FINANCE MANAGEMENT FIN420 chp 11

Capital Budgeting Chapter 11

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Since a firm’s investments involve large cash outlays

and the amount of time involved is long, a firm has to

find profitable project by using a well- developed

evaluation process.

Learning objectives

After learning this chapter, you should be able to:

1. Define capital budgeting

2. Evaluate proposals according to respective capital budgeting

techniques

3. Select the best proposal

Capital Budgeting

GOAL

Chapter 11 Capital Budgeting

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11.0 INTRODUCTION Capital budgeting is in essence similar to cost-benefit analysis that involves comparison of

expected returns generated and the costs incurred. It involves the whole process of planning

for capital investment or fixed assets, with the expectation of future cash flows beyond one-

year period. Capital investment or capital expenditures may consist of the following

expenditures:

1. Replacement of existing facilities;

2. Expansion of current facilities;

3. Safety and/or environmental projects; and

4. Any other expenditure that affects the firm's cash flow beyond one-year period.

The process of capital budgeting involves measuring the incremental cash flows associated

with the investment proposal and evaluating its attractiveness relative to the costs of the

project. Therefore, it is the process of:

1. Estimating the cash flows after tax generated from the investment;

2. Estimating the level of risk associated with the project; and

3. Employing ways or methods to evaluate the proposed project(s); and

4. Making effective decision to ensure it has a positive contribution to the firm's value.

Proper estimations and evaluations are necessary because it is costly to reverse any capital

decisions made and to ensure the firm's viability. Thus, this chapter will present the process

of estimating the cash flows from capital investment and several capital budgeting

techniques that are commonly used for project's evaluation under: (1) non discounted cash

flows method; and (2) discounted cash flows method. These techniques will enable the

financial managers to identify and choose capital investments that are viable and profitable

for the firm to venture into.

11.1 ESTIMATION OF CASH FLOW Estimation of cash flows associated with the project over its useful life is the first and utmost

important step in capital budgeting process to evaluate the proposed project. The accuracy

of the estimation is crucial, as it will affect the decisions made by the financial manager. The


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focus is on after tax cash flows, whether earnings after taxes (EAT) or cash flows after tax (CFAT). Cash flow after tax equals to:

CFATt = EATt + Non cash expenses for the period

In an attempt to estimate cash flows associated with capital investment, explicit

considerations should be given to its amount, timing and appropriate tax treatments. Note

however, the cost of interests or financing costs for the proposed project should be ignored,

as its implications will take in form of discount rate or required rate of return in the capital

budgeting process. Cash flows after taxes consist of three components that are net initial

cash flows, net annual cash flows, and terminal cash flows.

a) Net Initial Cash Flows (NICF)

Net initial cash flows are the initial investment or initial outlay, associated with the

initial cost of implementing the proposed capital project. It represents the net outflows

incurred to implement a proposed capital project at time zero; that is CFAT0.

Outflows:

1. Cost of equipment and facilities acquired.

2. All cost related to the acquisitions, transportation, and legal fees, training,

spare parts and installations.

3. Other tangible or intangible assets acquired.

4. Additional requirement for net working capital.

5. Tax liability on disposed assets; sold above the book value.

Inflows:

1. Investments tax credit, if any.

2. Proceeds from disposal of old assets.

3. Tax shield on disposed assets; sold less than the book value.

Not all of the listing above is applicable in all capital budgeting analysis, but any cash

outflows and inflows associated with the initial set up of the capital investment must

be considered, explicitly.


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b) Net Annual Cash Flows (NACF)

Net annual cash flows are the net cash inflows from expanded operations or the net

cash outflows saved from cost reduction projects. NACF also referred as operating cash flows which occur at time (t) through (n), CFATt; that is from year one through

n years of the project's life.

CFBTt : Cash inflowst minus Cash outflowst; excluding taxes and depreciation

It is also known as Cash Flows before Depreciation and Taxes (CFBDT)

T : Marginal corporate tax rate

Dept : Depreciation expenses for year t

∆ : Refer to incremental change

The NACF requires different treatments when dealing with expansion and

replacement capital investments. The basic determination CFAT is similar, except

that incremental cash flows must be used in determining CFATt of capital

investments that involve replacement. The calculations of CFAT under the tax shield

approach are as follows:

Operating cash flows for expansions project:

CFATt = CFBTt(1 – T) + Dept(T)

Operating cash flows for replacement project:

∆CFATt = ∆CFBTt(1 – T) + ∆Dept(T)

Where ∆ represent the incremental or change in cash flows. It is determined

by deducting the present cash flows from the expected cash flows due to the

replacements.

Both of the above equations assume that the firm is profitable. In the event the firm is

operating at a loss and where there is no tax liability, depreciation tax shield (=CFATt

(T)) does not exist.


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c) Terminal Cash Flows (TCF)

Terminal cash flows refer to the terminal value associated with the net cash inflows

realized in disposed asset. It represents the end value of a given asset at the end of

its economic life or end of usage due to disposal for replacement. Thus, CFATn of the

project are as follows:

Inflows:

1. Proceeds from the sale of assets.

2. Recovery of net working capital initially required.

3. Tax shields from the sale of assets; sold for less than book value

Outflows:

1. Cost of disposing the assets.

2. Tax liability from the sale of assets; sold above the book value.

The most commonly used term for terminal cash flows is salvage value. However, it

only refers to the expected book value of the assets at the end of its usage (end of

life or for disposal); without consideration of tax effects and other cash flow

associated with its disposal.

In the following sections, a sample of expansion and replacement projects will be

discussed starting from the determination of relevant cash flows and its application in

capital budgeting process. In most cases, the decision to accept or reject a particular

project will be based on the net present value method, since its measure is superior

to others for reasons mentioned earlier.

d) Example for Expansion Decisions

To illustrate, Zaza Products Inc. is considering an investment in a new computerized

machine to expand its production facilities that could increase sales and revenues.

The new machine has a 5-year useful life with a price tag of RM49,000. In addition,

freight and installation costs are RM1,000 and the increase in net working capital of

RM10,000 can be expected. This is due to additional requirements in accounts

receivable and inventory investment.


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The project is expected to generate additional cash flows of RM30,000 per year over

its useful life. The firm will also incurs additional cash outflows of RM5,000 per year

for the first three years, and the cost is expected to increase RM1,000 per year

thereafter as the machine wears out. Currently, the firm's marginal tax rate is 40%

and all assets are depreciated based on the straight-line method (SLM). There is no

salvage value expected at the end of 5 years. The determination of NACF requires

more than one calculation due to changes in cash outflows, and hence cash flows

before tax.

1. Net Initial Investment at year 0 or NICF: CFAT0

Purchase price 49,000

Plus: Freight and installation 1,000

Increase in net working capital 10,000

NICF or CFAT0 60,000

2. Operating Cash Flows in Years 1-5 or NACF1-5: CFAT1-5

CFAT1-3 = CFBTt (1 – T) + Dept (T)

= (30,000 – 5,000)(1 – 0.40) + (50,000 / 5)(0.40)

= RM19,000

Note that CFAT for year 1 through 3 is constant as it has the same CFBT and

Depreciation. However, CFAT for year 4 and 5 must be calculated

individually, as its CFBT are not the same.

CFAT4 = CFBT4 (1 – T) + Dep4 (T)

= (30,000 – 6,000)(1 – 0.40) + 10,000(0.40)

= RM18,400

CFAT5 = CFBT5 (1 – T) + Dep5 (T)

= (30,000 – 7,000)(1 – 0.40) + 10,000(0.40)

= RM17,800


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Another method to determine the CFAT is by using the income statement

format or the bottom up approach that uses the basic equation for CFAT, that

is:

CFATt = EATt + Depreciation

It will result in similar answers but with multiple stages of calculations as

shown in Table 11-1.

Table 11-1 Determination of CFAT under Bottom Up Approach

CFAT1-3 FATt CFAT5

Sales 30,000 30,000 30,000

Less: Cost of Goods Sold 5,000 6,000 7,000

Gross Profit 25,000 24,000 23,000

Less: Other costs - - -

Depreciation 10,000 10,000 10,000

Operating profit or EBIT 15,000 14,000 13,000

Less: Interest _ .

Taxable Income or EBT 15,000 14,000 13,000

Less: Tax at 40% 6,000 5,600 5,200

Net profit or EAT 9,000 8,400 7,800

Plus: Depreciation 10,000 10,000 10,000

NACFt or CFATt 19,000 18,400 17,800

3. Terminal cash flows in year 5 of TCF: CFAT5

Recovery of net working capital RM10,000

Salvage value 0

The TCF value of RM10,000 represents the recovery of working capital

initially invested that is no longer needed after the useful life of the machine.

In addition, the book values or salvage value of zero is based on the

assumption that the assets not sold after its useful life.


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In the event that the assets are sold after its useful life, for example at

RM20,000, the computation for the terminal cash flows will differ as follows:

Selling Price (SP) 20,000

Less: Book Value (BV) 0

Other costs 0.

Profits from sale or recaptured dep. 20,000

Note that there are no capital gains as selling price is less than the cost of

assets.

Tax liability from sale = 20,000(0.40) 8,000

Net proceeds from sale = 20,000 – 8,000 12,000

Therefore, terminal cash flows for the disposed asset:

Recovery of net working capital 10,000

Plus: Net proceeds from sale 12,000

Terminal cash flows 22,000

The above calculation can be simplified in the following equation.

TCFn = Recovery of net working capital + SP – (SP – BV)(T)

= 10,000 + 20,000 – (20,000 – 0)(0.4)

= 22,000

Note that he above equation is not applicable if the selling price is above the

cost of assets as capital gains require different tax treatments.

4. Time Line and Decision. To have a better view of its flows, a time line can

be developed as follows before the evaluation process:

Year 0 1 2 3 4 5 CFATt TCF

–60,000 19,000 19,000 19,000 18,400 17,800 10,000

It is advisable to develop the time line as it provides better view of the cash

flows involved in the particular project and ease of determining its present

value for capital budgeting decisions.


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Example for Replacement Decisions

Determining CFATs for replacement project is more complicated than the

expansion project as it involves incremental cost-benefit analysis. Other

procedures will remain the same.

For example, Iza Company is considering replacing an existing machine that

was purchased 2 years ago for RM50,000 with a computerized system that

could improve the company's operations. The old machine is being

depreciated under straight-line method over its useful life of 5 years with no

salvage value. Its current market value is RM40,000.

The new machine has a purchase price of RM60,000 and an estimated

salvage value of RM6,000 at the end of its useful life of 3 years. If the new

machine is purchased, the cash inflows are expected to increase by 10%

from the current level of RM30,000 per year. In addition, the cash outflows of

RM15,000 associated with the old machine are expected to decrease to

RM8,000 per year. Assume that the firm's cost of capital is 10%, marginal tax

rate is 40%, and capital gains rate is 28%.

1. Net Initial Investment at year or NICF: CFAT0

Purchase price of new machine 60,000

Less: Net proceeds from sale of old machine 40,000

Plus: Tax liability from sale of old machines 4,000a

NICF or CFAT0 24,000

a Computation of tax liability from the sale of old machine:

Book value = COA – Accumulated depreciation

= 50,000 – (50,000 / 5) 2

= RM30,000

Profit/Loss = SP – BV – Other costs

= 40,000 – 30,000 – 0

= RM10,000


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Since the company realized a profit of RM10,000 from the sale, it creates tax

liability:

Tax Liability = Profit/Loss (T)

= 10,000 (0.40)

= RM4,000

2. Operating cash flows in years 1-3 or NACF1-3: CFAT1-3

∆CFBT1-3 = Increase in cash inflows t + Decrease in cash outflows t

= (30,000)(0.10) + (15,000 – 8,000)

= RM10,000

∆Dep1-3 = (New Dep. t – Old Dep. t)

= ((60,000 – 6,000) / 3) – (50,000 / 5)

= RM18,000 – RM10,000

= RM8,000

∆CFAT1-3 = ∆CFBT t (1 – T) + ∆Dep. t (T)

= 10,000 (1 – 0.40) + 8,000 (0.40)

= RM9,200

3. Terminal cash flows in year 3; or TCF: CFAT3

Salvage value of the new machine RM6,000

4. Time Line and Decision. A proper time line can be developed to

show the cash flows associated with the above project after which it

can be evaluated for its attractiveness:

Year 0 1 2 3

CFATt

TCF

–24,000 9,200 9,200 9,200

6,000

In the incremental cash flow analysis, the focus is on the cash flows that

would change due to the acceptance of the proposed capital investment. Any


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existing cash flow that is irrelevant and does not change due to the proposed

project should be ignored in capital budgeting process. The net present value

method is the most common approach to evaluate the acceptability of the

proposed projects. This is due the fact that NPV is best method of evaluation

under normal circumstances.

11.2 CAPITAL BUDGETING TECHNIQUES The last part of capital budgeting is to develop proper evaluations and decisions making to

ensure the capital investment employed will contribute to the firm's value. Proper and

appropriate techniques must be employed in determining the worth of the projects before

accept-reject decisions is applied.

To illustrate the techniques involved, consider the alternative projects that Kurnia

Corporation is planning to evaluate for investment in 1995, as presented in Table 11-2. It

shows that both projects have the same initial investment or initial outlay of RM6,000 with

depreciation expenses of RM1,500 (=6,000 / 4) based on straight-line method with no

salvage value.

Table 11-2 Cash Flows of Investment Alternatives for Kurnia

Year Project A EAT CFAT Project B EAT CFAT1 2 3 4

RM900900900900

RM2,4002,4002,4002,400

RM500 700 900

1,200

RM2,0002,2002,4002,700

Total cash inflows RM3,600 RM9,600 RM3,300 RM9,300Average inflows RM 900 RM2,400 RM 825 RM2,325Salvage value RM - RM - Initial outlay RM6,000 RM6,000 Where EAT : Earnings after tax or net income

CFAT : Cash flows after tax = EAT + Depreciation


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11.2.1 Non-Discounted Cash Flow Method

Non discounted cash flow methods do not consider the time value of money

in the their analysis of capital investment. Two methods are average rate of

return and payback period.

Average Rate of Return (ARR)

The average rate of return or accounting rate of return measures

the profitability of a proposed capital investment as the ratio of

average earnings after taxes (EAT) to average investment. For Kurnia:

ARR = AEAT / AI

n

Where AEAT = ∑ (EAT t ) / n

t=1

AI = (IO + SV) / 2

Where AEAT : Average earnings after taxes

AI : Average investment

SV : Estimated salvage value of the project

IO : Initial outlay or Initial investment

ARRA = ((900 + 900 + 900 + 900) / 4) / ((6,000 + 0)/ 2)

= 900 / 3,000

= 30.00%

ARRB = ((500 + 700 + 900 + 1,200) / 4) / ((6,000 + 0) / 2)

= 825 / 3,000

= 27.50%

As an investment criterion, high average rate of return is better as it

represents greater accounting rate of return on the average.

1. Independent projects. The firm should accept all projects that

provide returns above the minimum required rate of return.


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2. Mutually exclusive projects. Kurnia should adopt project 'A' as

it gives higher return as only one project will be accepted.

Average rate of return method is simple to calculate but has some

drawbacks. It fails to account for the time value of money and uses

earnings after taxes in the analysis. In actual sense, the use of cash

flows after taxes (CFAT) is more appropriate as net cash flows is more

important in determining the firm's success in the long run than net

profit (EAT).

Payback Period (PB) The payback period measures the length of time in years for the firm

to recover back its initial investment; that is the amount of time for an

investment to pay for or liquidate itself. Thus, payback occurs when

the sums of cash inflows or CFAT equal the initial cash investment:

? PB = (IO – ∑ CFATt) = 0

t=1

PB = (Yr. – 1) + [(IO – Cumulative cash inflows before Yr.) / Cash

inflows in Yr.]

Where IO : Initial outlay or cash investment; CFAT0

Yr. : Years to recovery of initial outlay; where total CFATt

exceeds the IO

PB : Payback period

Using the relevant financial data in Table 12-2,

PBA = (3 – 1) + [(6,000 – 4,800) / 2,400]

= 2.5 years


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Year CFAT for A Cumulative CFAT

1

2

3

4

RM2,400

2,400

2,400

2,400

RM2,400

4,800

7,200

If the cash flows are an annuity, such as in project “A” a simplified

formula can be used to determine the payback as follows:

PBA = IO / Annuity cash flow

= 6,000 / 2,400

= 2.5 years

The above equation is not applicable for uneven cash flows such as in

project B.

PBB = (3 – 1) + [(6,000 – 4,200) / 2,400]

= 2.75 years

Year CFAT for B Cumulative CFAT

1

2

3

4

RM2,000

2,200

2,400

2,700

RM2,000

4,200

6,600

The above calculations show that both projects give the same

recovery period. Other things being equal, short recovery time indicate

the liquidity of the project that could provide rapid cash return and

securing the certainty of cash inflows from the project in relatively

short time. As a decision criterion, projects with shorter payback or

payback period smaller than the maximum payback established are

acceptable.

1. Independent projects. The firm should accept all projects that

provide payback less than maximum payback period as stated

by the firm.

Exceeds initial outlay of RM6,000. Therefore yr. = 3

Exceeds initial outlay of RM6,000. Therefore yr. = 3


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2. Mutually exclusive projects. Kurnia should adopt project 'A' as

it can recover the initial costs faster than ‘B’ and thus reduces

risks and increases liquidity.

The payback method is very useful to evaluate; (1) risky projects; (2)

estimations of cash flow associate with the projects are difficult; and

(3) if the company itself is facing liquidity problems. In such cases, it is

to the best interest of the firm to recover the initial cash investment as

soon as possible. The payback method is simple to calculate, and is a

better measure than average rate of return, since it considers cash

flows after tax (CFAT) rather than accounting profit (EAT).

The major drawbacks are the failure: (1) to consider time value of

money that plays an important part of all investment decisions; and (2)

to recognize cash flows that occurs after the payback period. Thus,

payback method is a bad profitability indicator of the proposed capital

investment.

11.2.2 Discounted Cash Flows Method

Unlike non-discounted cash flows method discussed above, discounted

method explicitly considers the time value of money and employs the

discounted cash flow framework in the analysis. These methods of capital

budgeting support the wealth maximization goal of the firm, as it considers

time value of money and marginal cost of capital as the minimum required

rate of return from the investment. The three common discounted cash flow

techniques are net present value, internal rate of return and profitability index.

Net Present Value (NPV)

One of the widely used capital budgeting techniques is the net present

value. It explicitly considers time value of money and defined as: (1)

the net of cumulative present value of cash flows; plus (2) the present

value of terminal value of the project; minus (3) the initial cash

investment:


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NPV = Present value of cash flows – Initial investment

n NPV = ∑ (CFATt / (1 + k) t) – IO t=1

n Alternatively NPV = ∑ (CFATt x PVIFk,n) – IO t=1

If marginal cost of capital for Kurnia Corporation is 10%, the net

present value for project 'A' and 'B' are as follows:

NPVA = 2,400 (PVIFA10%,4) – 6,000

= 2,400 (3.1699) – 6,000

= 7,607.76 – 6,000

= RM1,607.76

NPVB = 2,000 (PVIF10%,1) + 2,200 (PVIF10%,2) + 2,400 (PVIF10%,3) +

2,700 (PVIF10%,4) – 6,000

= 2,000 (0.9091) + 2,200 (0.8264) + 2,400 (0.7513) + 2,700

(0.6830) – 6,000

= 7,283.66 – 6,000

= RM1,283.66

As investment criterion, the basic rule for NPV is to accept projects

with NPV greater than zero. At this level, it indicates that the firm will

earn a return greater than or equal to the required rate of return.

1. Independent projects. The firm should accept both projects “A”

and “B as both projects give a positive net present value.

2. Mutually exclusive projects. Kurnia should accept project 'A' as

its NPV is higher than of “B” and will better increase the firm’s

value.

The accuracy of NPV method will significantly depend on the accuracy

of the cash flow estimates and the estimates of “k,” the required rate

of return. This leads to a major drawback in NPV in some cases as


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difficulty may arise in (1) estimation of the relevant cash flows with

accuracy, especially when involve with longer time period, and (2)

estimation of the risk level or the discount rate to use due to the

uncertainty of the business environment.

Despite the difficulties, it is accepted as "the method" to use in capital

budgeting as its assumptions are more sound and logical theoretically;

that is all cash inflows generated from the capital project can be

invested at the cost of capital or the required rate of return.

Profitability Index (PI)

The concept behind this method is quite similar to that of net present

values. Profitability index is a relative measure that shows the present

value of cash flows earned per Ringgit of initial cash invested;

whereas NPV gives the difference between the present value of cash

flows and the initial cash investment. The profitability index equals

(data form NPV calculations):

PI = Present value of cash flows / Initial investment

n = ∑ (CFATt / (1 + k) t) / IO t=1

n Alternatively PI = ∑ CFATt x PVIFk,n / IO

t=1

PIA = 7,615.44 / 6,000

= 1.269

PIB = 7,292.41 / 6,000

= 1.215

The decision criterion with PI is to accept any project that gives PI

greater than 1.0. The above computations indicate that project “A” and

“B” returns RM1.269 and RM1.219 Ringgits, respectively for each

Ringgit initially invested.


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1. Independent projects. The firm should accept both projects “A”

and “B as the PIs for both project is greater than 1.

2. Mutually exclusive projects. Kurnia should accept project 'A' as

its PI is greater than of “B.”

Due to their similarity is equation base, PI will give similar ranking as

NPV.

Internal Rate of Return (IRR)

The internal rate of return of the capital investment is the discount rate

that causes the NPV to equal zero. In other words, the discount rate

that equates total present value of cash inflows to initial cash

investment to zero. Therefore, IRR is whereby NPV equals to zero:

n IRR = ∑ (CFATt / (1 + IRR) t) – IO = 0 t=1 n Alternatively IRR = ∑ (CFATt)(PVIFIRR,n) – IO = 0 t=1

As investment criterion, the firm should accept projects with IRR

higher than or equal to the required rate of return or the marginal cost

of capital. Unlike other methods, calculating the IRR is more complex

at times especially when the cash flows involved are uneven and of

longer periods. Single lump sum or an annuity payment is easier to

calculate and others may involve determination of IRR by trial an

error:

1. Lump Sums. To illustrate, consider a project with initial

investment of RM4,000, which give single cash inflow at the

end of year 3 of RM5,720.


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a. Divide the initial investment by the lump sum cash

inflow to determine the PVIFk,3 factor:

PV0 = FV3 (PVIFk,3)

PVIFk, 3 = PV0 / FV3

= 4,000 / 5,720

= 0.6993

b. Refer to PVIF table for 0.699 in row 3: 0.6993 is

between 12% (0.7118) and 14% (0.6750). Therefore,

interpolation is necessary to estimates the IRR with

relative accuracy. By interpolation, IRR is:

IRR = 12% + (0.0125 / 0.0368)(14 – 12)

= 12.68%

2. Annuities. To illustrate, consider project A for Kurnia, with

initial investment of RM6,000, which give cash flows of

RM2,400 annually for 4 years.

a. Divide the Initial cash investment by annuity cash flow

to determine a PVIFA k,4 factor:

PV0 = Annuity (PVIFAk,4)

PVIFAk,4 = PV0 / Annuity

= 6,000 / 2,400

= 2.5

Percent PVIFk,n 12% 0.7118

K 0.6993 0.0125 14% 0.6750 0.0368


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b. Refer to PVIFA table for 2.5 in row 4; 2.5 are between

20% (2.5887) and 24% (2.4044). Thus by interpolation

IRR equals to:

IRRA = 20% + (0.0887 / 0.1843) 4

= 21.93%

The above project is acceptable as long as the IRR is

greater than the firm's marginal cost of capital or the

required rate of return. For example if the required rate

of 10%, the project is acceptable.

3. Uneven Stream of Cash Flows. Calculating IRR under these

circumstances is more complexes and a tedious process. One

way to simplify the trial and error process is to use a 'simulated

annuity' as a starting point. To illustrate, consider project 'B' of

Kurnia Corporation. It involves:

a. Determine the simulated annuity; that is average CFAT

for the project:

Avg. CFATB = (2,000+ 2,200 + 2,400 + 2,700) / 4

= RM2,325.00

b. Determine the approximate or simulated IRR (SIRR);

that is by dividing the initial cash investment by the

simulated annuity.

6,000 = 2,325 (PVIFAk,4)

PVIFAk,4 = 6,000 / 2,325

= 2.5806

Percent PVIFAk,n 20% 2.5887

K 2.5000 0.0887 24% 2.4044 0.1843


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By looking at PVIFA table in row 4; 2.5806 lies between

18% (2.6901) and 20% (2.5887). Thus, the

approximate or simulated IRR for “B” is between 18%

and 20%.

c. Adjustment of approximates IRR. It is necessary to

adjust the rough estimate of IRR accordingly in relation

to the cash flows pattern of the project. In the event of

higher cash inflows in the early years compared to

later years, adjust the estimated IRR upward a few

percentage points, and vice versa. In our case, the

adjustment is downwards since the cash inflows for the

project is higher in later years. Therefore, 20% is the

focal point of adjustment. Since the differences in cash

flows are not significant, the trial and error can begins

at 20% as a starting point.

d. Trial and error. By using the adjusted approximate IRR

of 20% as the initial discount rate, calculations for IRR

by using NPV concept are as follows:

At 20% NPVB = 2,000(PVIF20%,1) + 2,200(PVIF20%,2) +

2,400(PVIF20%,3) + 2,700(PVIF20%,4) –

6,000

= 2,000(0.8333) + 2,200(0.6944) +

2,400(0.5789) + 2,700(0.4823)

– 6,000

= –RM114.15


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NPV at 20% is negative; therefore, the true IRR should

be below 20%. Let discount rate equals to 18%,

calculate the second trial and error:

At 18% NPVB = 2,000(PVIF18%,1) + 2,200(PVIF18%,2) +

2,400(PVIF18%,3) + 2,700(PVIF18%,4)

– 6,000

= 2,000(0.8475) + 2,200(0.7182) +

2,400(0.6086) + 2,700(0.5158)

– 6,000

= RM128.34

Since the NPV at 18% is positive RM128.34 and at

20% is negative RM114.15, the true IRR for project B is

at NPV of zero between 18% and 20%. In order to

estimate the true IRR, interpolation is required.

Therefore IRR:

Percent NPV(RM) 8% 128.34 K 0.00 128.34

20% –114.15 242.79

IRRB = 18% + (128.34 / 242.79) 2

= 19.06%

As investment criterion, accept all independent projects

with IRR greater than the required rate of return.

1. Independent projects. The firm should accept

both projects “A” and “B as the IRRs for both

project are greater than the required rate of

return of 10%.


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2. Mutually exclusive projects. Kurnia should

accept project 'A' with higher IRR of 21.93%

compared to “B” at 19.06%.

Theoretically, IRR is inferior to either NPV or the PI.

This is because the most of the time the firm cannot

achieve return from the reinvestments of cash flows

from the investment at IRR rate. On the other hand,

NPV and the PI use the cost of capital to discount all of

the cash flows and it is sounder to say that the firm can

manage to earn at that going rate from the

reinvestment made.

11.3 PROJECTS WITH UNEQUAL LIFE In the previous example, the replacement decision was simplified by assuming that the

useful life of the new machine matches equally to the remaining life of the old machine. In

practice, the probability of this to occur is low. For example, consider the following projects :

Year CFAT for

X CFAT for Y

1 2 3 4 5 6

RM5,000 5,000 5,000

RM4,000 4,000 4,000 4,000 4,000 4,000

Initial Outlay NPV at 10% Project's life

RM12,000 435 3 years

RM16,000 1,4206 years

A choice can be made if these projects are evaluated independently; under NPV criteria

project Y is better. But, it could be an incorrect decision. This issue can be resolved by

comparing the projects based on NPV's of both projects for the same number of years.

Thus, a proper method to evaluate projects with unequal lives must be developed. There are

three methods that are commonly used for evaluations are least common life, equivalent

annual cost, and annualized net present value. For our purpose, the latter method will be

used.


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Annualized Net Present Value (ANPV)

One of the methods for making unequal lived projects comparable is by

finding the net present value of each project assuming continuous

replacement chains to infinity. This is called annualized net present value

approach. Though it seems complex, but it only involves three basic steps:

1. Determine the original NPV for each project individually.

2. Divide the original NPV of each project from step 1, by the annuity

factor for the project life to obtain the equivalent annuity amount.

3. Choose the project with the highest NPV of the infinite annuity.

In all cases, the ANPV method leads to the same decision as the simple

chain method, or the least common life. In addition, ANPV is easier to

calculate but its concept sometimes is not easy to comprehend as it involves

an infinite time horizon. Under ANPV:

ANPVi = NPVi / PVIFAk,n

ANPVX = 435 / PVIFA10%,3

= 435 / 2.4868

= RM174.92

ANPVY = 1,420 / PVIFA10%,6

= 1,420 / 4.3585

= RM325.80

Based on ANPV method, project Y should be accepted as its ANPV is greater

than ANPV of X. As a general rule, the replacement chain issue only arise in

a mutually exclusive projects with different lives are evaluated.


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11.4 COMPARISONS OF CAPITAL BUDGETING TECHNIQUES Most of the time NPV, IRR and PI will give consistent decisions particularly if evaluations

involve only a single project or the multiple independent projects. In mutually exclusive

projects, not all of the discounted cash flows methods give consistent ranking. To illustrate,

let assume that the initial investment for Kurnia in the previous example equals to RM4,000,

instead of RM8,000 previously; with no salvage value. Table 11-3 presents all relevant data

and capital budgeting results associate with the old and new initial investment for Kurnia.

Table 11-3 Mutually Exclusive Projects Ranking at Different Initial Outlay

Note: All data are from discussions presented

Different ranking problems will be dealt with exclusively in advance finance courses. Under

normal circumstances, discounted cash flows method will give similar rankings. However,

conflicting rankings may result due to:

1. Size disparity. It refers to the differences in the initial cash investment of the projects

involved that is one project may have substantially higher initial cash investment

compared to the other.

2. Time disparity. Refer to the differences in timing of cash flows of the project. That is

one project may have higher CFAT in the early years, while the other has higher

CFAT in later years.

NPV and PI generally will give the same ranking due to similarity in information used.

However conflicting rankings may occur if the initial investments of the projects are different

in size; size disparity. The use of PI to evaluate mutually projects, is therefore requires

cautions when the initial investments of the projects are not the same.

Initial investment RM6,000 Project A Project B Decision

Average rate of return 30.00% 27.50% A

Payback period 2.50 years 2.75 years A

Net present value RM1,615.44 RM1,292.41 A

Profitability index 1.269 1.215 A

Internal rate of return 21.93% 19.06% A


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In the case of NPV and IRR, it may give different rankings in case of the presence of size

and/or time disparity. In case of conflicts, decision under NPV criterion should have the

priority due to its more realistic assumption of reinvestment rate compared to IRR. The NPV

method assumes that the cash flows generated from the project can be invested at the cost

of capital or the required rate of return. On the other hand, IRR assumes that the

reinvestment is at the project's IRR that is not that reasonable, especially when the project

has high IRR.


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QUESTION 1

Putra Sdn Bhd is in the process of evaluating capital investment proposals. This

company has to consider two (2) investment projects, A and B:

A B

Initial Outlay RM10,000 RM10,000

Annual Net Cash Flow:

Year 1

2

3

4

RM6,000

4,000

3,000

2,000

RM4,000

4,000

4,000

4,000

As a friend to EN Putra the owner of Putra Sdn Bhd you are asked to advise in

determining which project to choose. Cost of capital is 10% and you are required to

evaluate according to these techniques:

a) Payback Period

b) Net Present Value (NPV)

c) Internal Rate of Return (IRR)

(20 marks)


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QUESTION 2

a) Setron Berhad is considering two mutually projects with widely differing lives.

The company’s cost of capital is 10%. The project cash flows are summarized

as follows:

Project A (RM) Project B (RM)

Initial Investment 25,000 23,000

Year 1 9,742 4,641

Year 2 9,742 4,641

Year 3 9,742 4,641

Year 4 - 4,641

Year 5 - 4,641

Year 6 - 4,641

Year 7 - 4,641

Year 8 - 4,641

Year 9 - 4,641

You are required to choose the project that Setron should tahe by using:

i) Payback Period technique

ii) Net Present Value (NPV) technique

iii) Internal Rate of Return (IRR) technique

(3+5+9=17 marks)

b) Briefly explain the meaning of mutually exclusive projects.

(3 marks)

(Total : 20 marks)


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QUESTION 3

a) Inamoto Inc. is considering two mutually exclusive pieces of machinery that

perform the same task. The two alternative machineries provide the following

set of after-tax net cash flow :

Equipment Y Equipment X

Initial outlay RM50,000 RM50,000

Inflow year 1 RM15,625 0




Inflow year 5 RM15,625 RM100,000

Calculate each project’s :

i) Payback Period

ii) Net Present Value (NPV)

iii) Internal Rate of Return (Approximate)

(15 marks)

b) Batis Tuta & Son Oil Company is considering two drilling proposals. Proposal

A lasts for three years, costs RM20 million to start, pays back quickly, and

has an NPV of RM15 million.

Proposal B also costs about RM20 million, but has an expected life of seven

years, takes much longer to pay-back, and has an NPV of RM17 million.

Mr. Batis, the company’s founder, favors proposal A because of the quick

investment recovery. His son Gabriel, however, has taken a Finance course

at college and insists that the only way to judge projects is by its NPV. He

therefore favors proposal B.

What is your advice to them? Explain.

(5 marks)

(Total : 20 marks)


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QUESTION 4

Triple AAA Company is considering investment in one of the three mutually exclusive

projects listed below.

Year Project Intelek (RM)

Project Integresi (RM)

Project Bistari (RM)

0 -12,000 -10,000 -17,000

1 5,000 6,000 5,000

2 5,000 3,000 8,000

3 5,000 3,000 10,000

The firm’s average cost of capital is 12%.

a) Calculate:

i) Payback period for each project.

ii) Net Present Value for each project.

iii) Internal rate of return for Project Intelek (estimated).

(18 marks)

b) Based on the answer a) (i) and a) (ii), which project is preferred?

(2 marks)

FINANCE MANAGEMENT FIN420 chp 11

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