Chapter 6 Investment Decision Rules. 2 Chapter Outline 6.1 NPV and Stand-Alone Projects 6.2 Alternative Decision Rules 6.3 Mutually Exclusive Investment

Chapter 6

Investment Decision Rules

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Chapter Outline

6.1 NPV and Stand-Alone Projects

6.2 Alternative Decision Rules

6.3 Mutually Exclusive Investment Opportunities

6.4 Project Selection with Resource Constraints

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Learning Objectives

1. Define net present value, payback period, internal rate of return, profitability index, and incremental IRR.

2. Describe decision rules for each of the tools in objective 1, for both stand-alone and mutually exclusive projects.

3. Given cash flows, compute the NPV, payback period, internal rate of return, profitability index, and incremental IRR for a given project.

4. Compare each of the capital budgeting tools above, and tell why NPV always gives the correct decision.

5. Define Economic Value Added, and describe how it can be used in capital budgeting.

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6.1 NPV and Stand-Alone Projects Consider a take-it-or-leave-it investment

decision involving a single, stand-alone project for Fredrick Feed and Farm (FFF).

The project costs $250 million and is expected to generate cash flows of $35 million per year, starting at the end of the first year and lasting forever.

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NPV Rule

The NPV of the project is calculated as:

The NPV is dependent on the discount rate.

35NPV 250

r

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Figure 6.1 NPV of FFF’s New Project

If FFF’s cost of capital is 10%, the NPV is $100 million and they should undertake the investment.

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Measuring Sensitivity with IRR At 14%, the NPV is equal to 0, thus the

project’s IRR is 14%. For FFF, if their cost of capital estimate is more than 14%, the NPV will be negative, as illustrated on the previous slide.

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Alternative Rules Versus the NPV Rule Sometimes alternative investment rules may

give the same answer as the NPV rule, but at other times they may disagree.

When the rules conflict, the NPV decision rule should be followed.

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6.2 Alternative Decision Rules The Payback Rule

The payback period is amount of time it takes to recover or pay back the initial investment. If the payback period is less than a pre-specified length of time, you accept the project. Otherwise, you reject the project. The payback rule is used by many companies because

of its simplicity. However, the payback rule does not always give a

reliable decision since it ignores the time value of money.

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Example 6.1

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Example 6.1 (cont'd)

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Alternative Example 6.1

Problem

Projects A, B, and C each have an expected life of 5 years.

Given the initial cost and annual cash flow information below, what is the payback period for each project?

A B C

Cost $80 $120 $150

Cash Flow

$25 $30 $35

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Solution

Payback A $80 ÷ $25 = 3.2 years

Project B $120 ÷ $30 = 4.0 years

Project C $150 ÷ $35 = 4.29 years

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The Internal Rate of Return

Internal Rate of Return (IRR) Investment Rule Take any investment where the IRR exceeds the

cost of capital. Turn down any investment whose IRR is less than the cost of capital.

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The Internal Rate of Return (cont'd) The IRR Investment Rule will give the same

answer as the NPV rule in many, but not all, situations.

In general, the IRR rule works for a stand-alone project if all of the project’s negative cash flows precede its positive cash flows. In Figure 6.1, whenever the cost of capital is

below the IRR of 14%, the project has a positive NPV and you should undertake the investment.

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The Internal Rate of Return (cont'd) In other cases, the IRR rule may disagree

with the NPV rule and thus be incorrect.

Situations where the IRR rule and NPV rule may be in conflict: Delayed Investments Nonexistent IRR Multiple IRRs

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The Internal Rate of Return (cont'd) Delayed Investments

Assume you have just retired as the CEO of a successful company. A major publisher has offered you a book deal. The publisher will pay you $1 million upfront if you agree to write a book about your experiences. You estimate that it will take three years to write the book. The time you spend writing will cause you to give up speaking engagements amounting to $500,000 per year. You estimate your opportunity cost to be 10%.

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Should you accept the deal? Calculate the IRR.

The IRR is greater than the cost capital. Thus, the IRR rule indicates you should accept the deal.

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Financial Calculator Solution

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Should you accept the deal?

Since the NPV is negative, the NPV rule indicates you should reject the deal.

2 3

500,000 500,000 500,000 1,000,000 $243,426

1.1 1.1 1.1 NPV

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Figure 6.2 NPV of Star’s $1 million Book Deal

When the benefits of an investment occur before the costs, the NPV is an increasing function of the discount rate.

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The Internal Rate of Return (cont'd) Nonexistent IRR

Assume now that you are offered $1 million per year if you agree to go on a speaking tour for the next three years. If you lecture, you will not be able to write the book. Thus your net cash flows would look like:

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The Internal Rate of Return (cont'd) Nonexistent IRR

By setting the NPV equal to zero and solving for r, we find the IRR. In this case, however, there is no discount rate that will set the NPV equal to zero.

2 3

500,000 500,000 500,000

1 (1 ) (1 )

NPV

r r r

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Figure 6.3 NPV of Lecture Contract

No IRR exists because the NPV is positive for all values of the discount rate. Thus the IRR rule cannot be used.

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The Internal Rate of Return (cont'd) Multiple IRRs

Now assume the lecture deal fell through. You inform the publisher that it needs to increase its offer before you will accept it. The publisher then agrees to make royalty payments of $20,000 per year forever, starting once the book is published in three years.

Should you accept or reject the new offer?

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The cash flows would now look like:

The NPV is calculated as:

2 3 4 5

3 3

500,000 500,000 50,000 20,000 20,000 1,000,000

1 (1 ) (1 ) (1 ) (1 )

500,000 1 1 20,000 1,000,000 1

(1 ) (1 )

NPVr r r r r

r r r r

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By setting the NPV equal to zero and solving for r, we find the IRR. In this case, there are two IRRs: 4.723% and 19.619%. Because there is more than one IRR, the IRR rule cannot be applied.

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Figure 6.4 NPV of Star’s Book Deal with Royalties

If the opportunity cost of capital is either below 4.723% or above 19.619%, you should accept the deal.

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Between 4.723% and 19.619%, the book deal has a negative NPV. Since your opportunity cost of capital is 10%, you should reject the deal.

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The Internal Rate of Return (cont'd) IRR Versus the IRR Rule

While the IRR rule has shortcomings for making investment decisions, the IRR itself remains useful. IRR measures the average return of the investment and the sensitivity of the NPV to any estimation error in the cost of capital.

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Economic Profit or EVA

EVA and Economic Profit Economic Profit

The difference between revenue and the opportunity cost of all resources consumed in producing that revenue, including the opportunity cost of capital

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Economic Profit or EVA (cont'd) EVA and Economic Profit

Economic Value Added (EVA)

The cash flows of a project minus a charge for the opportunity cost of capital

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Economic Profit or EVA (cont'd) EVA When Invested Capital is Constant

EVA in Period n (When Capital Lasts Forever)

where I is the project’s capital, Cn is the project’s cash flow in time period n, and r is the cost of capital. r × I is known as the capital charge

n nEVA C rI

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Economic Profit or EVA (cont'd) EVA When Invested Capital is Constant

EVA Investment Rule Accept any investment in which the present value (at the

project’s cost of capital) of all future EVAs is positive. When invested capital is constant, the EVA rule and the

NPV rule will coincide.

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Example 6.2

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Problem

Ranger has an investment opportunity which requires an upfront investment of $150 million.

The annual end-of-year cash flows of $14 million dollars are expected to last forever.

The firm’s cost of capital is 8%.

Compute the annual EVA and the present value of the project.

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Solution

Using Eq. 6.1, the EVA each year is:

The present value of the EVA perpetuity is:

n nEVA C rI

$14 million 8% $150 million $2 million nEVA

$2 million$25 million

8% PV

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Economic Profit or EVA (cont'd) EVA When Invested Capital Changes

EVA in Period n (When Capital Depreciates)

Where Cn is a project’s cash flow in time period n, In – 1 is the project’s capital at time period n – 1, and r is the cost

of capital

When invested capital changes, the EVA rule and the NPV rule coincide.

1 (Depreciation in Period ) n n nEVA C rI n

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Example 6.3

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6.3 Mutually Exclusive Investment Opportunities

Mutually Exclusive Projects When you must choose only one project among

several possible projects, the choice is mutually exclusive.

NPV Rule Select the project with the highest NPV.

IRR Rule Selecting the project with the highest IRR may lead

to mistakes.

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Differences in Scale

If a project’s size is doubled, its NPV will double. This is not the case with IRR. Thus, the IRR rule cannot be used to compare projects of different scales.

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Differences in Scale (cont'd)

Identical Scale Consider two projects:

Girlfriend’s Business

Laundromat

Initial Investment $1,000 $1,000

Cash FlowYear 1 $1,100 $400

Annual Growth Rate -10% -20%

Cost of Capital 12% 12%

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Identical Scale Girlfriend’s Business

1100 1100 1000 1000 $4000

0.1 0.12 0.1

NPV

r

11001000 implies 100%

0.1

r

r

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Identical Scale Laundromat

IRR = 20%

Both the NPV rule and the IRR rule indicate the girlfriend’s business is the better alternative.

400 400 1000 1000 $250

0.2 0.12 0.2

NPV

r

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Figure 6.5 NPV of Investment Opportunities

The NPV of the girlfriend’s business is always larger than the NPV of the single machine laundromat. The IRR of the girlfriend’s business is 100%, while the IRR for the laundromat is 20%.

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Changes in Scale What if the laundromat project was 20 times

larger?

The NPV would be 20 times larger, but the IRR remains the same at 20%. Give an discount rate of 12%, the NPV rule indicates you

should choose the 20-machine laundromat (NPV = $5,000) over the girlfriend’s business (NPV = $4,000).

400 20 1000 $5000

0.12 0.2

NPV

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Figure 6.6 NPV of Investment Opportunities with the 20-Machine Laundromat

The NPV of the 20-machine laundromat is larger than the NPV of the girlfriend’s business only for discount rates less than 13.9%.

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Percentage Return Versus Impact on Value

The girlfriend’s business has an IRR of 100%, while the 20-machine laundromat has an IRR of 20%, so why not choose the girlfriend’s business? Because the 20-machine laundromat makes more

money It has a higher NPV.

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Percentage Return Versus Impact on Value

Would you prefer a 200% return on $1 dollar or a 10% return on $1 million? The former investment makes only $2, while the latter

opportunity makes $100,000.

The IRR is a measure of the average return, but NPV is a measure of the total dollar impact on value.

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Timing of Cash Flows

Another problem with the IRR is that it can be affected by changing the timing of the cash flows, even when that change in timing does not affect the NPV. It is possible to alter the ranking of projects’ IRRs

without changing their ranking in terms of NPV.

Hence you cannot use the IRR to choose between mutually exclusive investments.

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Timing of Cash Flows (cont'd) Assume you are offered a maintenance

contract on the laundromat machines which would cost $250 per year per machine. With this contract, you would not have to pay for maintenance and so the cash flows from the machines would not decline. The expected cash flows would then be:

$400 – $250 = $150 per year per machine

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Timing of Cash Flows (cont'd) The time line would now be:

The NPV of the project remains $5,000 but the IRR falls to 15%.

150 20 1000 $5000

NPV

r

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Figure 6.7 NPV With and Without

the Maintenance Contract

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Timing of Cash Flows (cont'd) The NPV without the maintenance contract

exceeds the NPV with the contract for discount rates that are greater than 12%. The IRR without the maintenance contract (20%)

is larger than the IRR with the maintenance contract (15%).

The correct decision is to agree to the contract if the cost of capital is less than 12% and to decline the contract if the cost of capital exceeds 12%. With a 12% cost of capital, you are indifferent.

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The Incremental IRR Rule

Incremental IRR Investment Rule Apply the IRR rule to the difference between the

cash flows of the two mutually exclusive alternatives (the increment to the cash flows of one investment over the other).

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The Incremental IRR Rule (cont'd) Incremental IRR Rule Application

The following timeline illustrates the incremental cash flows of the maintenance contract laundromat over the laundromat without the contract.

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The Incremental IRR Rule (cont'd) Incremental IRR Rule Application

Setting this equation equal to zero and solving for r gives an IRR of 12%. Applying the incremental IRR rule, you should take the

contract when the cost of capital is less than 12%. Because your cost of capital is 12%, you are indifferent. This finding concurs with the NPV rule.

150 400

0.2

NPV

r r

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The Incremental IRR Rule (cont'd) Shortcomings of the Incremental IRR Rule

The fact that the IRR exceeds the cost of capital for both projects does not imply that both projects have a positive NPV.

The incremental IRR may not exist.

Multiple incremental IRRs could exist.

You must ensure that the incremental cash flows are initially negative and then become positive.

The incremental IRR rule assumes that the riskiness of the two projects is the same.

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6.4 Project Selection with Resource Constraints Evaluation of Projects with Different

Resource Constraints Consider three possible projects that require

warehouse space.

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Profitability Index

The profitability index can be used to identify the optimal combination of projects to undertake.

From Table 6.1, we can see it is better to take projects B & C together and forego project A.

Value Created NPVProfitability Index

Resource Consumed Resource Consumed

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Example 6.4

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Shortcomings of the Profitability Index In some situations the profitability Index does

not give an accurate answer. Suppose in Example 6.4 that NetIt has an

additional small project with a NPV of only $100,000 that requires 3 engineers. The profitability index in this case is 0.1 / 3 = 0.03, so this project would appear at the bottom of the ranking. However, 3 of the 190 employees are not being used after the first four projects are selected. As a result, it would make sense to take on this project even though it would be ranked last.

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Shortcomings of the Profitability Index (cont'd) With multiple resource constraints, the

profitability index can break down completely.

Documents

Chapter 6 Investment Decision Rules. 2 Chapter Outline 6.1 NPV and Stand-Alone Projects 6.2 Alternative Decision Rules 6.3 Mutually Exclusive Investment