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CHAPTER 10

CAPITAL BUDGETING FOCUS Our focus in this first capital budgeting chapter begins with the time value concepts behind methods and then moves on to computational and decision making techniques. The problems of cash flow estimation and risk encountered in practice are touched upon here in anticipation of a detailed treatment in a later chapter. PEDAGOGY A brief overview of the cost of capital concept is presented early in the chapter even though it is the subject of Chapter 13. The knowledge is necessary to understand and motivate the capital budgeting models. It relates NPV - IRR procedures to the required rate of return idea, something with which students are already familiar. We explicitly tie NPV and IRR together by emphasizing that the IRR comes from the NPV equation as the interest rate that sets NPV=0. This helps to develop an overall understanding of both procedures. TEACHING OBJECTIVES After this chapter students should: 1. appreciate the discounted cash flow basis of capital budgeting theory, and 2. be able to make the computations associated with the major capital budgeting techniques. They should also be marginally aware of the difficulties associated with estimating cash flows and differences in project risk. Along these lines, care should be taken not to form the impression that capital budgeting is an engineering-like process that always gives exactly the right answer. OUTLINE I. CHARACTERISTICS OF BUSINESS PROJECTS The nature of projects requiring capital budgeting decisions. A. Project Types and Risk Replacement, expansion, and new venture projects and their order of risk. B. Stand-alone and Mutually Exclusive Projects Projects considered by themselves and in competition with one another. C. Project Cash Flows Representing projects as streams of cash for analysis. D. The Cost of Capital A brief introduction to the concept of cost of capital at this point makes the NPV and IRR techniques easier to understand. II. CAPITAL BUDGETING TECHNIQUES A general statement defining the techniques as methods of analysis and decision making. A. Payback Period The payback method explained and illustrated. Its uses and drawbacks discussed. B. Net Present Value (NPV) The NPV concept and the defining equation. The relationship to shareholder wealth. Calculations, decision rules, and applications. C. Internal Rate of Return (IRR)

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D. E. F. G. H. I.

The IRR concept and the relation to a required rate of return. The defining equation and its relationship to NPV. Decision rules, calculations, and examples. Comparing IRR and NPV Which is better and why. Possible conflicts NPV and IRR Solutions Using Financial Calculators and Spreadsheets Instruction on using calculators and spreadsheets in capital budgeting. Projects With A Single Outflow and Regular Inflows Solution techniques when annuity methods are possible. Profitability Index (PI) PI as a variation on the NPV concept. Decision rules, calculations, and examples. Comparing Projects with Unequal Lives Chaining and Equivalent Annual Annuity methods. Capital Rationing Allocating a limited Capital Budget among available projects.

QUESTIONS 1. Define mutual exclusivity and describe ways in which projects can be mutually exclusive. ANSWER: A mutually exclusive decision is one in which the selection of any option precludes the selection of all others. In other words, you can't "do both." Mutual exclusivity can be rooted in either the nature of the project or in the availability of resources. Replacements and many expansion projects tend to be mutually exclusive, because there's just one job to be done. Once the method of getting it accomplished is selected, there are simply no other opportunities. Other expansion projects and most new ventures tend to be mutually exclusive because of resource constraints. The firm usually doesn't have enough money to do everything presented as a viable opportunity. 2. Capital budgeting is based on the idea of identifying incremental cash flows, so overheads aren't generally included. Does this practice create a problem for a firm that over a long period of time takes on a large number of projects that are just barely acceptable under capital budgeting rules? ANSWER: Yes! This is a major problem in incremental thinking. If everything is incrementally just viable, over a long period the firm can wind up with no income to support necessary overhead. 3. Relate the idea of cost of capital to the opportunity cost concept. Is the cost of capital the opportunity cost of project money? ANSWER: The cost of capital is an opportunity cost because project funds could always be alternatively used to pay down debt and/or distributed to shareholders as dividends. 4. The payback technique is criticized for not using discounted cash flows. Under what conditions will this matter most? That is, under what patterns of cash flow will payback and NPV or IRR be likely to give different answers? ANSWER: Recognizing the time value of money will matter most when substantial cash flows are projected in the distant future. The discounting methods reduce the value of those flows a lot relative to payback, which gives them their face value. 5. Explain the rationale behind the NPV method in your own words. Why is a higher NPV conceptually better than a lower one?

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ANSWER: The NPV method adds up the PV of all of a project's cash flows thereby calculating its effect on the wealth of the firm (and its shareholders). The more NPV a project has, the bigger is its wealth contribution. It is this direct relation with wealth that makes NPV a very good measure of a project's worth. 6. Projects A and B have approximately the same NPV. Their initial outlays are similar in size. Project A has early positive cash flows, and little or nothing is expected to come in later on. Project B has much larger positive cash flows than A, but they're farther in the future. Can you make any general statement about which project might be better? ANSWER: The project with the cash flows that come in earlier may be better because of the uncertainty of the future. The large flows predicted far out in time are less likely to come true than modest flows predicted in the short run. In fact, this is a major business problem. People tend to predict marvelous results in the distant future that are often very unrealistic. (We'll have a great deal to say about this in later chapters.) 7. Suppose the present value of cash ins and outs is very close to balanced for a project to build a new $50M factory, so that the NPV is +$25,000. The same company is thinking about buying a new trailer truck for $150,000. The NPV of projected cash flows associated with the truck is also about $25,000. Does this mean that the two projects are comparable? Is one more desirable than the other? How are their IRRs likely to compare? If the cash flows have similar risks are the projects equally risky? (Hint: Think in terms of the size of the investment placed at risk relative to the financial rewards expected.) ANSWER: Projects of grossly different sizes are not readily comparable. In this case, the factory project is marginal, because its NPV is minimally positive relative to the size of the investment required to undertake it. Conversely, the truck is a pretty good deal because its NPV is substantial relative to the investment required to get it. The factory's IRR would be just a hair above the cost of capital while the truck's IRR would exceed k by quite a bit. The factory is really a risky project because a small unfavorable percentage variation in the cash flows planned could result in a big dollar loss relative to the capital budgeting analysis. 8. Think about the cash flows associated with putting $100,000 in the bank for five years, assuming you draw out the interest each year and then close the account. Now think about a set of hypothetical cash flows associated with putting the same money in a business, operating for five years, and then selling out. Write an explanation of why the IRR on the business project is like the bank's interest rate. How are the investments different? ANSWER: Both uses of the money involve receiving a series of cash inflows over the five-year period and a large inflow at the end. The IRR is defined as the interest rate that makes the present value of these payments just equal to the initial investment of $100K (project NPV = 0). But the bank's interest rate does exactly the same thing. If we take the present value of the interest payments and the final withdrawal at the bank's interest rate, we'll get the amount of the initial deposit. (This is also exactly like a bond's yield.) There are two major differences between the bank account and the business. The bank account's periodic cash flows will be constant while the business's are likely to vary. Further, all of the bank's flows are nearly certain while the business's are subject to considerable risk. 9. What is it about the cash flows associated with business projects that makes the NPV profile slope downward to the right? Would the NPV profile of any randomly selected set of positive and negative flows necessarily slope one way or the other? Why?

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ANSWER: The bulk of negative project cash flows are generally in the early years, while most of the positive flows are in the more distant future. This means that the discounting factors make a bigger impact on the distant positives than on the near term negatives. This in turn means larger interest rates shrink the positives more than the negatives because they tend to be further into the future. Hence total NPV becomes less positive (declines) as the interest rate increases. This produces a downsloping curve when a project's NPV is graphed versus the interest rate. A randomly selected series of flows would not tend to slope one way or the other. 10. The following set of cash flows changes sign twice and has two IRR solutions. Identify the sign changes. Demonstrate mathematically that 25% and 400% are both solutions to the IRR equation. C0 C1 C2 ($320) $2,000 ($2,000) On the basis of this example, why would you expect multiple solutions to be an unusual problem in practice? ANSWER: The sign changes from minus to plus between C0 and C1 and from plus to minus from C1 to C2. k = 25% NPV = −$320 +

$2,000 − $2,000 + = −$320 + $1,600 − $1,280 = $0 (1.25 ) (1.25 ) 2

NPV = −$320 +

$2,000 − $2,000 + = −$320 + $400 − $80 = $0 (5.00 ) (5.00 ) 2

k = 400%

It's not likely that anyone would mistake the 400% solution as real. Further, multiple sign changes with substantial negative flows in the future are rare. 11. Under what conditions will the IRR and NPV methods give conflicting results for mutually exclusive decisions? Will they ever give conflicting results for stand-alone decisions? Why? ANSWER: Results can conflict when the project's NPV profiles cross in the first quadrant of the (k, NPV) plane. The methods will never give conflicting results for standalone decisions. Examination of a graph shows that for a single down-sloping NPV profile, IRR>k always implies a positive NPV and IRR0

IRRk

NPV

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CAPITAL BUDGETING FOCUS Our focus in this first capital budgeting chapter begins with the time value concepts behind methods and then moves on to computational and decision making techniques. The problems of cash flow estimation and risk encountered in practice are touched upon here in anticipation of a detailed treatment in a later chapter. PEDAGOGY A brief overview of the cost of capital concept is presented early in the chapter even though it is the subject of Chapter 13. The knowledge is necessary to understand and motivate the capital budgeting models. It relates NPV - IRR procedures to the required rate of return idea, something with which students are already familiar. We explicitly tie NPV and IRR together by emphasizing that the IRR comes from the NPV equation as the interest rate that sets NPV=0. This helps to develop an overall understanding of both procedures. TEACHING OBJECTIVES After this chapter students should: 1. appreciate the discounted cash flow basis of capital budgeting theory, and 2. be able to make the computations associated with the major capital budgeting techniques. They should also be marginally aware of the difficulties associated with estimating cash flows and differences in project risk. Along these lines, care should be taken not to form the impression that capital budgeting is an engineering-like process that always gives exactly the right answer. OUTLINE I. CHARACTERISTICS OF BUSINESS PROJECTS The nature of projects requiring capital budgeting decisions. A. Project Types and Risk Replacement, expansion, and new venture projects and their order of risk. B. Stand-alone and Mutually Exclusive Projects Projects considered by themselves and in competition with one another. C. Project Cash Flows Representing projects as streams of cash for analysis. D. The Cost of Capital A brief introduction to the concept of cost of capital at this point makes the NPV and IRR techniques easier to understand. II. CAPITAL BUDGETING TECHNIQUES A general statement defining the techniques as methods of analysis and decision making. A. Payback Period The payback method explained and illustrated. Its uses and drawbacks discussed. B. Net Present Value (NPV) The NPV concept and the defining equation. The relationship to shareholder wealth. Calculations, decision rules, and applications. C. Internal Rate of Return (IRR)

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D. E. F. G. H. I.

The IRR concept and the relation to a required rate of return. The defining equation and its relationship to NPV. Decision rules, calculations, and examples. Comparing IRR and NPV Which is better and why. Possible conflicts NPV and IRR Solutions Using Financial Calculators and Spreadsheets Instruction on using calculators and spreadsheets in capital budgeting. Projects With A Single Outflow and Regular Inflows Solution techniques when annuity methods are possible. Profitability Index (PI) PI as a variation on the NPV concept. Decision rules, calculations, and examples. Comparing Projects with Unequal Lives Chaining and Equivalent Annual Annuity methods. Capital Rationing Allocating a limited Capital Budget among available projects.

QUESTIONS 1. Define mutual exclusivity and describe ways in which projects can be mutually exclusive. ANSWER: A mutually exclusive decision is one in which the selection of any option precludes the selection of all others. In other words, you can't "do both." Mutual exclusivity can be rooted in either the nature of the project or in the availability of resources. Replacements and many expansion projects tend to be mutually exclusive, because there's just one job to be done. Once the method of getting it accomplished is selected, there are simply no other opportunities. Other expansion projects and most new ventures tend to be mutually exclusive because of resource constraints. The firm usually doesn't have enough money to do everything presented as a viable opportunity. 2. Capital budgeting is based on the idea of identifying incremental cash flows, so overheads aren't generally included. Does this practice create a problem for a firm that over a long period of time takes on a large number of projects that are just barely acceptable under capital budgeting rules? ANSWER: Yes! This is a major problem in incremental thinking. If everything is incrementally just viable, over a long period the firm can wind up with no income to support necessary overhead. 3. Relate the idea of cost of capital to the opportunity cost concept. Is the cost of capital the opportunity cost of project money? ANSWER: The cost of capital is an opportunity cost because project funds could always be alternatively used to pay down debt and/or distributed to shareholders as dividends. 4. The payback technique is criticized for not using discounted cash flows. Under what conditions will this matter most? That is, under what patterns of cash flow will payback and NPV or IRR be likely to give different answers? ANSWER: Recognizing the time value of money will matter most when substantial cash flows are projected in the distant future. The discounting methods reduce the value of those flows a lot relative to payback, which gives them their face value. 5. Explain the rationale behind the NPV method in your own words. Why is a higher NPV conceptually better than a lower one?

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ANSWER: The NPV method adds up the PV of all of a project's cash flows thereby calculating its effect on the wealth of the firm (and its shareholders). The more NPV a project has, the bigger is its wealth contribution. It is this direct relation with wealth that makes NPV a very good measure of a project's worth. 6. Projects A and B have approximately the same NPV. Their initial outlays are similar in size. Project A has early positive cash flows, and little or nothing is expected to come in later on. Project B has much larger positive cash flows than A, but they're farther in the future. Can you make any general statement about which project might be better? ANSWER: The project with the cash flows that come in earlier may be better because of the uncertainty of the future. The large flows predicted far out in time are less likely to come true than modest flows predicted in the short run. In fact, this is a major business problem. People tend to predict marvelous results in the distant future that are often very unrealistic. (We'll have a great deal to say about this in later chapters.) 7. Suppose the present value of cash ins and outs is very close to balanced for a project to build a new $50M factory, so that the NPV is +$25,000. The same company is thinking about buying a new trailer truck for $150,000. The NPV of projected cash flows associated with the truck is also about $25,000. Does this mean that the two projects are comparable? Is one more desirable than the other? How are their IRRs likely to compare? If the cash flows have similar risks are the projects equally risky? (Hint: Think in terms of the size of the investment placed at risk relative to the financial rewards expected.) ANSWER: Projects of grossly different sizes are not readily comparable. In this case, the factory project is marginal, because its NPV is minimally positive relative to the size of the investment required to undertake it. Conversely, the truck is a pretty good deal because its NPV is substantial relative to the investment required to get it. The factory's IRR would be just a hair above the cost of capital while the truck's IRR would exceed k by quite a bit. The factory is really a risky project because a small unfavorable percentage variation in the cash flows planned could result in a big dollar loss relative to the capital budgeting analysis. 8. Think about the cash flows associated with putting $100,000 in the bank for five years, assuming you draw out the interest each year and then close the account. Now think about a set of hypothetical cash flows associated with putting the same money in a business, operating for five years, and then selling out. Write an explanation of why the IRR on the business project is like the bank's interest rate. How are the investments different? ANSWER: Both uses of the money involve receiving a series of cash inflows over the five-year period and a large inflow at the end. The IRR is defined as the interest rate that makes the present value of these payments just equal to the initial investment of $100K (project NPV = 0). But the bank's interest rate does exactly the same thing. If we take the present value of the interest payments and the final withdrawal at the bank's interest rate, we'll get the amount of the initial deposit. (This is also exactly like a bond's yield.) There are two major differences between the bank account and the business. The bank account's periodic cash flows will be constant while the business's are likely to vary. Further, all of the bank's flows are nearly certain while the business's are subject to considerable risk. 9. What is it about the cash flows associated with business projects that makes the NPV profile slope downward to the right? Would the NPV profile of any randomly selected set of positive and negative flows necessarily slope one way or the other? Why?

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ANSWER: The bulk of negative project cash flows are generally in the early years, while most of the positive flows are in the more distant future. This means that the discounting factors make a bigger impact on the distant positives than on the near term negatives. This in turn means larger interest rates shrink the positives more than the negatives because they tend to be further into the future. Hence total NPV becomes less positive (declines) as the interest rate increases. This produces a downsloping curve when a project's NPV is graphed versus the interest rate. A randomly selected series of flows would not tend to slope one way or the other. 10. The following set of cash flows changes sign twice and has two IRR solutions. Identify the sign changes. Demonstrate mathematically that 25% and 400% are both solutions to the IRR equation. C0 C1 C2 ($320) $2,000 ($2,000) On the basis of this example, why would you expect multiple solutions to be an unusual problem in practice? ANSWER: The sign changes from minus to plus between C0 and C1 and from plus to minus from C1 to C2. k = 25% NPV = −$320 +

$2,000 − $2,000 + = −$320 + $1,600 − $1,280 = $0 (1.25 ) (1.25 ) 2

NPV = −$320 +

$2,000 − $2,000 + = −$320 + $400 − $80 = $0 (5.00 ) (5.00 ) 2

k = 400%

It's not likely that anyone would mistake the 400% solution as real. Further, multiple sign changes with substantial negative flows in the future are rare. 11. Under what conditions will the IRR and NPV methods give conflicting results for mutually exclusive decisions? Will they ever give conflicting results for stand-alone decisions? Why? ANSWER: Results can conflict when the project's NPV profiles cross in the first quadrant of the (k, NPV) plane. The methods will never give conflicting results for standalone decisions. Examination of a graph shows that for a single down-sloping NPV profile, IRR>k always implies a positive NPV and IRR0

IRRk

NPV

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