s5m7jU.dpuf

Sales Mix VarianceDefinition

Sales Mix Variance measures the change in profit or contribution attributable to the variation in the proportion of the different products from the standard mix.

Topic Contents:

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

Formula

Sales Mix Variance (where standard costing is used):

= (Actual Unit Sold - Unit Sales at Standard Mix)   x   Standard Profit Per Unit

Sales Mix Variance (where marginal costing is used):

= (Actual Unit Sold - Unit Sales at Standard Mix)   x   Standard Contribution Per Unit

Explanation

Sales Mix Variance is one of the two sub-variances of sales volume variance (the other being sales quantity variance). Sales mix variance quantifies the effect of the variation in the proportion of different products sold during a period from the standard mix determined in the budget-setting process.

Sales mix variance, as with sales volume variance, should be calculated using the standard profit per unit in case of absorption costing and standard contribution per unit in case of marginal costing system.

Example

Aliengear Inc. is a small company that specializes in the manufacture and sale of gaming computers. Currently, the company offers two models of gaming PCs:

Turbox - A professional gaming PC with a water-cooling system priced at $2,500 Speedo - An entry level gaming PC with standard fan cooling priced at $1,000

Aliengear budgeted sales of 1,600 units of Turbox and 2,400 units of Speedo in the last year. The standard variable costs of a single unit of Turbox and Speedo were set at $1,500 and $750 respectively.

The sales team at Aliengear managed to sell 1,300 units of Turbox and 3,700 units of Speedo during the last year.

Step 1: Calculate the standard mix ratio

40% Turbox* and 60% Speedo**  Standard mix ratio:

 * 1,600 / (1,600 + 2,400) % = 40% Turbox

** 100% - 40% = 60% Speedo

Step 2: Calculate the sales quantities in proportion to the standard mix

Total sales during the period: 1,300 Turbox + 3,700 Speedo = 5,000 units

Unit Sales at Standard Mix:

Sales of Turbox in standard mix @ 40% of 5,000 = 2,000 units

Sales of Speedo in standard mix @ 60% of 5,000 = 3,000 units

Step 3: Calculate the difference between actual sales quantities and the sales quantities in standard mix

TurboxUnits

SpeedoUnits

Actual sales quantities (as per question) 1,300 3,700

Unit sales at standard mix (Step 2) (2000) (3000)

Difference (700) Adverse 700 Favorable

Step 4: Calculate the standard contribution per unit

Turbox$

Speedo$

Revenue 2,500 1,000

Variable cost (1,500) (750)

Standard contribution per unit 1,000 250

Step 5: Calculate the variance for each product

Turbox Speedo

Standard contribution per unit (Step 4) $1,000 $250

Actual quantity - Standard mix (Step 3) x (700 units) x 700 units

Variance $700,000 Adverse $175,000 Favorable

Step 6: Add the individual variances

 Sales Mix Variance =    ($700,000 - $175,000) $525,000 Adverse =

Sales mix variance is adverse in this example because a lower proportion (i.e. 26%) of Turbox (which is more profitable than Speedo) were sold during the year as compared to the standard mix (i.e. 40%).

Analysis

Sales mix variance is only a relative measure of the variation in performance of an organization and should be interpreted with care. For instance, an adverse sales mix variance may be perfectly fine where a company is able to earn extra revenue through sale of lower margin products if such sales are in addition to high sales of the products with higher margins.

Favorable sales mix variance suggests that a higher proportion of more profitable products were sold during the period than was anticipated in the budget.

Reasons for favorable sales mix variance may include:

Concentration of sales and marketing efforts towards selling the more profitable products Increase in the demand for the higher margin products (where demand is a limiting factor)

Increase in the supply of the more profitable products due to for example addition to the production capacity (where supply is a limiting factor)

Decrease in the demand or supply of the less profitable products

Adverse sale mix variance suggests that a higher proportion of the low margin products were sold during the period than expected in the budget.

Reasons for adverse sales mix variance may include:

Demand for the more profitable products being lower than anticipated Decrease in the production of the high margin products due to supply side limiting factors (e.g.

shortage of raw materials or labor)

Sales team not focusing on selling products with higher margins due to for example lack of awareness or misaligned performance incentives (e.g. uniform sales commission on the entire product range may not motivate sales staff to compete for high margin sales)

Increase in demand or supply of the less profitable products

- See more at: http://accounting-simplified.com/management/variance-analysis/sales/mix.html#sthash.Nt12FwqE.dpuf

Sales Quantity Variance

Definition

Sales Quantity Variance measures the change in standard profit or contribution arising from the difference between actual and anticipated number of units sold during a period.

Topic Contents:

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

Formula

Sales Quantity Variance may be calculated as follows:

Sales Quantity Variance:

= (Budgeted sales - Unit Sales at Standard Mix)   x   Standard Contribution*

*Where marginal costing is used

Sales Quantity Variance:

= (Budgeted sales - Unit Sales at Standard Mix)   x   Standard Profit*

*Where absorption costing is used

Explanation

Sales quantity variance is an extension of the sales volume variance which demonstrates the impact of a higher or lower sales quantity as compared to budget.

The difference between sales volume variance and sales quantity variance is that the former is calculated using the actual sales volume whereas the latter is calculated using the sales volume of products in the proportion of standard mix (see example below).

Since sales quantity variance is calculated using the standard mix, any difference between the standard and actual mix of products is to be ignored (since the difference is accounted for separately under the sales mix variance).

Example

Aliengear Inc. is a small company that specializes in the manufacture and sale of gaming computers. Currently, the company offers two models of gaming PCs:

Turbox - A professional gaming PC with a water-cooling system priced at $2,500 Speedo - An entry level gaming PC with standard fan cooling priced at $1,000

Aliengear budgeted sales of 1,600 units of Turbox and 2,400 units of Speedo in the last year. The standard variable costs of a single unit of Turbox and Speedo were set at $1,500 and $750 respectively.

The sales team at Aliengear managed to sell 1,300 units of Turbox and 3,700 units of Speedo during the last year.

Sales Quantity Variance shall be calculated as follows:

Step 1: Calculate the standard mix ratio

40% Turbox* and 60% Speedo**  Standard mix ratio:

 * 1,600 / (1,600 + 2,400) % = 40% Turbox

** 100% - 40% = 60% Speedo

Step 2: Calculate the sales quantities in proportion to the standard mix

The objective is to find the respective sales quantities of products as if the total sales during the period where distributed among the two products in proportion to their standard mix.

Total sales during the period: 1,300 Turbox + 3,700 Speedo = 5,000 units

Unit Sales at Standard Mix:

Sales of Turbox in standard mix @ 40% of 5,000 = 2,000 units

Sales of Speedo in standard mix @ 60% of 5,000 = 3,000 units

Step 3: Calculate the difference between actual sales quantities and the sales quantities in standard mix

TurboxUnits

SpeedoUnits

Budgeted sales quantities (as per question) 1,600 2,400

Unit sales at standard mix (Step 2) (2000) (3000)

Difference 400 Favorable 600 Favorable

Step 4: Calculate the standard contribution per unit

Turbox$

Speedo$

Revenue 2,500 1,000

Variable cost (1,500) (750)

Standard contribution per unit 1,000 250

Step 5: Calculate the variance for each product

Turbox Speedo

Standard contribution per unit (Step 4) $1,000 $250

Budgeted Sales - Sales in Standard mix (Step 3) x 400 units x 600 units

Variance $400,000 Fav $150,000 Fav

Step 6: Add the individual variances

 Sales Mix Variance =    $400,000 - $150,000 $550,000 Favorable =

Step 7: Proof check

The sum of sales mix variance and sales quantity variance should equal sales volume variance.

Therefore:

$

Sales Quantity Variance (Step 6) 550,000 Favorable

Sales Mix Variance (see solution here) (525,000) Adverse

Total 25,000 Favorable

Equals-

Sales Volume Variance:

Turbox Speedo Total

Actual Sales 1,300 3,700

Budgeted Sales (1,600) (2,400)

Difference (Units) (300) 1,300

Standard Contribution ($) x 1,000 x 250

Sales Volume Variance ($300,000) $325,000 $25,000 Favorable

Analysis

Favorable sales quantity variance suggests that the company was able to sell a higher number of products in aggregate as compared to the total number of units budgeted to be sold during a period.

Favorable sales quantity variance may be achieved through:

Improvement in demand side factors where demand is the limiting factor such as by: o Improved marketing of company products

o Higher overall demand in industry (e.g. due to increase in population, reduction in supply of substitutes, etc)

Improvement in supply side factors where excess demand exists in the market for example through:

o Installation of a new production plant

o More efficient production (this may be evident in a favorable labor efficiency variance)

Adverse sales quantity variance indicates that the company sold lesser number of goods on aggregate basis as compared to the total number of units budgeted to be sold during a period.

Adverse sales quantity variance may be caused by the following:

Decline in demand side factors where demand is the limiting factor such as by: o A reduction in the overall demand in industry (e.g. due to the introduction of a better or

cheaper substitute in the market, etc)

Decrease in the quantity and quality of supply side factors where excess demand exists in the market for example due to:

o Unavailability of a critical manufacturing component or raw material

o Decline in the productivity of the workforce (this should be evident in an adverse labor efficiency variance)

- See more at: http://accounting-simplified.com/management/variance-analysis/sales/quantity.html#sthash.DvhE96tj.dpuf

Sales Price VarianceDefinition

Sales Price Variance is the measure of change in sales revenue as a result of variance between actual and standard selling price.

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

Formula

Sales Price Variance:

Actual Units Sold  x   (Actual Price - Standard Price)  =

Standard Price x Actual Units Sold  -   Actual Price x Actual Units Sold  =

Actual Sales Revenue = Standard Revenue of Actual Units Sold   -   

Explanation

Sales Price Variance can be calculated in a number of ways as illustrated in the formulas given above. The calculation of the variance is in fact very simple if you just remember the objective of finding the variance, i.e. how much change in sales revenue is attributable to the change in selling price from the standard?

Example

ABC PLC is a fertilizer producer which specializes in the manufacture of NHK-II (a chemical fertilizer) and ORG-I (a types of organic fertilizer).

Following information relates to the sale of fertilizers by ABC PLC during the period:

Material Quantity Acutal Price Standard Price

NHK-II 200 tons $380/ton $400/ton

ORG-I 300 tons $660/ton $600/ton

Sales Price Variance shall be calculated as follows:

ActualPrice (a)

StandardPrice (b)

a - b = cUnit Sold (d)

(tons)c x d

NHK-II 380 400 20 2004,000

Adverse

ORG-I 660 600 60 30018,000

Favorable

Total14,000

Favorable

Analysis

Favorable sales price variance suggests higher selling price realized during the period than anticipated in the standard. Reasons for favorable sales price variance may include:

Decrease in the number of competitors in the market Improved product differentiation and market segmentation

Better promotion and aggressive sales campaign

Adverse sales price variance indicates that sales were made at a lower average price than the standard. Causes for adverse sales price variance may include:

Increase in competition in the market Decrease in demand for the products

Reduction in price enforced by regulatory authorities

Direct Material Price VarianceDefinition

Direct Material Price Variance is the difference between the actual cost of direct material and the standard cost of quantity purchased or consumed.

1. Definition 2. Formula

3. Example

4. Analysis

5. MCQ

Formula

Direct Material Price Variance:

Actual Quantity x Standard Price  -   Actual Quantity x Actual Price  =

Actual Cost      = Standard Cost of Actual Quantity  -     

Where:

Actual Quantity is the quantity purchased during a period if the variance is calculated at the time of material purchase

Actual Quantity is the quantity consumed during a period if the variance is calculated at the time of material consumption

Example

Cement PLC manufactured 10,000 bags of cement during the month of January. Following raw materials were purchased and consumed by Cement PLC during the period:

Material Quantity Actual Price Standard Price

Limestone 100 tons $75/ton $70/ton

Clay 150 tons $20/ton $24/ton

Sand 250 tons $10/ton $12/ton

Material Price Variance will be calculated as follows:

Step 1: Calculate Actual Cost

Actual Cost = Actual Quantity x Actual Price

Limestone: 100 tons x $75 = $7,500

Clay: 150 tons x $20 = $3,000

Sand: 250 tons x $10 = $2,500

Step 2: Find the Standard Cost of Actual Quantity

Standard Cost = Actual Quantity x Standard Price

Limestone: 100 tons x $70 = $7,000

Clay: 150 tons x $24 = $3,600

Sand: 250 tons x $12 = $3,000

Step 3: Calculate the Variance

Material Price Variance = Actual Cost (Step 1) - Standard Cost (Step 2)

Limestone: $7,500 - $7,000 = ($500) Adverse

Clay: $3,000 - $3,600 = $600 Favorable

Sand: $2,500 - $3,000 = $500 Favorable

Total Price Variance $600 Favorable

Analysis

A favorable material price variance suggests cost effective procurement by the company.

Reasons for a favorable material price variance may include:

An overall decrease in the market price level Purchase of materials of lower quality than the standard (this will be reflected in adverse

material usage variance)

Better price negotiation by the procurement staff

Implementation of better procurement practices (e.g. invitation of price quotations from multiple suppliers)

Purchase discounts on larger orders

An adverse material price variance indicates higher purchase costs incurred during the period compared with the standard.

Reasons for adverse material price variance include:

An overall hike in the market price of materials Purchase of materials of higher quality than the standard (this will be reflected in favorable

material usage variance)

Increase in bargaining power of suppliers

Loss of purchase discounts due to smaller order sizes

Inefficient buying by the procurement staff

MCQ

Test Your Understanding

Fresh PLC is a manufacturer of toothpaste. One of the ingredients of Fresh Toothpaste is sodium fluoride powder. During a period, Fresh PLC purchased 10,000 KG of sodium fluoride at the cost of $20,000 ($2 per KG). Further information includes the following:

-Standard price of sodium fluoride is $1.5 per KG-Fresh PLC was only able to use 9,000 KG of the material during the period-Fresh PLC values stock on standard cost basis

What is the material price variance?

$4500 Adverse

$5,000 Adverse

-

Direct Material Usage VarianceDefinition

Direct Material Usage Variance is the measure of difference between the actual quantity of material utilized during a period and the standard consumption of material for the level of output achieved.

1. Definition 2. Formula

3. Example

4. Analysis

5. MCQ

Formula

Direct Material Usage Variance:

Standard Quantity x Standard Price  -   Actual Quantity x Standard Price  =

Standard Cost of Standard Quantity  -   Standard Cost of Actual Quantity  =

(Actual Quantity = - Standard Quantity) x Standard Price

Since the effect of any variation in material price from the standard is calculated in the material price variance, material usage variance is calculated using the standard price.

Example

Cement PLC manufactured 10,000 bags of cement during the month of January. Consumption of raw materials during the period was as follows:

Material Quantity Used Standard Usage Per Bag Actual Price Standard Price

Limestone 100 tons 11 KG $75/ton $70/ton

Clay 150 tons 14 KG $21/ton $20/ton

Sand 250 tons 26 KG $11/ton $10/ton

Material Usage Variance will be calculated as follows:

Step 1: Calculate Standard Quantity

Limestone: 10,000 units x 11 / 1000 = 110 tons

Clay: 10,000 units x 14 / 1000 = 140 tons

Sand: 10,000 units x 26 / 1000 = 260 tons

Step 2: Calculate the Variance

Material Usage Variance = [Actual Quantity - Standard Quantity (Step 2)] x Standard Price

Limestone: (100 - 110) x $70 = ($700) Favorable

Clay: (150 - 140) x $20 = $200 Adverse

Sand: (250 - 260) x $10 = ($100) Favorable

Total Usage Variance ($600) Favorable

Note: Actual price paid for the acquisition of materials shall be ignored since the variation between standard price is already accounted for in the material price variance.

Analysis

A favorable material usage variance suggests efficient utilization of materials.

Reasons for a favorable material usage variance may include:

Purchase of materials of higher quality than the standard (this will be reflected in adverse material price variance)

Greater use of skilled labor

Training and development of workforce to improve productivity

Use and improvement of automated manufacturing tools and processes

An adverse material usage variance indicates higher consumption of material during the period as compared with the standard usage.

Reasons for adverse material usage variance include:

Purchase of materials of lower quality than the standard (this will be reflected in a favorable material price variance)

Use of unskilled labor

Increase in material wastage due to depreciation of plant and equipment

MCQ

Test Your Understanding

Fresh PLC is a manufacturer of toothpaste. One of the ingredients of Fresh Toothpaste is sodium fluoride powder. Fresh PLC purchased 10,000 KG of sodium fluoride at the cost of $20,000 ($2 per KG) out of which it utilized 9,000 KG during the period.

Further information includes the following:

-Standard price of sodium fluoride is $1.5 per KG-Standard usage of fluoride is 10 grams per toothpaste-Fresh PLC manufactured 1 million toothpastes during the period

What is the material usage variance?

Zero

-$1,500 Favorable

-$1,500 Adverse

-$2,000 Adverse

Direct Material Mix VarianceDefinition

Direct Material Mix Variance is the measure of difference between the cost of standard proportion of materials and the actual proportion of materials consumed in the production process during a period.

1. Definition 2. Formula

3. Example

4. Explanation

5. Analysis

Formula

Direct Material Mix Variance:

Standard Mix Quantity x Standard Price  -   Actual Quantity x Standard Price  =

Standard Cost of Standard Mix    -     Standard Cost of Actual Actual Mix  =

(Actual Mix Quantity = - Standard Mix Quantity) x Standard Price

As material mix variance is an extension of the material usage variance, the variance is based on the standard price rather than actual price since the difference between actual and standard material price is accounted for separately in the material price variance.

Example

Cement PLC manufactured 10,000 bags of cement during the month of January. Consumption of raw materials during the period was as follows:

Material Quantity Used Standard Mix Per Bag Actual Price Standard Price

Limestone 100 tons 11 KG $75/ton $70/ton

Clay 150 tons 14 KG $21/ton $20/ton

Sand 250 tons 26 KG $11/ton $10/ton

Material Mix Variance will be calculated as follows:

Step 1: Calculate the total consumption of raw materials

Total Raw Materials Consumption (100 + 150 + 250) = 500 tons

Step 2: Calculate the Standard Mix

We need to calculate the quantity of each raw material which would have been consumed had the total usage of raw materials (500 tons) been based on the standard mix.

Limestone: 500 tons units x 11 / 51* = 108 tons

Clay: 500 tons units x 14 / 51* = 137 tons

Sand: 500 tons units x 26 / 51* = 255 tons

* Total Quantity under Standard Usage (11 + 14 + 26) = 51 KG per bag

Note that the sum of the standard mix of raw materials calculated above equals the actual total consumption of 500 tons. This is because in material mix variance, we are not concerned about the efficiency of raw material consumption but rather their relevant proportions.

Step 3: Calculate the Variance

Material Usage Variance = [Actual Mix - Standard Mix (Step 2)] x Standard Price

Limestone: (100 - 108) x $70 = ($560) Favorable

Clay: (150 - 137) x $20 = $260 Adverse

Sand: (250 - 255) x $10 = ($50) Favorable

Total Usage Variance ($350) Favorable

Note: Actual price paid for the acquisition of materials shall be ignored since any variation between standard price is already accounted for in the material price variance..

Explanation

Material Mix Variance quantifies the effect of a variation in the proportion of raw materials used in a production process over a period.

Material mix variance is a sub-division of material usage variance. While material usage variance illustrates the overall efficiency of raw material consumption during a period (in terms of the difference between the amount of materials which should have been used and the actual usage), material mix variance focuses on the aspect of proportion of raw materials used in the production process.

Material mix variance is only suitable for performance measurement and control where the proportion of inputs to the production process can be altered without reducing the effectiveness of the final product. It may not therefore be used in industries that require a high degree of precision in the input variables such as in the pharmaceuticals sector.

Analysis

A favorable material mix variance suggests the use of a cheaper mix of raw materials than the standard. Conversely, an adverse material mix variance suggests that a more costly combination of materials have been used than the standard mix.

A change in the material mix must also be analyzed in the context of other organization wide implications that may follow. Some of the effects a change in direct material mix include:

Change in the quality, performance and durability of the final product Price offered by customers may vary as a result of a change in perceived quality of the product

Change in material mix may affect the workability of materials which may in turn affect labor efficiency

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Direct Material Yield VarianceDefinition

Direct Material Yield Variance is a measure of cost differential between output that should have been produced for the given level of input and the level of output actually achieved during a period.

Contents:

1. Definition 2. Formula

3. Example

4. Explanation

5. Analysis

Formula

Direct Material Yield Variance:

= (Actual Yield - Standard Yield) x Standard Material Cost Per Unit

Example

Cement PLC manufactured 10,000 bags of cement during the month of January. Consumption of raw materials during the period was as follows:

Material Quantity Used Standard Mix Per Bag Actual Price Standard Price

Limestone 100 tons 11 KG $75/KG $70/KG

Clay 150 tons 14 KG $21/KG $20/KG

Sand 250 tons 26 KG $11/KG $10/KG

Material Yield Variance shall be calculated as follows:

Step 1: Calculate the Standard Yield for the total materials input

500 tons of materials should have yielded 9,804 bags

Standard Yield = 500 tons x 1000 / 51 KG = 9,804 bags

Step 2: Calculate the Standard Cost of materials per bag

Total material cost of 1 bag of cement:

Limestone: 11 KG x $70 = $770

Clay: 14 KG x $20 = $280

Sand: 26 KG x $10 = $260

Total $1,310 per bag

Actual material price should be ignored since the variance between actual and standard price is accounted for in the material price variance.

Step 3: Calculate the Total Yield Variance

Material Usage Variance = [Actual Yield - Standard Yield (Step 1)] x Standard Cost / Unit (Step 2)

Actual Yield - Standard Yield = 10,000 - 9,804 (Step 1) = 196 bags

Total Material Yield Variance = 196 bags x $1,310 (Step 2)

= $256,760 Favorable

As the actual output achieved during the period is higher than the standard yield, the variance is favorable. Favorable material yield variance indicates the amount of savings in material costs as a result of better output yield than the standard.

Step 4: Calculate the Material Wise Yield Variances

Individual material yield variance can be calculated in a similar way to the total yield variance.

Materials:Actual Yield - Standard Yield

(Step 3)x

Standard Cost per bag(Step 2)

= Yield Variance

Limestone: 196 bags x $770 = $150,920

Clay: 196 bags x $280 = $54,880

Sand: 196 bags x $260 = $50,960

$256,760

Note that sum of individual material yield variances equals the total yield variance calculated in step 3.

Explanation

Material Yield Variance measures the effect on material cost of a change in the production yield from the standard.

Material yield variance is used in conjunction with material mix variance in order to provide additional analysis of the material usage variance.

The difference between material usage and material yield variance is that the former focuses on the utilization of input at the start of production process whereas latter focuses on the efficiency in terms of the output yield during a period.

Analysis

A favorable material yield variance indicates better productivity than the standard yield resulting in lower material cost.

Conversely, an adverse material yield variance suggests lower production achieved during a period for the given level of input resulting in higher material cost.

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Direct Labor Rate Variance

Definition

Direct Labor Rate Variance is the measure of difference between the actual cost of direct labor and the standard cost of direct labor utilized during a period.

1. Definition 2. Formula

3. Example

4. Analysis

Formula

Direct Labor Rate Variance:

Actual Quantity x Standard Rate  -   Actual Quantity x Actual Rate  =

Actual Cost      = Standard Cost of Actual Hours  -     

Example

DM is a denim brand specializing in the manufacture and sale of hand-stitched jeans trousers.

DM manufactured and sold 10,000 pairs of jeans during a period.

Information relating to the direct labor cost and production time per unit is as follows:

Actual HoursPer Unit

Standard HoursPer Unit

Actual RatePer Hour

Standard RatePer Hour

Direct Labor 0.50 0.60 $12 $10

Labor rate variance shall be calculated as follows:

Step 1: Calculate Actual hours

Actual Hours = 10,000 units x Actual Price

= 5,000 hours.

Step 2: Calculate the actual cost

Actual Cost = Actual Hours x Actual Rate

= 5,000 hours (Step 1) x $12 per hour

= $60,000.

Step 3: Calculate the standard cost of actual number of hours

Standard Cost of actual hours = Actual Hours x Standard Rate

= 5,000 hours (Step 1) x $10 per hour

= $50,000.

Step 4: Calculate the variance

Labor Rate Variance = Actual Cost - Standard Cost of the Actual Hours

= $60,000 (Step 2) - $50,000 (Step 3)

= $10,000 Adverse.

Analysis

A favorable labor rate variance suggests cost efficient employment of direct labor by the organization.

Reasons for a favorable labor rate variance may include:

Hiring of more un-skilled or semi-skilled labor (this may adversely impact labor efficiency variance)

Decrease in the overall wage rates in the market due to an increase in the supply of labor which may be caused, for example, due to the influx of immigrants as a result of the relaxation of immigration policy

Inappropriately high setting of the standard cost of direct labor which may, in the hindsight, be attributed to inaccurate planning

An adverse labor rate variance indicates higher labor costs incurred during a period compared with the standard.

Causes for adverse labor rate variance may include:

Increase in the national minimum wage rate Hiring of more skilled labor than anticipated in the standard (this should be reflected in a

favorable labor efficiency variance)

Inefficient hiring by the HR department

Effective negotiations by labor unions

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Direct Labor Efficiency VarianceDefinition

Direct Labor Efficiency Variance is the measure of difference between the standard cost of actual number of direct labor hours utilized during a period and the standard hours of direct labor for the level of output achieved.

1. Definition 2. Formula

3. Example

4. Analysis

Formula

Direct Labor Effciency Variance:

Standard Hours x Standard Rate  -   Actual Hours x Standard Rate  =

Standard Cost of Actual Hours  = Standard Cost    -   

Note: As the effect of difference between standard rate and actual rate of direct labor is accounted for separately in the direct labor rate variance, the efficiency variance is calculated using the standard rate.

Example

DM is a denim brand specializing in the manufacture and sale of hand-stitched jeans trousers.

DM manufactured and sold 10,000 pairs of jeans during a period.

Information relating to the direct labor cost and production time per unit is as follows:

Actual HoursPer Unit

Standard HoursPer Unit

Actual RatePer Hour

Standard RatePer Hour

Direct Labor 0.50 0.60 $12 $10

Labor rate variance shall be calculated as follows:

Step 1: Calculate Actual hours

Actual Hours = 10,000 units x 0.5 hours per unit

= 5,000 hours.

Step 2: Calculate the standard cost of actual number of hours

Standard Cost of Actual Hours = Actual Hours x Standard Rate

= 5,000 hours (Step 1) x $10 per hour

= $50,000.

Step 3: Calculate the standard hours

Standard hours = 10,000 units x 0.60 hours per unit

= 6,000 hours.

Step 4: Calculate the standard cost

Standard Cost = Standard Hours x Standard Rate

= 6,000 hours (Step 3) x $10 per hour

= $60,000.

Step 5: Calculate the variance

Labor Efficiency Variance = Standard Cost of Actual Hours - Standard Cost

= $50,000 (Step 2) - $60,000 (Step 4)

= $10,000 Favorable.

Analysis

A favorable labor efficiency variance indicates better productivity of direct labor during a period.

Causes for favorable labor efficiency variance may include:

Hiring of more higher skilled labor (this may adversely impact labor rate variance) Training of work force in improved production techniques and methodologies

Use of better quality raw materials which are easier to handle

Higher learning curve than anticipated in the standard

An adverse labor efficiency variance suggests lower productivity of direct labor during a period compared with the standard.

Reasons for adverse labor efficiency variances may include:

Hiring of lower skilled labor than the standard (this should be reflected in a favorable labor rate variance)

Lower learning curve achieved during the period than anticipated in the standard

Decrease in staff morale and motivation

Idle time incurred during a period caused by disruption or stoppage of activities (idle time variance may be calculated separately from the labor efficiency variance to reflect the underlying increase or decrease in labor productivity during a period)

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Direct Labor Idle Time VarianceDefinition

Labor Idle Time Variance is the cost of the standby time of direct labor which could not be utilized in the production due to reasons including mechanical failure of equipment, industrial disputes and lack of orders.

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

Formula

Standard labor rate  x   Number of idle hours    =   Idle Time Variance:

Explanation

Idle time variance illustrates the adverse impact on the profitability of an organization as a result of having paid for the labor time which did not result in any production. Idle time variance is therefore always described as an 'adverse' variance.

The separate calculation of idle time variance ensures a more meaningful analysis of the underlying productivity of the workforce demonstrated in the labor efficiency variance as illustrated in the example below.

As with the labor efficiency variance, the calculation of idle time variance is based on the standard rate since the variance between actual and standard labor rate is separately accounted for in the labor rate variance.

Example

DM is a denim brand specializing in the manufacture and sale of hand-stitched jeans trousers.

DM manufactured and sold 10,000 pairs of jeans during a period.

Information relating to the direct labor cost and production time per unit is as follows:

Actual HoursPer Unit

Standard HoursPer Unit

Actual RatePer Hour

Standard RatePer Hour

Direct Labor 0.65 0.60 $12 $10

During the period, 800 hours of idle time was incurred. In order to motivate and retain experienced workers, DM has devised a policy of paying workers the full hourly rate in case of any idle time.

Note: 0.65 hours per unit of actual time includes the idle time.

Calculation of idle time variance and labor efficiency variance will be as follows:

(a) Idle Time Variance:

Idle time variance = number of idle hours x standard rate

= 800 hours x $10

= $8,000 Adverse.

(b) Labor Efficiency Variance:

Step 1: Calculate the total number of hours

Total Hours = 10,000 units x 0.65 hours per unit

= 65,000 hours.

Step 2: Calculate the number of active hours

Active Hours = 6,500 hours (Step 1) - 800 idle hours

= 5,700 hours.

Step 3: Calculate the standard cost of active hours

Standard Cost = Active Hours x Standard Rateof Active Hours

= 5,700 hours (Step 2) x $10 per hour

= $57,000

Step 4: Calculate the standard hours

Standard Hours = 10,000 units x 0.60 hours per unit

= 6,000 hours.

Step 5: Calculate the standard cost

Standard Cost = Standard Hours x Standard Rate

= 6,000 hours (Step 3) x $10 per hour

= $60,000

Step 6: Calculate the variance

Labor Efficiency Variance = Standard Cost of Active Hours - Standard Cost

= $57,000 (Step 3) - $60,000 (Step 5)

= $3,000 Favorable

Step 7: Perform check

The sum of idle time variance and labor efficiency variance calculated above should equal the labor efficiency variance ignoring idle time.

Sum of variances = Idle time variance + Labor efficiency variance

= $8,000 Adverse + ($3,000 Favorable)

= $5,000 Adverse

Labor efficiency variance = Standard Cost of Actual Hours - Standard Cost(without idle time variance)

= 6,500 Hours (Step 1) x $10 - $60,000 (Step 5)

= $5,000 Adverse

Comment

Without considering the impact of idle time, it would appear that the productivity of workforce (1.53 units per hour*) had been lower than the standard (1.67 units per hour**) due to inefficient workflow and production process. However, taking into consideration the unavoidable production time lost (idle time), we can conclude that the underlying efficiency of the workforce improved (1.75 units per hour***) compared with the standard.

*   10,000 units / 6,500 hours (total)

**  10,000 units / 6,000 hours (standard)

*** 10,000 units / 5,700 hours (active)

Analysis

Reasons for idle time may include:

Disruption of production activities due to mechanical failures Lack of purchase orders especially in case of seasonal businesses

Industrial disputes

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Variable Manufacturing Overhead Spending Variance

Definition

Variable Overhead Spending Variance is the difference between variable production overhead expense incurred during a period and the standard variable overhead expenditure. The variance is also referred to as variable overhead rate variance and variable overhead expenditure variance.

Topic Contents:

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

6. Limitations

Formula

Variable Overhead Spending Variance:

= Actual Manufacturing Variable Overheads Expenditure

Less

Standard Variable Overhead Rate per hour  x  Actual hours

where:

Actual Hours is the number of machine hours or labor hours during a period.

Explanation

Variable Overhead Spending Variance is essentially the difference between what the variable production overheads did cost and what they should have cost given the level of activity during a period.

Standard variable overhead rate may be expressed in terms of the number of machine hours or labor hours. So for example, in case of a labor intensive manufacturing business, standard variable overhead rate may be expressed in terms of the number of labor hours whereas in case of predominantly automated production processes, a standard rate based on the number of machine hours may be more appropriate. Very often however, companies have a combination of

manual and automated business processes which may necessitate the use of both basis of variable overhead absorption.

Example

AAA Sports LTD is a small manufacturing company specializing in the production of cricket bats. AAA Sports LTD currently manufactures 2 types of bats:

AAA Plus - a hand-crafted English Willow bat designed for professional use

AAA Gold - a machine-manufactured cheaper bat designed for casual cricket

Following is a break-up of standard variable manufacturing overhead cost:

AAA Plus AAA Gold

Number of Hours 2 direct labor hours 1 machine hour

Overheads:

Indirect Labor $10 -

Polish $5 $1

Sand paper $1 -

Glue $1 $0.5

Machine lubricants - $0.5

Electricity $3 $10

Total $20($10 per direct labor hour)

$12($12 per machine hour)

Following information relates to the actual data from last month:

Variable Manufacturing Overheads $175,000

Direct Labor Hours 10,000

Machine Hours 5,000

Variable Overhead Spending Variance shall be calculated as follows:

AAAPlus

AAAGold

Total$

Actual Variable Overhead Expense 175,000

Less:

Actual Hours 10,000 5,000

Standard Variable O.H. Rate x $10 x $12

Standard Overhead Expense 100,000 60,000 (160,000)

Variable Overhead Expenditure Variance 15,000 Adverse

Analysis

Favorable variable manufacturing overhead spending variance indicates that the company incurred a lower expense than the standard cost.

Possible reasons for favorable variance include:

Economies of scale (e.g. increase in order size of indirect material leading to bulk discounts on purchase)

A decrease in the general price level of indirect supplies

More efficient cost control (e.g. optimizing electricity consumption through the installation of energy efficient equipment)

Planning error (e.g. failing to take into account the learning curve effect which could have reasonably be expected to result in a more efficient use of indirect materials in the upcoming period)

An adverse variable manufacturing overhead spending variance suggests that the company incurred a higher cost than the standard expense.

Potential causes for an adverse variance include:

A rise in the national minimum wage rate leading to a higher cost of indirect labor A decrease in the level of activity not fully offset by a decrease in overheads (e.g. electricity

consumption of machines during set up is usually same even if a smaller batch of output is required to be produced)

In efficient cost control (e.g. not optimizing the batch production quantities leading to higher set up costs)

Planning error (e.g. failing to take into account the increase in unit rates of electricity applicable for the level of activity budgeted during a period)

Limitations

Variable production overheads by their nature include costs that cannot be directly attributed to a specific unit of output unlike direct material and direct labor which vary directly with output. Variable overheads do however vary with a change in another variable. Traditional management accounting often define blanket variables such as machine hours or labor hours which seldom provides a meaningful basis of cost control. The use of activity based costing to calculate overhead variances can significantly enhance the usefulness of such variances.

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Variable Manufacturing Overhead Efficiency VarianceDefinition

Variable Overhead Efficiency Variance is the measure of impact on the standard variable overheads due to the difference between standard number of manufacturing hours and the actual hours worked during the period.

Topic Contents:

1. Definition 2. Formula

3. Explanation

4. Example

5. Analysis

6. Limitations

Formula

Variable Overhead Spending Variance:

Standard Variable Overhead Rate per hour  x  = Standard hours

Less

Standard Variable Overhead Rate per hour  x  Actual hours

where:

Hours refers to the number of machine hours or labor hours incurred in the production of output during a period.

Explanation

Variable Overhead Efficiency Variance is calculated to quantify the effect of a change in manufacturing efficiency on variable production overheads. As in the case of variable overhead spending variance, the overhead rate may be expressed in terms of labor hours or machine hours (or both) depending on the degree of automation of production processes.

Example

AAA Sports LTD is a small manufacturing company specializing in the production of cricket bats. AAA Sports LTD currently manufactures 2 types of bats:

AAA Plus - a hand-crafted English Willow bat designed for professional use

AAA Gold - a machine-manufactured cheaper bat designed for casual cricket

Following is a break-up of the standard variable manufacturing overhead costs:

AAA Plus AAA Gold

Number of Hours 2 direct labor hours 1 machine hour

Overheads:

Indirect Labor $10 -

Polish $5 $1

Sand paper $1 -

Glue $1 $0.5

Machine lubricants - $0.5

Electricity $3 $10

Total $20($10 per direct labor hour)

$12($12 per machine hour)

Following information relates to the actual data from last month:

Variable Manufacturing Overheads $175,000

Direct Labor Hours 10,000

Machine Hours 5,000

Production (units) - AAA Plus 4,500

Production (units) - AAA Gold 5,200

Variable Overhead efficiency Variance shall be calculated as follows:

AAAPlus

AAAGold

Total$

Standard Hours x Standard Rate / hour

Standard Hours (4500x2 / 5200x1) 9,000 5,200

Standard Variable Overhead Rate / hour x $10 x $12

90,000 62,400 152,400

Less:

Actual Hours x Standard Rate / hour

Actual Hours 10,000 5,000

Standard Variable Overhead Rate / hour x $10 x $12

100,000 60,000 152,400

Variable Overhead Efficiency Variance 7,600 Adverse

Proof check:

Adding variable overhead spending and efficiency variances to the standard cost should equal to actual variable overheads during the period.

Standard Cost (Standard hours x Standard rate) = $152,400 (see above)

Variable overhead spending variance = $15,000 A (see solution)

Variable overhead efficiency variance = $7,600 A (see above)

Total = $175,000

Actual Overheads $175,000 (from question)

Analysis

Favorable variable overhead efficiency variance indicates that fewer manufacturing hours were expended during the period than the standard hours required for the level of actual output.

Reasons for a favorable variance may include:

Use of a raw material which is easier to work with (this should be evident in a favorable material usage variance and possibly an adverse material price variance)

Employment of a higher skilled labor or improvement of skills of existing workforce through training and development leading to improved productivity (this should be indicated by a favorable labor efficiency variance and potentially an adverse labor rate variance)

Installation of a more efficient manufacturing equipment

Planning error (e.g. ignoring or under estimating the impact of learning curve effect on productivity)

An adverse variable overhead efficiency variance suggests that more manufacturing hours were expended during the period than the standard hours required for the level of actual production.

Possible causes for adverse variance include:

Use of a cheaper raw material which is harder to work with (this should be corroborated with an adverse material usage variance and a favorable a href="/management/variance-analysis/material/price.html">material price variance)

Inefficient production caused by the employment of lower skilled labor (this shall be evident in an adverse direct labor efficiency variance and probably a favorable labor rate variance)

Decline in the productivity of manufacturing equipment due to for example technical problems or wear and tear

Planning error (e.g. over calculating the impact of learning curve effect on the manufacturing efficiency)

Limitations

Variable Overhead Efficiency Variance is traditionally calculated on the assumption that the overheads could be expected to vary in proportion to the number of manufacturing hours. While there is usually correlation between manufacturing hours and variable overheads when considered on aggregate basis, the number of manufacturing hours may not be the factor that drives the cost of many types of variable overheads (e.g. setup costs vary with the number of setups). Using Activity based costing in the calculation of variable overhead variances might therefore provide more relevant information for management control purposes.

Also, in case where variable overhead rate is based on labor hours, the variable overhead efficiency variance does not offer any additional information than provided by the labor efficiency variance.

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Fixed Manufacturing Overhead Expenditure / Spending VarianceDefinition

Fixed Overhead Expenditure Variance, also known as fixed overhead spending variance, is the difference between budgeted and actual fixed production overheads during a period.

Topic Contents:

1. Definition 2. Formula

3. Example

4. Explanation

5. Analysis

Formula

Fixed Overhead Expenditure Variance:

= Actual Fixed Overheads - Budgeted Fixed Overheads

Example

Motors PLC is a manufacturing company specializing in the production of automobiles.

Information relating to its fixed manufacturing overhead expense of last period is as follows:

Million

$

Actual fixed overheads A 526

Budgeted fixed overheads B 500

Fixed Overhead Expenditure Variance A - B 26 Adverse

The variance is adverse since actual expense is higher than the budgeted expense.

Explanation

Fixed Overhead Spending Variance is calculated to illustrate the deviation in fixed production costs during a period from the budget. The variance is calculated the same way in case of both marginal and absorption costing systems. As under marginal costing fixed overheads are not absorbed in the standard cost of a unit of output, fixed overhead expenditure variance is the only variance relating to fixed overheads calculated under marginal costing (i.e. fixed overhead expenditure variance is equal to fixed overhead total variance under marginal costing system).

Analysis

Favorable fixed overhead expenditure variance suggests that actual fixed costs incurred during the period have been lower than budgeted cost.

Reasons for a favorable variance may include:

Planned business expansion, which was anticipated to cause a stepped increase in fixed overheads, not being undertaken during the period.

Cost rationalization measures carried out during the period aimed at reducing fixed overheads by elimination of inefficiencies (e.g. through process re-engineering and optimization of the usage of shared resources and facilities).

Planning inaccuracies (e.g. actual salary raise being lower than anticipated in budget).

Adverse fixed overhead expenditure variance indicates that higher fixed costs were incurred during the period than planned in the budget.

An adverse variance may be caused by the following:

Expansion of business undertaken during the period, which was not taken into consideration in the budget setting process, causing a stepped increase in fixed overheads.

Inefficient fixed overheads management (e.g. due to empire building pursuits of senior management).

Planning errors (e.g. increase in insurance premium being higher than budget due to changes in the risk profile of business).

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Fixed Overhead Volume Variance Topic Contents:

1. Definition 2. Formula

3. Example 1

4. Explanation

5. Fixed Overhead Capacity Variance

6. Fixed Overhead Efficiency Variance

7. Example 2

8. Limitations

Definition

Fixed Manufacturing Overhead Volume Variance quantifies the difference between budgeted and absorbed fixed production overheads.

FormulaFixed Overhead Volume Variance = Absorbed Fixed overheads - Budgeted Fixed Overheads

= Actual Output x FOAR* - Budgeted Output x FOAR*

* Fixed Overhead Absorption Rate per unit of output

Example

Motors PLC is a manufacturing company specializing in the production of automobiles.

Information from its last budget period is as follows:

Actual Production 275,000 units

Budgeted Production 250,000 units

Standard Fixed Overhead Absorption Rate $2,000 per unit

Calculate the fixed overhead volume variance.

Fixed Overhead Volume Variance

Absorbed Fixed Overheads (275,000 x $2,000) $550 m

Budgeted Fixed Overheads (250,000 x $2,000) ($500 m)

Fixed Overhead Volume Variance $50 m Favorable

Note:

It may appear strange to you that even though the absorbed fixed overheads are higher than the budgeted overheads, the variance is described as being 'favorable' which is usually not how cost variances are interpreted. In short, this variance is used as a balancing exercise when fixed overhead expenditure variance is calculated. For more detail on this, see the explanation below.

Explanation

Fixed Overhead Volume Variance is the difference between the fixed production cost budgeted and the fixed production cost absorbed during the period. The variance arises due to a change in the level of output attained in a period compared to the budget.

The variance can be analyzed further into two sub-variances:

Fixed Overhead Capacity Variance Fixed Overhead Efficiency Variance

The sum of the above two variances should equal to the volume variance.

Fixed overhead volume variance helps to 'balance the books' when preparing an operating statement under absorption costing.

Sales Quantity Variance already takes into account the change in budgeted fixed production overheads as a result of increase or decrease in sales quantity along with other expenses.

At the same time, fixed overhead expenditure variance accounts for the difference between actual and budgeted expense rather than the flexed expense unlike other expenditure variances.

This implies that the difference between budgeted and flexed fixed cost is included twice in the operating statement. Sales volume variance removes the effect of such duplication.

As fixed costs are not absorbed under marginal costing system, fixed overhead volume variance (and its sub-variances) are to be calculated only when absorption costing is applied.

Fixed Overhead Capacity Variance

Fixed Overhead Capacity Variance calculates the variation in absorbed fixed production overheads attributable to the change in the number of manufacturing hours (i.e. labor hours or machine hours) as compared to the budget.

The variance can be calculated as follows:

Fixed Overhead Capacity Variance:

= (budgeted production hours - actual production hours) x FOAR*

* Fixed Overhead Absorption Rate / unit of hour

Fixed Overhead Efficiency Variance

Fixed Overhead Efficiency Variance calculates the variation in absorbed fixed production overheads attributable to the change in the manufacturing efficiency during a period (i.e. manufacturing hours being higher or lower than standard ).

The variance can be calculated as follows:

Fixed Overhead Efficiency Variance:

= (standard production hours - actual production hours) x FOAR*

* Fixed Overhead Absorption Rate / unit of hour

Example

Continuing the Motors PLC example above, we have the following data from its last period:

Actual Production 275,000 units

Budgeted Production 250,000 units

Standard Fixed Overhead Absorption Rate $2,000 per unit

Additional information:

Standard machine hours per unit 10 hours

Actual number of machine hours 3,000,000

Calculate the fixed overhead capacity and fixed overhead efficiency variance.

Fixed Overhead Capacity Variance Budgeted production hours (250,000 x 10) 2,500,000

Less: Actual production hours (3,000,000)

500,000

Fixed Overhead Absorption Rate / unit of hour ($2,000 / 10) x 200

Variance 100,000,000 Favorable

The variance is favorable because Motors PLC managed to operate more manufacturing hours than anticipated in the budget.

Fixed Overhead Efficiency Variance Standard production hours (275,000 x 10) 2,750,000

Less: Actual production hours (3,000,000)

250,000

Fixed Overhead Absorption Rate / unit of hour ($2,000 / 10) x 200

Variance 50,000,000 Adverse

The variance is adverse because Motors PLC utilized more manufacturing hours in the production of 275,000 units than the standard.

Proof Check

Fixed Overhead Capacity Variance $100,000,000 Favorable

Fixed Overhead Capacity Variance $50,000,000 Adverse

Total $50,000,000 Favorable

Fixed Overhead Volume Variance $50,000,000 Favorable

Limitations

Fixed Overhead Volume Variance is necessary in the preparation of operating statement under absorption costing as it removes the arithmetic duplication as discussed earlier. However, besides its role as a balancing agent, the variance offers little information in its own right over and above what can be ascertained from other variances (e.g. sales quantity variance already illustrates the effect of an increase in sales quantity on the overall profitability).

The traditional calculation of sub-variances (i.e. fixed overhead capacity and efficiency variances) does not provide a meaningful analysis of fixed production overheads. For instance, if the workforce utilized fewer manufacturing hours during a period than the standard (the effect of which is more adequately reflected in labor efficiency variance), it is hard to imagine a significant benefit of calculating a favorable fixed overhead efficiency variance.

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Fixed Manufacturing Overhead Total Variance Topic Contents:

1. Definition 2. Formula

3. Example (summarized)

4. Explanation

5. Example (detailed)

Definition

Fixed Overhead Total Variance is the difference between actual and absorbed fixed production overheads during a period.

Formula

Fixed Overhead Total Variance = Actual Fixed Overheads - Absorbed Fixed Overheads

Actual Output x FOAR*

* Fixed Overhead Absorption Rate

Example

Motors PLC is a manufacturing company involved in the production of automobiles.

Information from its last budget period is as follows:

Actual Production 275,000 units

Budgeted Production 250,000 units

Actual Fixed Production Overheads $526,000,000

Budgeted Fixed Production Overheads $500,000,000

Calculate the fixed overhead total variance.

In order to calculate the required variance, we first need to find out the standard absorption rate:

Fixed Overhead Absorption Rate = budgeted fixed overheads

budgeted output

=$50,000,000 = $2,000 per unit

250,000 units

Now we can apply the formula to calculate the fixed overhead total variance as follows:

= Actual Fixed Overheads - Absorbed Fixed Overheads

= $526,000,000 - 275,000 x $2,000

= $526,000,000 - $550,000,000

= $24,000,000 Favorable

The variance is favorable because the actual expense is lower than the fixed overheads absorbed during the period.

Explanation

Fixed Overhead Total Variance is the difference between the actual fixed production overheads incurred during a period and the 'flexed' cost (i.e. fixed overheads absorbed).

In case of absorption costing, the fixed overhead total variance comprises the following sub-variances:

Fixed Overhead Expenditure Variance : the difference between actual and budgeted fixed production overheads.

Fixed Overhead Volume Variance : the difference between fixed production overheads absorbed (flexed cost) and the budgeted overheads.

Under marginal costing system, fixed production overheads are not absorbed in the cost of output. Fixed overhead total variance in such instance will therefore equal to the fixed overhead expenditure variance because the budgeted and flexed overhead cost shall be the same.

Example

Continuing the Motors PLC example above, we have the following information:

Actual Production 275,000 units

Budgeted Production 250,000 units

Actual Fixed Production Overheads $526,000,000

Budgeted Fixed Production Overheads $500,000,000

Calculate the fixed overhead volume variance and fixed overhead expenditure variance.

Fixed Overhead Expenditure Variance Actual Production $526,000,000

Less: Budgeted Fixed Overheads $500,000,000

Variance $26,000,000 Adverse

The variance is adverse because Motors PLC incurred greater expense than provided for in the budget.

Fixed Overhead Volume Variance Budgeted Production $500,000,000

Less: Absorbed Fixed Overheads [above example] $550,000,000

Variance $50,000,000 Favorable

The variance is favorable because Motors PLC yielded a higher output than anticipated in the budget.

Proof Check The sum of fixed overhead expenditure and volume variances should equal to the fixed overhead total variance as calculated in above Example : Fixed Overhead Expenditure Variance $ 26,000,000 Adverse

Fixed Overhead Volume Variance $ 50,000,000 Favorable

Total $ 24,000,000 Adverse

Fixed Overhead Total Variance $ 24,000,000 Adverse

The variance is favorable because Motors PLC yielded a higher output than anticipated in the budget.

The following diagram summarizes the breakup of the total variance into its sub-components:

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MARGINAL COST

The increase or decrease in the total cost of a production run for making one additional unit of an item. It is computed in situations where the breakeven point has been reached: the fixed costs have already been absorbed by the already produced items and only the direct (variable) costs have to be accounted for.

Marginal costs are variable costs consisting of labor and material costs, plus an estimated portion of fixed costs (such as administration overheads and selling expenses). In companies where average costs are fairly constant, marginal cost is usually equal to average cost. However, in industries that require heavy capital investment (automobile plants, airlines, mines) and have high average costs, it is comparatively very low. The concept of marginal cost is critically important in resource allocation because, for optimum results, management must concentrate its resources where the excess of marginal revenue over the marginal cost is maximum. Also called choice cost, differential cost, or incremental cost.

Read more: http://www.businessdictionary.com/definition/marginal-cost.html#ixzz3moDrXtkp

Marginal Costing & Absorption Costing

Marginal Costing and Absorption Costing

Learning Objectives

To understand the meanings of marginal cost and marginal costing To distinguish between marginal costing and absorption costing

To ascertain income under both marginal costing and absorption costing

IntroductionThe costs that vary with a decision should only be included in decision analysis. For many decisions that involve relatively small variations from existing practice and/or are for relatively limited periods of time, fixed costs are not relevant to the decision. This is because either fixed costs tend to be impossible to alter in the short term or managers are reluctant to alter them in the short term.

Marginal costing - definition

Marginal costing distinguishes between fixed costs and variable costs as convention ally classified.

The marginal cost of a product –“ is its variable cost”. This is normally taken to be; direct labour, direct material, direct expenses and the variable part of overheads.

Marginal costing is formally defined as:

‘the accounting system in which variable costs are charged to cost units and the fixed costs of the period are written-off in full against the aggregate contribution. Its special value is in decision making’. (Terminology.)

The term ‘contribution’ mentioned in the formal definition is the term given to the difference between Sales and Marginal cost. Thus

MARGINAL COST = VARIABLE COST DIRECT LABOUR

+

DIRECT MATERIAL

+

DIRECT EXPENSE

+

VARIABLE OVERHEADS

CONTRIBUTION SALES - MARGINAL COST

The term marginal cost sometimes refers to the marginal cost per unit and sometimes to the total marginal costs of a department or batch or operation. The meaning is usually clear from the context.

Note

Alternative names for marginal costing are the contribution approach and direct costing In this lesson, we will study marginal costing as a technique quite distinct from absorption costing.

Theory of Marginal Costing

The theory of marginal costing as set out in “A report on Marginal Costing” published by CIMA, London is as follows:

In relation to a given volume of output, additional output can normally be obtained at less than proportionate cost because within limits, the aggregate of certain items of cost will tend to remain fixed and only the aggregate of the remainder will tend to rise proportionately with an increase in output. Conversely, a decrease in the volume of output will normally be accompanied by less than proportionate fall in the aggregate cost.

The theory of marginal costing may, therefore, by understood in the following two steps:

1. If the volume of output increases, the cost per unit in normal circumstances reduces. Conversely, if an output reduces, the cost per unit increases. If a factory produces 1000 units at a total cost of $3,000 and if by increasing the output by one unit the cost goes up to $3,002, the marginal cost of additional output will be $.2.

2. If an increase in output is more than one, the total increase in cost divided by the total increase in output will give the average marginal cost per unit. If, for example, the output is increased to 1020 units from 1000 units and the total cost to produce these units is $1,045, the average marginal cost per unit is $2.25. It can be described as follows:

Additional cost =

Additional units

$ 45 = $2.25

20

The ascertainment of marginal cost is based on the classification and segregation of cost into fixed and variable cost. In order to understand the marginal costing technique, it is essential to understand the meaning of marginal cost.

Marginal cost means the cost of the marginal or last unit produced. It is also defined as the cost of one more or one less unit produced besides existing level of production. In this connection, a unit may mean a single commodity, a dozen, a gross or any other measure of goods.

For example, if a manufacturing firm produces X unit at a cost of $ 300 and X+1 units at a cost of $ 320, the cost of an additional unit will be $ 20 which is marginal cost. Similarly if the production of X-1 units comes down to $ 280, the cost of marginal unit will be $ 20 (300–280).

The marginal cost varies directly with the volume of production and marginal cost per unit remains the same. It consists of prime cost, i.e. cost of direct materials, direct labor and all variable overheads. It does not contain any element of fixed cost which is kept separate under marginal cost technique.

Marginal costing may be defined as the technique of presenting cost data wherein variable costs and fixed costs are shown separately for managerial decision-making. It should be clearly understood that marginal costing is not a method of costing like process costing or job costing. Rather it is simply a method or technique of the analysis of cost information for the guidance of management which tries to find out an effect on profit due to changes in the volume of output.

There are different phrases being used for this technique of costing. In UK, marginal costing is a popular phrase whereas in US, it is known as direct costing and is used in place of marginal costing. Variable costing is another name of marginal costing.

Marginal costing technique has given birth to a very useful concept of contribution where contribution is given by: Sales revenue less variable cost (marginal cost)

Contribution may be defined as the profit before the recovery of fixed costs. Thus, contribution goes toward the recovery of fixed cost and profit, and is equal to fixed cost plus profit (C = F + P).

In case a firm neither makes profit nor suffers loss, contribution will be just equal to fixed cost (C = F). this is known as break even point.

The concept of contribution is very useful in marginal costing. It has a fixed relation with sales. The proportion of contribution to sales is known as P/V ratio which remains the same under given conditions of production and sales.

The principles of marginal costing

The principles of marginal costing are as follows.

a. For any given period of time, fixed costs will be the same, for any volume of sales and production (provided that the level of activity is within the ‘relevant range’). Therefore, by selling an extra item of product or service the following will happen.

Revenue will increase by the sales value of the item sold.

Costs will increase by the variable cost per unit.

Profit will increase by the amount of contribution earned from the extra item.

b. Similarly, if the volume of sales falls by one item, the profit will fall by the amount of contribution earned from the item.

c. Profit measurement should therefore be based on an analysis of total contribution. Since fixed costs relate to a period of time, and do not change with increases or decreases in sales volume, it is misleading to charge units of sale with a share of fixed costs.

d. When a unit of product is made, the extra costs incurred in its manufacture are the variable production costs. Fixed costs are unaffected, and no extra fixed costs are incurred when output is increased.

Features of Marginal CostingThe main features of marginal costing are as follows:

1. Cost ClassificationThe marginal costing technique makes a sharp distinction between variable costs and fixed costs. It is the variable cost on the basis of which production and sales policies are designed by a firm following the marginal costing technique.

2. Stock/Inventory ValuationUnder marginal costing, inventory/stock for profit measurement is valued at marginal cost. It is in sharp contrast to the total unit cost under absorption costing method.

3. Marginal ContributionMarginal costing technique makes use of marginal contribution for marking various decisions. Marginal contribution is the difference between sales and marginal cost. It forms the basis for judging the profitability of different products or departments.

Advantages and Disadvantages of Marginal Costing TechniqueAdvantages

1. Marginal costing is simple to understand.

2. By not charging fixed overhead to cost of production, the effect of varying charges per unit is avoided.

3. It prevents the illogical carry forward in stock valuation of some proportion of current year’s fixed overhead.

4. The effects of alternative sales or production policies can be more readily available and assessed, and decisions taken would yield the maximum return to business.

5. It eliminates large balances left in overhead control accounts which indicate the difficulty of ascertaining an accurate overhead recovery rate.

6. Practical cost control is greatly facilitated. By avoiding arbitrary allocation of fixed overhead, efforts can be concentrated on maintaining a uniform and consistent marginal cost. It is useful to various levels of management.

7. It helps in short-term profit planning by breakeven and profitability analysis, both in terms of quantity and graphs. Comparative profitability and performance between two or more products and divisions can easily be assessed and brought to the notice of management for decision making.

Disadvantages

1. The separation of costs into fixed and variable is difficult and sometimes gives misleading results.

2. Normal costing systems also apply overhead under normal operating volume and this shows that no advantage is gained by marginal costing.

3. Under marginal costing, stocks and work in progress are understated. The exclusion of fixed costs from inventories affect profit, and true and fair view of financial affairs of an organization may not be clearly transparent.

4. Volume variance in standard costing also discloses the effect of fluctuating output on fixed overhead. Marginal cost data becomes unrealistic in case of highly fluctuating levels of production, e.g., in case of seasonal factories.

5. Application of fixed overhead depends on estimates and not on the actuals and as such there may be under or over absorption of the same.

6. Control affected by means of budgetary control is also accepted by many. In order to know the net profit, we should not be satisfied with contribution and hence, fixed overhead is also a valuable item. A system which ignores fixed costs is less effective since a major portion of fixed cost is not taken care of under marginal costing.

7. In practice, sales price, fixed cost and variable cost per unit may vary. Thus, the assumptions underlying the theory of marginal costing sometimes becomes unrealistic. For long term profit planning, absorption costing is the only answer.

Presentation of Cost Data under Marginal Costing and Absorption CostingMarginal costing is not a method of costing but a technique of presentation of sales and cost data with a view to guide management in decision-making.

The traditional technique popularly known as total cost or absorption costing technique does not make any difference between variable and fixed cost in the calculation of profits. But marginal cost statement very clearly indicates this difference in arriving at the net operational results of a firm.

Following presentation of two Performa shows the difference between the presentation of information according to absorption and marginal costing techniques:

MARGINAL COSTING PRO-FORMA

£ £

Sales Revenue xxxxx

Less Marginal Cost of Sales

Opening Stock (Valued @ marginal cost) xxxx

Add Production Cost (Valued @ marginal cost) xxxx

Total Production Cost xxxx

Less Closing Stock (Valued @ marginal cost) (xxx)

Marginal Cost of Production xxxx

Add Selling, Admin & Distribution Cost xxxx

Marginal Cost of Sales (xxxx)

Contribution xxxxx

Less Fixed Cost (xxxx)

Marginal Costing Profit xxxxx

ABSORPTION COSTING PRO-FORMA

£ £

Sales Revenue xxxxx

Less Absorption Cost of Sales

Opening Stock (Valued @ absorption cost) xxxx

Add Production Cost (Valued @ absorption cost) xxxx

Total Production Cost xxxx

Less Closing Stock (Valued @ absorption cost) (xxx)

Absorption Cost of Production xxxx

Add Selling, Admin & Distribution Cost xxxx

Absorption Cost of Sales (xxxx)

Un-Adjusted Profit xxxxx

Fixed Production O/H absorbed xxxx

Fixed Production O/H incurred (xxxx)

(Under)/Over Absorption xxxxx

Adjusted Profit xxxxx

Reconciliation Statement for Marginal Costing and Absorption Costing Profit

$

Marginal Costing Profit xx

ADD

(Closing stock – opening Stock) x OAR

xx

= Absorption Costing Profit xx

Where OAR( overhead absorption rate) =Budgeted fixed production overhead

Budgeted levels of activities

Marginal Costing versus Absorption Costing

After knowing the two techniques of marginal costing and absorption costing, we

have seen that the net profits are not the same because of the following reasons:1. Over and Under Absorbed Overheads

In absorption costing, fixed overheads can never be absorbed exactly because of difficulty in forecasting costs and volume of output. If these balances of under or over absorbed/recovery are not written off to costing profit and loss account, the

actual amount incurred is not shown in it. In marginal costing, however, the actual fixed overhead incurred is wholly charged against contribution and hence, there will be some difference in net profits.

2. Difference in Stock Valuation

In marginal costing, work in progress and finished stocks are valued at marginal cost, but in absorption costing, they are valued at total production cost. Hence, profit will differ as different amounts of fixed overheads are considered in two accounts.

The profit difference due to difference in stock valuation is summarized as follows:

a. When there is no opening and closing stocks, there will be no difference in profit.

b. When opening and closing stocks are same, there will be no difference in profit, provided the fixed cost element in opening and closing stocks are of the same amount.

c. When closing stock is more than opening stock, the profit under absorption costing will be higher as comparatively a greater portion of fixed cost is included in closing stock and carried over to next period.

d. When closing stock is less than opening stock, the profit under absorption costing will be less as comparatively a higher amount of fixed cost contained in opening stock is debited during the current period.

The features which distinguish marginal costing from absorption costing are as follows.

a. In absorption costing, items of stock are costed to include a ‘fair share’ of fixed production overhead, whereas in marginal costing, stocks are valued at variable production cost only. The value of closing stock will be higher in absorption costing than in marginal costing.

b. As a consequence of carrying forward an element of fixed production overheads in closing stock values, the cost of sales used to determine profit in absorption costing will:

i. include some fixed production overhead costs incurred in a previous period but carried forward into opening stock values of the current period;

ii. exclude some fixed production overhead costs incurred in the current period by including them in closing stock values.

In contrast marginal costing charges the actual fixed costs of a period in full into the profit and loss account of the period. (Marginal costing is therefore sometimes known as period costing.)

c. In absorption costing, ‘actual’ fully absorbed unit costs are reduced by producing in greater quantities, whereas in marginal costing, unit variable costs are unaffected by the volume of production (that is, provided that variable costs per unit remain unaltered at the changed level of production activity). Profit per unit in any period can be affected by the actual volume of production in absorption costing; this is not the case in marginal costing.

d. In marginal costing, the identification of variable costs and of contribution enables management to use cost information more easily for decision-making purposes (such as in budget decision making). It is easy to decide by how much contribution (and therefore profit) will be affected by changes in sales volume. (Profit would be unaffected by changes in production volume).In absorption costing, however, the effect on profit in a period of changes in both:

i. production volume; and

ii. sales volume;is not easily seen, because behaviour is not analysed and incremental costs are not used in the calculation of actual profit.

Limitations of Absorption CostingThe following are the criticisms against absorption costing:

1. You might have observed that in absorption costing, a portion of fixed cost is carried over to the subsequent accounting period as part of closing stock. This is an unsound practice because costs pertaining to a period should not be allowed to be vitiated by the inclusion of costs pertaining to the previous period and vice versa.

2. Further, absorption costing is dependent on the levels of output which may vary from period to period, and consequently cost per unit changes due to the existence of fixed overhead. Unless fixed overhead rate is based on normal capacity, such changed costs are not helpful for the purposes of comparison and control.

The cost to produce an extra unit is variable production cost. It is realistic to the value of closing stock items as this is a directly attributable cost. The size of total contribution varies directly with sales volume at a constant rate per unit. For the decision-making purpose of management, better information about expected profit is obtained from the use of variable costs and contribution approach in the

accounting system.Summary

Marginal cost is the cost management technique for the analysis of cost and revenue information and for the guidance of management. The presentation of information through marginal costing statement is easily understood by all mangers, even those who do not have preliminary knowledge and implications of the subjects of cost and management accounting.

Absorption costing and marginal costing are two different techniques of cost accounting. Absorption costing is widely used for cost control purpose whereas marginal costing is used for managerial decision-making and control.

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Chapter 3 – Breakeven Analysis

Learning Objectives

To describe as to how the concepts of fixed and variable costs are used in C-V-P analysis

To segregate semi-variable expenses in C-V-P analysis

To identify the limiting assumptions of C-V-P analysis

To work out the breakeven analysis, contribution analysis and margin of safety

To understand how to draw a breakeven chart

To compute breakeven point

IntroductionIn this lesson, we will discuss in detail the highlights associated with cost function and cost relations with the production and distribution system of an economic entity.To assist planning and decision making, management should know not only the budgeted profit, but also:

the output and sales level at which there would neither profit nor loss (break-even point)

the amount by which actual sales can fall below the budgeted sales level, without a loss being incurred (the margin of safety)

MARGINAL COSTS, CONTRIBUTION AND PROFITA marginal cost is another term for a variable cost. The term ‘marginal cost’ is usually applied to the variable cost of a unit of product or service, whereas the term ‘variable cost’ is more commonly applied to resource costs, such as the cost of materials and labour hours.Marginal costing is a form of management accounting based on the distinction between:

a. the marginal costs of making selling goods or services, and

b. fixed costs, which should be the same for a given period of time, regardless of the level of activity in the period.

Suppose that a firm makes and sells a single product that has a marginal cost of £5 per unit and that sells for £9 per unit. For every additional unit of the product that is made and sold, the firm will incur an extra cost of £5 and receive income of £9. The net gain will be £4 per additional unit. This net gain per unit, the difference between the sales price per unit and the marginal cost per unit, is called contribution.

Contribution is a term meaning ‘making a contribution towards covering fixed costs and making a profit’. Before a firm can make a profit in any period, it must first of all

cover its fixed costs. Breakeven is where total sales revenue for a period just covers fixed costs, leaving neither profit nor loss. For every unit sold in excess of the breakeven point, profit will increase by the amount of the contribution per unit.

C-V-P analysis is broadly known as cost-volume-profit analysis. Specifically speaking, we all are concerned with in-depth analysis and application of CVP in practical world of industry management.

Cost-Volume-Profit (C-V-P) Relationship

We have observed that in marginal costing, marginal cost varies directly with the volume of production or output. On the other hand, fixed cost remains unaltered regardless of the volume of output within the scale of production already fixed by management. In case if cost behavior is related to sales income, it shows cost-volume-profit relationship. In net effect, if volume is changed, variable cost varies as per the change in volume. In this case, selling price remains fixed, fixed remains fixed and then there is a change in profit.

Being a manager, you constantly strive to relate these elements in order to achieve the maximum profit. Apart from profit projection, the concept of Cost-Volume-Profit (CVP) is relevant to virtually all decision-making areas, particularly in the short run.

The relationship among cost, revenue and profit at different levels may be expressed in graphs such as breakeven charts, profit volume graphs, or in various statement forms.

Profit depends on a large number of factors, most important of which are the cost of manufacturing and the volume of sales. Both these factors are interdependent. Volume of sales depends upon the volume of production and market forces which in turn is related to costs. Management has no control over market. In order to achieve certain level of profitability, it has to exercise control and management of costs, mainly variable cost. This is because fixed cost is a non-controllable cost. But then, cost is based on the following factors:

Volume of production Product mix

Internal efficiency and the productivity of the factors of production

Methods of production and technology

Size of batches

Size of plant

Thus, one can say that cost-volume-profit analysis furnishes the complete picture of the profit structure. This enables management to distinguish among the effect of sales, fluctuations in volume and the results of changes in price of product/services.In other words, CVP is a management accounting tool that expresses relationship among sale volume, cost and profit. CVP can be used in the form of a graph or an equation. Cost-volume- profit analysis can answer a number of analytical questions. Some of the questions are as follows:

1. What is the breakeven revenue of an organization?

2. How much revenue does an organization need to achieve a budgeted profit?

3. What level of price change affects the achievement of budgeted profit?

4. What is the effect of cost changes on the profitability of an operation?

Cost-volume-profit analysis can also answer many other “what if” type of questions. Cost-volume-profit analysis is one of the important techniques of cost and management accounting. Although it is a simple yet a powerful tool for planning of profits and therefore, of commercial operations. It provides an answer to “what if” theme by telling the volume required to produce.Following are the three approaches to a CVP analysis:

Cost and revenue equations Contribution margin

Profit graph

Objectives of Cost-Volume-Profit Analysis1. In order to forecast profits accurately, it is essential to ascertain the relationship

between cost and profit on one hand and volume on the other.

2. Cost-volume-profit analysis is helpful in setting up flexible budget which indicates cost at various levels of activities.

3. Cost-volume-profit analysis assist in evaluating performance for the purpose of control.

4. Such analysis may assist management in formulating pricing policies by projecting the effect of different price structures on cost and profit.

Assumptions and TerminologyFollowing are the assumptions on which the theory of CVP is based:

1. The changes in the level of various revenue and costs arise only because of the changes in the number of product (or service) units produced and sold, e.g., the number of television sets produced and sold by Sigma Corporation. The number of output (units) to be sold is the only revenue and cost driver. Just as a cost driver is any factor that affects costs, a revenue driver is any factor that affects revenue.

2. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output. Variable costs include the following:

o Direct materials

o Direct labor

o Direct chargeable expenses

Variable overheads include the following:

o Variable part of factory overheads

o Administration overheads

o Selling and distribution overheads

3. There is linear relationship between revenue and cost.

4. When put in a graph, the behavior of total revenue and cost is linear (straight line), i.e. Y = mx + C holds good which is the equation of a straight line.

5. The unit selling price, unit variable costs and fixed costs are constant.

6. The theory of CVP is based upon the production of a single product. However, of late, management accountants are functioning to give a theoretical and a practical approach to multi-product CVP analysis.

7. The analysis either covers a single product or assumes that the sales mix sold in case of multiple products will remain constant as the level of total units sold changes.

8. All revenue and cost can be added and compared without taking into account the time value of money.

9. The theory of CVP is based on the technology that remains constant.

10. The theory of price elasticity is not taken into consideration.

Many companies, and divisions and sub-divisions of companies in industries such as airlines, automobiles, chemicals, plastics and semiconductors have found the simple CVP relationships to be helpful in the following areas:

Strategic and long-range planning decisions Decisions about product features and pricing

In real world, simple assumptions described above may not hold good. The theory of CVP can be tailored for individual industries depending upon the nature and peculiarities of the same.For example, predicting total revenue and total cost may require multiple revenue drivers and multiple cost drivers. Some of the multiple revenue drivers are as follows:

Number of output units Number of customer visits made for sales

Number of advertisements placed

Some of the multiple cost drivers are as follows: Number of units produced Number of batches in which units are produced

Managers and management accountants, however, should always assess whether the simplified CVP relationships generate sufficiently accurate information for predictions of how total revenue and total cost would behave. However, one may come across different complex situations to which the theory of CVP would rightly be

applicable in order to help managers to take appropriate decisions under different

situations.Limitations of Cost-Volume Profit AnalysisThe CVP analysis is generally made under certain limitations and with certain assumed conditions, some of which may not occur in practice. Following are the main limitations and assumptions in the cost-volume-profit analysis:

1. It is assumed that the production facilities anticipated for the purpose of cost-volume-profit analysis do not undergo any change. Such analysis gives misleading results if expansion or reduction of capacity takes place.

2. In case where a variety of products with varying margins of profit are manufactured, it is difficult to forecast with reasonable accuracy the volume of sales mix which would optimize the profit.

3. The analysis will be correct only if input price and selling price remain fairly constant which in reality is difficulty to find. Thus, if a cost reduction program is undertaken or selling price is changed, the relationship between cost and profit will not be accurately depicted.

4. In cost-volume-profit analysis, it is assumed that variable costs are perfectly and completely variable at all levels of activity and fixed cost remains constant throughout the range of volume being considered. However, such situations may not arise in practical situations.

5. It is assumed that the changes in opening and closing inventories are not significant, though sometimes they may be significant.

6. Inventories are valued at variable cost and fixed cost is treated as period cost. Therefore, closing stock carried over to the next financial year does not contain any component of fixed cost. Inventory should be valued at full cost in reality.

Sensitivity Analysis or What If Analysis and UncertaintySensitivity analysis is relatively a new term in management accounting. It is a “what if” technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes.

In the context of CVP analysis, sensitivity analysis answers the following questions:

a. What will be the operating income if units sold decrease by 15% from original prediction?

b. What will be the operating income if variable cost per unit increases by 20%?

The sensitivity of operating income to various possible outcomes broadens the perspective of management regarding what might actually occur before making cost commitments.A spreadsheet can be used to conduct CVP-based sensitivity analysis in a systematic and efficient way. With the help of a spreadsheet, this analysis can be easily conducted to examine the effect and interaction of changes in selling prices, variable cost per unit, fixed costs and target operating incomes.

Example

Following is the spreadsheet of ABC Ltd.,

Statement showing CVP Analysis for Dolphy Software Ltd.

Revenue required at $. 200 Selling Price per unit to earn Operating Income of

Fixed cost

Variable cost

per unit

0 1,000 1,500 2,000

2,000 100 4,000 6,000 7,000 8,000

120 5,000 7,500 8,750 10,000

140 6,667 10,000 11,667 13,333

2,500 100 5,000 7,000 8,000 9,000

120 6,250 8,750 10,000 11,250

140 8,333 11,667 13,333 15,000

3,000 100 6,000 8,000 9,000 10,000

120 7,500 10,000 11,250 12,500

140 10,000 13,333 15,000 16,667

From the above example, one can immediately see the revenue that needs to be generated to reach a particular operating income level, given alternative levels of fixed costs and variable costs per unit. For example, revenue of $. 6,000 (30 units @ $. 200 each) is required to earn an operating income of $. 1,000 if fixed cost is $. 2,000 and variable cost per unit is $. 100. You can also use exhibit 3-4 to assess what revenue the company needs to breakeven (earn operating income of Re. 0) if, for example, one of the following changes takes place:

The booth rental at the ABC convention raises to $. 3,000 (thus increasing fixed cost to $. 3,000)

The software suppliers raise their price to $. 140 per unit (thus increasing variable costs to $. 140)

An aspect of sensitivity analysis is the margin of safety which is the amount of budgeted revenue over and above breakeven revenue. The margin of safety is sales quantity minus breakeven quantity. It is expressed in units. The margin of safety answers the “what if” questions, e.g., if budgeted revenue are above breakeven and start dropping, how far can they fall below budget before the breakeven point is reached? Such a fall could be due to competitor’s better product, poorly executed marketing programs and so on.Assume you have fixed cost of $. 2,000, selling price of $. 200 and variable cost per unit of $. 120. For 40 units sold, the budgeted point from this set of assumptions is 25 units ($. 2,000 ÷ $. 80) or $. 5,000 ($. 200 x 25). Hence, the margin of safety is $. 3,000 ($. 8,000 – 5,000) or 15 (40 –25) units.Sensitivity analysis is an approach to recognizing uncertainty, i.e. the possibility that an actual amount will deviate from an expected amount.

Marginal Cost Equations and Breakeven Analysis

From the marginal cost statements, one might have observed the following:

Sales – Marginal cost = Contribution ......(1)Fixed cost + Profit = Contribution ......(2)

By combining these two equations, we get the fundamental marginal cost equation as follows:

Sales – Marginal cost = Fixed cost + Profit ......(3)

This fundamental marginal cost equation plays a vital role in profit projection and has a wider application in managerial decision-making problems.The sales and marginal costs vary directly with the number of units sold or produced. So, the difference between sales and marginal cost, i.e. contribution, will bear a relation to sales and the ratio of contribution to sales remains constant at all levels. This is profit volume or P/V ratio. Thus,

P/V Ratio (or C/S Ratio) = Contribution (c)

......(4)Sales (s)

It is expressed in terms of percentage, i.e. P/V ratio is equal to (C/S) x 100.

Or, Contribution = Sales x P/V ratio ......(5)

Or, Sales = Contribution

......(6)P/V ratio

The above-mentioned marginal cost equations can be applied to the following heads:1. Contribution

Contribution is the difference between sales and marginal or variable costs. It contributes toward fixed cost and profit. The concept of contribution helps in deciding breakeven point, profitability of products, departments etc. to perform the following activities:

Selecting product mix or sales mix for profit maximization Fixing selling prices under different circumstances such as trade depression,

export sales, price discrimination etc.

2. Profit Volume Ratio (P/V Ratio), its Improvement and ApplicationThe ratio of contribution to sales is P/V ratio or C/S ratio. It is the contribution per rupee of sales and since the fixed cost remains constant in short term period, P/V ratio will also measure the rate of change of profit due to change in volume of sales. The P/V ratio may be expressed as follows:

P/V ratio =Sales – Marginal cost of sales

=Contribution

=Changes in contribution

=Change in profit

Sales Sales Changes in sales Change in sales

A fundamental property of marginal costing system is that P/V ratio remains constant at different levels of activity.

A change in fixed cost does not affect P/V ratio. The concept of P/V ratio helps in determining the following:

Breakeven point Profit at any volume of sales

Sales volume required to earn a desired quantum of profit

Profitability of products

Processes or departments

The contribution can be increased by increasing the sales price or by reduction of variable costs. Thus, P/V ratio can be improved by the following:

Increasing selling price Reducing marginal costs by effectively utilizing men, machines, materials and

other services

Selling more profitable products, thereby increasing the overall P/V ratio

3. Breakeven PointBreakeven point is the volume of sales or production where there is neither profit nor loss. Thus, we can say that:Contribution = Fixed cost

Now, breakeven point can be easily calculated with the help of fundamental marginal cost equation, P/V ratio or contribution per unit.a. Using Marginal Costing Equation

S (sales) – V (variable cost) = F (fixed cost) + P (profit) At BEP P = 0, BEP S – V = F

By multiplying both the sides by S and rearranging them, one gets the following equation:

S BEP = F.S/S-V

b. Using P/V Ratio

Sales S BEP =Contribution at BEP

=Fixed cost

P/ V ratio P/ V ratio

Thus, if sales is $. 2,000, marginal cost $. 1,200 and fixed cost $. 400, then:

Breakeven point =400 x 2000

= $. 10002000 - 1200

Similarly,P/V ratio

= 2000 – 1200 = 0.4 or 40%800

So, breakeven sales = $. 400 / .4 = $. 1000c. Using Contribution per unit

Breakeven point =Fixed cost

= 100 units or $. 1000Contribution per unit

4. Margin of Safety (MOS)

Every enterprise tries to know how much above they are from the breakeven point. This is technically called margin of safety. It is calculated as the difference between sales or production units at the selected activity and the breakeven sales or production.

Margin of safety is the difference between the total sales (actual or projected) and the breakeven sales. It may be expressed in monetary terms (value) or as a number of units (volume). It can be expressed as profit / P/V ratio. A large margin of safety indicates the soundness and financial strength of business.

Margin of safety can be improved by lowering fixed and variable costs, increasing volume of sales or selling price and changing product mix, so as to improve contribution and overall P/V ratio.

Margin of safety = Sales at selected activity – Sales at BEP =Profit at selected activity

P/V ratio

Margin of safety is also presented in ratio or percentage as follows:Margin of safety (sales) x 100 %

Sales at selected activity

The size of margin of safety is an extremely valuable guide to the strength of a business. If it is large, there can be substantial falling of sales and yet a profit can be made. On the other hand, if margin is small, any loss of sales may be a serious matter. If margin of safety is unsatisfactory, possible steps to rectify the causes of mismanagement of commercial activities as listed below can be undertaken.

a. Increasing the selling price-- It may be possible for a company to have higher margin of safety in order to strengthen the financial health of the business. It should be able to influence price, provided the demand is elastic. Otherwise, the same quantity will not be sold.

b. Reducing fixed costs

c. Reducing variable costs

d. Substitution of existing product(s) by more profitable lines e. Increase in the volume of output

e. Modernization of production facilities and the introduction of the most cost effective technology

Problem 1A company earned a profit of $. 30,000 during the year 2000-01. Marginal cost and selling price of a product are $. 8 and $. 10 per unit respectively. Find out the margin of safety.

Solution

Margin of safety =Profit

P/V ratio

P/V ratio =Contribution x 100

Sales

Problem 2

A company producing a single article sells it at $. 10 each. The marginal cost of production is $. 6 each and fixed cost is $. 400 per annum. You are required to calculate the following:

Profits for annual sales of 1 unit, 50 units, 100 units and 400 units P/V ratio

Breakeven sales

Sales to earn a profit of $. 500

Profit at sales of $. 3,000

New breakeven point if sales price is reduced by 10%

Margin of safety at sales of 400 units

Solution Marginal Cost Statement

Particulars Amount Amount Amount Amount

Units produced 1 50 100 400

Sales (units * 10) 10 500 1000 4000

Variable cost 6 300 600 2400

Contribution (sales- VC) 4 200 400 1600

Fixed cost 400 400 400 400

Profit (Contribution – FC) -396 -200 0 1200

Profit Volume Ratio (PVR) = Contribution/Sales * 100 = 0.4 or 40%

Breakeven sales ($.) = Fixed cost / PVR = 400/ 40 * 100 = $. 1,000

Sales at BEP = Contribution at BEP/ PVR = 100 units

Sales at profit $. 500

Contribution at profit $. 500 = Fixed cost + Profit = $. 900

Sales = Contribution/PVR = 900/.4 = $. 2,250 (or 225 units)

Profit at sales $. 3,000

Contribution at sale $. 3,000 = Sales x P/V ratio = 3000 x 0.4 = $. 1,200

Profit = Contribution – Fixed cost = $. 1200 – $. 400 = $. 800

New P/V ratio = $. 9 – $. 6/$. 9 = 1/3

Sales at BEP = Fixed cost/PV ratio =$. 400

= $. 1,2001/3

Margin of safety (at 400 units) = 4000-1000/4000*100 = 75 %

(Actual sales – BEP sales/Actual sales * 100)

Breakeven Analysis-- Graphical Presentation

Apart from marginal cost equations, it is found that breakeven chart and profit graphs are useful graphic presentations of this cost-volume-profit relationship.

Breakeven chart is a device which shows the relationship between sales volume, marginal costs and fixed costs, and profit or loss at different levels of activity. Such a chart also shows the effect of change of one factor on other factors and exhibits the rate of profit and margin of safety at different levels. A breakeven chart contains, inter alia, total sales line, total cost line and the point of intersection called breakeven point. It is popularly called breakeven chart because it shows clearly breakeven point (a point where there is no profit or no loss).

Profit graph is a development of simple breakeven chart and shows clearly profit at different volumes of sales.

Construction of a Breakeven Chart

The construction of a breakeven chart involves the drawing of fixed cost line, total cost line and sales line as follows:

1. Select a scale for production on horizontal axis and a scale for costs and sales on vertical axis.

2. Plot fixed cost on vertical axis and draw fixed cost line passing through this point parallel to horizontal axis.

3. Plot variable costs for some activity levels starting from the fixed cost line and join these points. This will give total cost line. Alternatively, obtain total cost at different levels, plot the points starting from horizontal axis and draw total cost line.

4. Plot the maximum or any other sales volume and draw sales line by joining zero and the point so obtained.

Uses of Breakeven ChartA breakeven chart can be used to show the effect of changes in any of the following profit factors:

Volume of sales Variable expenses

Fixed expenses

Selling price

ProblemA company produces a single article and sells it at $. 10 each. The marginal cost of production is $. 6 each and total fixed cost of the concern is $. 400 per annum.Construct a breakeven chart and show the following:

Breakeven point Margin of safety at sale of $. 1,500

Angle of incidence

Increase in selling price if breakeven point is reduced to 80 units

SolutionA breakeven chart can be prepared by obtaining the information at these levels:

Output units 40 80 120 200

Sales$. $. $. $.

400 800 1,200 2,000

Fixed cost 400 400 400 400

Variable cost 240 480 400 720

Total cost 640 880 1,120 1,600

Fixed cost line, total cost line and sales line are drawn one after another following the usual procedure described herein:

This chart clearly shows the breakeven point, margin of safety and angle of incidence.

a. Breakeven point-- Breakeven point is the point at which sales line and total cost line intersect. Here, B is breakeven point equivalent to sale of $. 1,000 or 100 units.

b. Margin of safety-- Margin of safety is the difference between sales or units of production and breakeven point. Thus, margin of safety at M is sales of ($. 1,500 - $. 1,000), i.e. $. 500 or 50 units.

c. Angle of incidence-- Angle of incidence is the angle formed by sales line and total cost line at breakeven point. A large angle of incidence shows a high rate of profit being made. It should be noted that the angle of incidence is universally denoted by data. Larger the angle, higher the profitability indicated by the angel of incidence.

d. At 80 units, total cost (from the table) = $. 880. Hence, selling price for breakeven at 80 units = $. 880/80 = $. 11 per unit. Increase in selling price is Re. 1 or 10% over the original selling price of $. 10 per unit.

Limitations and Uses of Breakeven ChartsA simple breakeven chart gives correct result as long as variable cost per unit, total fixed cost and sales price remain constant. In practice, all these facto$ may change and the original breakeven chart may give misleading results.

But then, if a company sells different products having different percentages of profit to turnover, the original combined breakeven chart fails to give a clear picture when the sales mix changes. In this case, it may be necessary to draw up a breakeven chart for each product or a group of products. A breakeven chart does not take into account capital employed which is a very important factor to measure the overall efficiency of business. Fixed costs may increase at some level whereas variable costs may sometimes start to decline. For example, with the help of quantity discount on materials purchased, the sales price may be reduced to sell the additional units produced etc. These changes may result in more than one breakeven point, or may indicate higher profit at lower volumes or lower profit at still higher levels of sales.

Nevertheless, a breakeven chart is used by management as an efficient tool in marginal costing, i.e. in forecasting, decision-making, long term profit planning and maintaining profitability. The margin of safety shows the soundness of business whereas the fixed cost line shows the degree of mechanization. The angle of incidence is an indicator of plant efficiency and profitability of the product or division

under consideration. It also helps a monopolist to make price discrimination for maximization of profit.

Multiple Product Situations

In real life, most of the firms turn out many products. Here also, there is no problem with regard to the calculation of BE point. However, the assumption has to be made that the sales mix remains constant. This is defined as the relative proportion of each product’s sale to total sales. It could be expressed as a ratio such as 2:4:6, or as a percentage as 20%, 40%, 60%.

The calculation of breakeven point in a multi-product firm follows the same pattern as in a single product firm. While the numerator will be the same fixed costs, the denominator now will be weighted average contribution margin. The modified formula is as follows:

Breakeven point (in units) =

Fixed costs

Weighted average contribution margin per unit

One should always remember that weights are assigned in proportion to the relative sales of all products. Here, it will be the contribution margin of each product multiplied by its quantity.

Breakeven Point in Sales Revenue

Here also, numerator is the same fixed costs. The denominator now will be weighted average contribution margin ratio which is also called weighted average P/V ratio. The modified formula is as follows:

B.E. point (in revenue) = Fixed cost

Weighted average P/V ratio

Problem Ahmedabad Company Ltd. manufactures and sells four types of products under the brand name Ambience, Luxury, Comfort and Lavish. The sales mix in value comprises the following:

Brand name                      Percentage

Ambience                     33 1/3

Luxury                              41 2/3

Comfort                             16 2/3

Lavish                              8 1/3

                                    ------

                                     100

         

The total budgeted sales (100%) are $. 6,00,000 per month.The operating costs are:

Ambience     60% of selling price Luxury

Luxury       68% of selling price Comfort

Comfort      80% of selling price Lavish

Lavish       40% of selling price

The fixed costs are $. 1,59,000 per month.

a. Calculate the breakeven point for the products on an overall basis.

b. It has been proposed to change the sales mix as follows, with the sales per month remaining at $. 6,00,000:

Brand Name    Percentage

Ambience             25

Luxury               40

Comfort              30

Lavish              05

                    ---

                    100

    

Assuming that this proposal is implemented, calculate the new breakeven point.Solution

a. Computation of the Breakeven Point on Overall Basis

b. Computation of the New Breakeven Point

Profit GraphProfit graph is an improvement of a simple breakeven chart. It clearly exhibits the relationship of profit to volume of sales. The construction of a profit graph is relatively easy and the procedure involves the following:

1. Selecting a scale for the sales on horizontal axis and another scale for profit and fixed costs or loss on vertical axis. The area above horizontal axis is called profit area and the one below it is called loss area.

2. Plotting the profits of corresponding sales and joining them. This is profit line.

Summary

1. Fixed and variable cost classification helps in CVP analysis. Marginal cost is also useful for such analysis.

2. Breakeven point is the incidental study of CVP. It is the point of no profit and no loss. At this specific level of operation, it covers total costs, including variable and fixed overheads.

3. Breakeven chart is the graphical representation of cost structure of business.

4. Profit/Volume (P/V) ratio shows the relationship between contribution and value/volume of sales. It is usually expressed as terms of percentage and is a valuable tool for the profitability of business.

5. Margin of safety is the difference between sales or units of production and breakeven point. The size of margin of safety is an extremely valuable guide to the financial strength of a business.