Alternative Investment Rules and Capital Budgeting Analysis

Capital budgeting is the planning for purchases of assets whose returns

are expected to continue beyond one year.

Common Models

• There are several common models used in evaluating capital budgeting decisions:– Net present value – Payback period– Average accounting return– Internal rate of return– Profitability index

Defining Project Type

• Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. – RANK all alternatives and select the best one.

• Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.– Must exceed a MINIMUM acceptance criteria.

The Net Present Value (NPV) Rule

• Net Present Value (NPV) = Total PV of future CF’s + Initial Investment

• Estimating NPV:– 1. Estimate future cash flows: how much? and when?

– 2. Estimate discount rate

– 3. Estimate initial costs

• Minimum Acceptance Criteria: Accept if NPV > 0• Ranking Criteria: Choose the highest NPV

Good Attributes of the NPV Rule

• 1. Uses cash flows

• 2. Uses ALL cash flows of the project

• 3. Discounts ALL cash flows properly

The Payback Period Rule

• How long does it take the project to “pay back” its initial investment?

• Payback Period = # of years to recover initial costs.

• Minimum Acceptance Criteria: set by management. Project must “pay back” within a certain period.

• Ranking Criteria: set by management.

Disadvantages of Payback Rule

• Ignores the time value of money.• Ignores CF after payback period.• Biased against long-term projects.• Payback period may not exist or there may

be multiple payback periods.• Requires an arbitrary acceptance criteria.• A project accepted based on the payback

criteria may not have a positive NPV.

Advantages of Payback Rule

• Easy to understand

• Biased toward liquidity

The Average Accounting Return (AAR) Rule

• AAR = Average NI / Average Book Value of Investment

• Minimum Acceptance Criteria: set by management.

• Ranking Criteria: set by management.

Disadvantages of AAR Rule

• Ignores the time value of money

• Uses an arbitrary benchmark cutoff rate

• Based on book values, not cash flows and market values

Advantages of AAR Rule

• The accounting information is usually available

• Easy to calculate

The Internal Rate of Return (IRR) Rule

• The IRR is the discount rate that sets the NPV to zero.

• Minimum Acceptance Criteria: Accept if the IRR > required return.

• Ranking Criteria: Select alternative with the highest IRR.

Disadvantages of IRR Rule

• Does not distinguish between investing and financing.

• IRR may not exist, or there may be multiple IRR’s

• Problems with mutually exclusive investments– borrowing or lending?– multiple (or no) rates of return– mutually exclusive projects: scale and timing

Advantages of IRR Rule

• Easy to understand and communicate

Problem # 1: Borrowing or LendingCf(0) Cf(1) Cf(2) Cf(3) IRR NPV @ 10%

+1000 -500 -500 -500 23.4% -243.43

This project represents the borrower’s side of a loan. Thus, as the discount rate increases, the NPV of the project increases.

23% r

NPV

Problem # 2: Multiple Rates of Return

NPV @

Cf(0) Cf(1) Cf(2) IRR 10%

-4,000 25,000 -25,000 25% -1,934

& 400%

NPV

r400%25%

Note: It is alsopossible there isno IRR.

Mutually Exclusive Projects: Problem # 1-- The Scale Problem

NPV

Cf(0) Cf(1) IRR @ 10%

Project 1 -100 200 100% $82

Project 2 -1000 1500 50% $323.6

Do not compare the IRR’s of mutually exclusive projects.

Mutually Exclusive Projects: Problem #2-- Timing Problem

Cf(0) Cf(1) Cf(2) Cf(3)

A: -$10,000 $10,000 $1,000 $1,000

B: -$10,000 $1,000 $1,000 $12,000

NPV NPV NPV

@ 0% @10% @15% IRR

A: $2,000 $669 $109 16.04%

B: $4,000 $751 -$484 12.94%

NPV & IRR for Timing Problem

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

0 10 20 30 40

rNP

V

When interest rates are low, Project B has the higher NPV. When interest rates are high,Project A has the higher NPV.

Project B

Project ACrossoverRate

The Profitability Index (PI) Rule

• PI = Total Present Value of future CF’s / Initial Investment

• Minimum Acceptance Criteria: Accept if PI > 1

• Ranking Criteria: Select alternative with highest PI

Disadvantages of PI Rule

• Problems with mutually exclusive investments

Advantages of PI Rule

• May be useful when available investment funds are limited

• Easy to understand and communicate

• Correct decision when evaluating independent projects

Example: Investment Rules

Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%.

Year Project A Project B

0 -$200 -$150

1 $200 $50

2 $800 $100

3 -$800 $150

Example of Investment Rules: NPV, IRR, PI

Project A Project B

CF0 -$200.00 -$150.00

PV0 of CF1-3 $241.92 $240.80

NPV = $41.92 $90.80

IRR = 0%, 100% 36.19%

PI = 1.2096 1.6053

Example of Investment Rules: Payback Period

Payback Period:

Project A Project B

Time CF Cum. CF CF Cum. CF

0 -200 -200 -150 -150

1 200 0 50 -100

2 800 800 100 0

3 -800 0 150 150

Payback Period (cont’d)

Payback period for project B = 2 years

Payback period for project A = 1 or 3 years?

Relationship Between NPV and IRR

Discount rate NPV for A NPV for B-10% -87.52 234.77

0% 0.00 150.0020% 59.26 47.9240% 59.48 -8.6060% 42.19 -43.0780% 20.85 -65.64

100% 0.00 -81.25

120% -18.93 -92.52

NPV Profiles

-150

-100

-50

0

50

100

150

200

250

300

-10 0 20 40 60 80 100 120

r

NP

V

Project A

Project B

CrossoverRate

NPV & Capital Budgeting

Four basic steps for project valuation:1. Generate proposals.

2. Estimate cash flows.

3. Evaluate and select projects.

4. Review decisions.

Generating Proposals

• Projects may come from growth opportunities.

• Projects may come from cost reduction opportunities.

• Projects may be required to meet legal requirements or health and safety standards.

Estimating Cash Flows

• Cash Flows should be estimated on an incremental basis. Compare the cash flows with the project to cash flows without the project.

• Cash flows should be measured on an after-tax basis, except for government projects.

• Use cash flows - not accounting income.

Estimating Cash Flows

• “Let bygones be bygones” - ignore sunk costs.

• Remember opportunity costs of resources used.

• Consider side effects - are cash flows from other projects affected? Either up or down?

Example: Project Valuation

• Suppose a steel company is thinking of adding a new blast furnace to its operations. You have just completed a $1 million feasibility study and have found the following:

• Adding the blast furnace will result in $50 million in new sales each year and will save $100 million per year in expenses. However, the furnace will cost $10 million per year to operate.

Example - Continued• Suppose the furnace costs $1,000 million and uses

some parts from a (fully depreciated) retired furnace that could be sold for $30 million. The new furnace will last 10 years and has a salvage value of $200 million. The project will require $20 million of working capital over its 10-year life.

• The firm uses straight-line depreciation for tax purposes and pays 40% in corporate income taxes.

• Assume the cost of capital is 10%.

Example - Continued• Step One (“No Rules, Just Right”, i.e., it works

for me...): Initial Cash Flow.• $1,000 million capital expenditure• $20 million working capital• $30 million lost gain on sale of old furnace• But, would have paid taxes on gain of (.40*$30

million) = $12 million. Net gain if sold old furnace = $18 million

• Total initial cash flow = -$1,038 million• (Negative sign reflects cash outflow.)

Example - Continued• Step Two: Operating Cash Flows.• Change in Depreciation each year =

$1,000 million ÷ 10 = $100 million• Change in Revenue = $50 million • Change in Expenses = $10 million - $100 million

(savings) = -$90 • Change in Taxes = ($50 - (-$90) - $100) * .40 =

$16 million• CFi = ($50 - (-$90) - $100) - $16 + $100 = $124

million

Example - Continued• In Cash Flow Statement Format:

Revenues $50- Expenses -(-90)- Depreciation -100= EBT = $40- Taxes (.40) -16= EAT = $24+ Depreciation +100= Cash Flow = $124

Example - Continued

• Step Three: Project Termination Cash Flows.

• Salvage Value = $200 million

• Owe taxes of (.40 * $200 million) = $80 million

• Release of Working Capital = $20 million

• Total = $200 - $80 + $20 = $140 million

Example - Continued

• Step Four: Find NPV

• NPV = -$1,038 million + $124 million * (PVIFA10%, 9) + ($124 million + $140 million) * PVIF10%, 10)

• CF0 = -1,038, C01 = 124, F01 = 9, C02 = 264, F02 = 1, I% =10%

• NPV = -$222 million, IRR = 5.10%

Example - Continued

• Step Five: Make decision.

• Reject project since NPV is less than zero.

Additional Considerations

• Inflation

• Comparing Projects with Different Lives

Cash Flows and Inflation

• It is important to recognize the effects of inflation on cash flows.

• The Fisher equation says:• (1 + nominal rate of interest) = (1 + real

interest rate) * (1 + inflation rate)• Example: If the real interest rate is 5% and

inflation is 4%, the nominal rate of interest is 9.2% (1.05 x 1.04 = 1.092, or 9.2%)

Consistency

• The most important lesson in choosing the appropriate discount rate is to be consistent.

• Nominal cash flows must be discounted with the nominal interest rate.

• Real cash flows must be discounted with the real interest rate.

Projects with Different Lives - Replacement Chain Analysis

• Replacement chain analysis assumes that alternative projects can and will be repeated.

• Matching-cycle analysis finds a common multiple of both projects and finds NPV for project string, i.e., if one project last 2 years and the other lasts 3 years, compare NPVs if invest in the first project 3 times consecutively and the second project 2 times consecutively.

• Huh?

Projects with Different Lives - Replacement Chain Analysis

• Equivalent annual cost analysis finds the equal annual payments over the life of the project that have the same NPV as the true cash flows.

• Generally, easier to compute than matching-cycle analysis.

Example: Equivalent Annual Cost

Suppose we’re looking at the cost of two machines, A and B, r = 5%. (All cash outflows.)

Machine A Machine B

t=0 $15 million $20 million

t=1 $2 million $1 million

t=2 $2 million $1 million

t=3 $1 million

Example - Continued

• Project A lasts two years.

• Find the NPV of A = -$18.72 million.

• Find the equal annual amount that gives an NPV of -$18.72 million over 2 years.

• N=2, I=5, PV=-$18.72, FV=0 ==> PMT= $10.07 million

• Payments of $10.07 million gives same NPV as Machine A’s Cash Flows

Example - Continued

• Project B lasts 3 years and has NPV=-22.72• Find the equal annual amount that gives an

NPV of -$22.72 million over 3 years.• N=3, I=5, PV=-$22.72, FV=0 ==> PMT=

$8.34 million• Payments of $8.34 million gives same NPV

as Machine B’s Cash Flows• Choose Machine B - Lowest Cost