Chapter 10 Capital Budgeting and Decision Methods

Overview: Firms use several methods for evaluating proposed capital budgeting projects.

The main methods are: the payback method, the net present value method, and the internal rate of return methods. This chapter explains the application of each of these methods and how to adjust for differential project risk. After reading this chapter and working through the problems, you should be able to evaluate and rank proposed projects based on these techniques.

What You Should Know From This Chapter: 1. Explain the capital budgeting process:

Capital budgeting is the process of evaluating proposed long-term investments. Once the firm has identified a list of potential investment projects, the next step in the process is to estimate the expected cash flows and riskiness of each potential project. Based on these estimates, the manager must evaluate each project and decide which set of projects are the best for the firm to undertake. The primary decision methods used to evaluate the projects are payback, net present value, and internal rate of return.

2. Calculate the payback period, net present value, and internal rate of return

for a proposed capital budgeting project: The simplest capital budgeting method is the payback method. The analyst must

calculate the number of years it will take to recoup the project’s initial investment. This is done by adding up the project’s cash inflows one year at a time until the sum equals the amount of the project’s initial investment. The number of years is the payback period. To evaluate this method, the manager must have in mind a particular number of years that is acceptable to the firm. If the payback period is less than or equal to that predetermined number, then the project is accepted.

The net present value (NPV) of a proposed project is equal to the present value of

the cash inflows minus the present value of the cash outflows (which is usually the initial investment). The general equation is:

Investment Initial)1(

.......)1()1(

NPV 22

11 −⎟⎟

⎠

⎞⎜⎜⎝

⎛+

++⎟⎟⎠

⎞⎜⎜⎝

⎛+

+⎟⎟⎠

⎞⎜⎜⎝

⎛+

= nn

kCF

kCF

kCF

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where CFt is the cash flow at time t, k is the appropriate discount rate. The project is acceptable if the NPV is greater than or equal to zero and unacceptable otherwise. An NPV profile that shows the NPV for various discount rates will show how sensitive the project’s NPV is to the discount rate assumption.

Internal rate of return (IRR) is the rate of return the project will earn, given its

incremental cash flows and initial investment. It is the discount rate that makes the project’s NPV = 0. IRR is calculated by setting the NPV to zero and solving for the discount rate. This can be done mathematically using trial and error, but a financial calculator makes the solution of this type of problem much easier. A project is acceptable if the IRR is greater than or equal to the firm’s required rate of return (or hurdle rate).

It will generally be the case that the accept or reject decision under NPV and IRR

will be the same. However, when projects are mutually exclusive, there may be instances in which the two methods give conflicting accept/reject decisions. In such a case, the project with the highest NPV should be chosen since it will add the most to firm value.

The IRR method assumes that future cash flows in a project are reinvested at a

rate of return equal to the IRR. This can result in overly optimistic expectations when the IRR is high and cash flows cannot be reinvested. To produce more realistic results, the Modified Internal Rate of Return (MIRR) method was developed. This method assumes that future cash flows from a project are reinvested at a rate of return equal to the cost of capital. This will give you an amount that is called the terminal value. Once you have this value, divide it by the original investment raised to 1/n –1. The rate of return now calculated is often more realistic because it is lower than the expected IRR. Again, the assumption is that the cash flows will be reinvested—even at the cost of capital.

−⎟⎠⎞

⎜⎝⎛=

n

PVFVMIRR

1

1

where:

MIRR is the modified internal rate of return and FV= Future value PV= Present value

n = number of investment periods

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3. Describe capital rationing and how firms decide which projects to select: Capital rationing is the process of setting dollar limits on the total size of the

capital budget. Although this practice may not be consistent with shareholder wealth maximization, it is not uncommon for firms to ration capital. If capital rationing is imposed, then financial managers should seek the combination of capital budgeting projects that maximizes the value of the firm within the capital limit.

4. Measure the risk of a capital budgeting project: Financial managers are generally risk averse and will prefer projects that are less

risky to those that are more risky, all else equal. To measure the risk of a capital budgeting project, managers look at how the project would affect the risk of the firm’s existing asset portfolio. To do this, you must compare the coefficient of variation (CV) of the returns on the existing portfolio (based on the probability distribution of the IRR) with the CV of the portfolio including the new project. The formula for CV is:

IRR of ValueExpected

IRR ofDeviation StandardCV=

The difference between the two CVs is a measure of the risk of the capital budgeting project and can be used to develop a risk adjusted discount rate.

5. Explain risk-adjusted discount rates: One way to factor risk into the capital budgeting process is to adjust the required

returns used in NPV and IRR analysis upward for higher-than-average risk projects and downward for projects that have lower-than-average risk. The resulting required return is called a risk-adjusted discount rate (RADR) and is also often called a “hurdle rate” since it is the rate that the IRR must exceed to be acceptable. If the CV is the risk measure that is being used by the firm, a RADR can be calculated by defining a percentage change in CV that the manager feels will require an adjustment in required rate of return. This adjustment is a subjective decision and will not be the same for all firms. Note that adjusting the discount upward will make NPV lower and will make it less likely that the calculated IRR will exceed the hurdle rate.

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Terminology and Concept Review 10-1. _________________________ is the process of evaluating proposed large,

long-term investment projects. 10-2. The two types of decision practices that financial managers apply when

selecting between mutually exclusive capital budgeting projects are___________________ and ___________________.

10-3. Projects that do not compete with each other are called ___________________ . 10-4. If a firm is deciding between leasing a fleet of trucks and buying the trucks,

these capital budgeting projects are ________________________ since the firm can only accept one of them.

10-5. A cash flow that will occur if a project is undertaken but will not occur if the

project is not undertaken is an ___________________________ cash flow to the project.

10-6. The number of time periods that it will take to recoup the initial cash outlay for a

capital budgeting project is called the _____________________. 10-7. The __________________________________ is a more realistic rate of return expectation than that of IRR as it uses cost of capital to reinvest future cash flows.

10-8. The projected rate of return that a proposed project will earn, given its

incremental cash flows and required initial cash outlay, is called the _____________________________.

10-9. The practice of placing dollar limits on the total size of the capital budget is

called ___________________________. 10-10. ____________________ is often the preferred capital budgeting decision

method because managers and owners prefer to work with percentage returns that can be compared easily with alternatives.

10-11. Conflicts between decision methods occasionally arise when projects are

__________________________; in such a case, the one with the highest __________________________ should be chosen.

10-12. When projects differ in risk, the manager should estimate the riskiness by

comparing the _________________ of the firm’s portfolio with and without the projects under consideration.

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10-13. For projects that are determined to be riskier than average, _______________ ____________________ should be used to calculate NPV and to evaluate IRR.

10-14. A ________________________________ , a graph that shows a project’s NPV

at many different discount rates, is used to show how sensitive a project’s NPV is to changes in the discount rate.

10-15. For independent projects, firms should accept every project with net present

value _______________ than zero and internal rate of return ______________ than the required rate of return.

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Problems and Short-Answer Questions 10-16. What are the four major steps in the capital budgeting process? 10-17. What are the three major capital budgeting decision methods? 10-18. What are the main advantages and disadvantages of using the payback method to make capital budgeting decisions? 10-19. What are the main advantages and disadvantages of using net present value to make capital budgeting decisions? 10-20. What are the main advantages and disadvantages of using internal rate of return to make capital budgeting decisions? 10-21. What are risk-adjusted discount rates?

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10-22. What is capital rationing, and is it consistent with the goal of maximizing shareholder wealth? Why or why not? 10-23. When NPV and IRR give inconsistent ranking for mutually exclusive projects, which method should be chosen and why? Use the following information to answer questions 10-24 to 10-29:

You are considering three capital budgeting projects: Alpha, Beta, and Gamma. Each project requires an initial investment of $50,000. The projected cashflows from the projects are provided in the table below. Your discount rate is 10%.

Time Alpha Beta Gamma 0 ($50,000) ($50,000) ($50,000) 1 40,000 5,000 20,000 2 10,000 10,000 20,000 3 8,000 50,000 20,000 10-24. Calculate the payback for each project.

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10-25. Calculate the net present value for each project. 10-26. Calculate the internal rate of return for each project. 10-27. Which project(s) would you accept if they are all independent? 10-28. Which project(s) would you accept if Alpha and Beta are mutually exclusive? 10-29. If the Gamma project is determined to be of lower-than-average risk and therefore subject to a discount rate of 9%, how would your answers to the questions above change?

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10-30. Draw an NPV profile for project Alpha for discount rates of 0%, 2%, 4%, 6%, 8%, 10%, 12%. 10-31. You are considering two independent capital budgeting projects: A and B. The

expected IRR of project A is 10% and the IRR has a standard deviation of 2%. The expected IRR of project B is 20% with a 12% standard deviation. The firm’s existing portfolio of assets has an expected IRR of 15% and standard deviation of 5%. Assume that the new project’s returns are uncorrelated with the existing assets of the firm. Project A, if adopted, will constitute 8% of the firm’s total portfolio and Project B will be 5% of the total portfolio. Which project has the highest risk for the firm? Explain.

10-32. The Ellis Corporation, whose required rate of return is 14%, is considering three

mutually exclusive projects with the following cash flows:

Project X Project Y Project Z Initial Investment -5,000 -100,000 -50,000 1 2,000 52,000 45,000 2 1,500 50,000 15,000 3 1,500 10,000 4 1,500 10,000 5 1,500 10,000

Calculate NPV and IRR for each project. Which project should Ellis choose and why?

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10-33. Assume that you are considering several 5-year projects that have varying risk levels. You normally adjust your required return upward by 2% for higher-than-average risk projects and down by 2% for lower-than-average risk projects. The required return for average risk projects is 12%. After evaluating the risk of the projects under consideration, you have the following information:

Project A B C Initial Investment ($50,000) ($50,000) ($50,000) Cash flows for years 1–5 14,000 14,750 13,500 Risk Level Average Above Average Below Average

Calculate IRR and NPV for each project using risk-adjusted discount rates. If

the projects are independent, which would you accept? If they are mutually exclusive, which would you accept? How would your answers have differed if you had not adjusted for risk?

10-34. Allay Chemicals has been offered an investment in which he expects to receive payments of $2800 at the end of each of the next 5 years in return for an initial investment of $8,000 now.

a. What is the IRR of the proposed investment?

b. What is the MIRR of the proposed investment?

c. Why is the MIRR thought of as a more realistic indication of a project’s potential than IRR?

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Answers 10-1. Capital budgeting (Page 271) 10-2. Accept/reject; ranking (Page 272) 10-3. Independent (Page 272) 10-4. Mutually exclusive (Page 272) 10-5. Incremental (Page 272) 10-6. Payback period (Page 273) 10-7. MIRR (Page 284) 10-8. Internal rate of return (Page 280) 10-9. Capital rationing (Page 286) 10-10. IRR (Page 280) 10-11. Mutually exclusive; NPV (Page 283) 10-12. Coefficient of variation (Page 288) 10-13. Risk-adjusted discount rates (Page 289) 10-14. NPV profile (Page 280) 10-15. Greater; greater (Page 277) 10-16. The four major steps in the capital budgeting process are: (a) finding projects;

(b) estimating the incremental cash flows associated with the projects; (c) evaluating and selecting projects; and (d) implementing and monitoring projects. (Page 273)

10-17. The three major capital budgeting decision methods that are introduced in this

chapter are: payback, net present value, and internal rate of return. (Page 273) 10-18. The major advantage of the payback method is its simplicity. It is useful as a

rough measure of a project’s risk and liquidity. Its major disadvantages are that it does not consider cash flows that occur beyond the payback period, and it does not consider the time value of money. (Page 273)

10-19. The major advantage of the NPV rule is that it is consistent with the goal of

maximizing shareholder value. If a firm consistently picks the projects with highest NPV, this will ensure that they are choosing the projects that add value to the firm. Furthermore, the NPV method considers all incremental cash flows and takes into account the time value of money. However, it has two main disadvantages. First, it is difficult to explain this method to non-finance people. Second, the fact that the measure is in dollars instead of percent terms makes it more difficult for managers to compare alternatives. (Page 274)

10-20. The benefits of IRR are that it focuses on all cash flows associated with the

project, it adjusts for the time value of money, and it describes projects in terms of the rate of return they earn which makes them easier to compare to other investments and the firm’s hurdle rate. The problems with the IRR measure are that it does not show how much the project will add to firm value and the IRR earned only if all incremental cash flows are reinvested at the IRR. For high IRR

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projects, this may not be likely. Furthermore, for some projects, there may be more than one IRR. (Page 289)

10-21. One way to factor risk into the capital budgeting process is to adjust the required

returns used in NPV and the IRR hurdle rate upward for higher-than-average risk projects and downward for projects that have lower-than-average risk. The resulting required return is called a risk-adjusted discount rate (RADR) and is called a “hurdle rate” because it is the rate that IRR must be greater than to be acceptable. (Page 289)

10-22. Capital rationing is the process of setting dollar limits on the total size of the

capital budget. Although this practice may not be strictly consistent with shareholder value maximization, it is not uncommon for firms to ration capital. Some of the possible reasons for doing so include a desire to avoid external financing in unfavorable economic climates, concerns about potential loss of control, and the possible inadequacy of resources such as managerial talent. (Page 286)

10-23. For mutually exclusive projects, conflicts in ranking based on NPV and IRR

may sometimes occur. These are generally due to differences in timing of cash flows or scale of the projects. For example, a small project may have a very large IRR but will add very little to the value of the firm. Another project may have an IRR fairly close to the hurdle rate, but the sheer size of the project means that it will add significantly to firm value. When conflicts arise, the decision should be based on NPV because this is a measure of the impact on the firm’s value. (Page 283)

The following table provides the answers for problems 10-24 to 10-28. Problem: 10-24 10-25 10-26 10-27 10-28 Method: Payback NPV IRR Indep. Mut. Excl. Alpha 2 years $638.62 11.0% Accept Accept Beta 2.7 years 375.66 10.3% Accept Reject Gamma 2.5 years -262.96 9.7% Reject Reject Page Ref. (266) (267) (273) (264) (264) 10-29. Gamma-adj 2.5 years 625.89 9.7% Accept Reject

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10-30. The NPV at each discount rate is: Discount rate NPV 0% $8,000 2% 6,366 4% 4,819 6% 3,353 8% 1,961 10% 639 12% -620

-2,000

0

2,000

4,000

6,000

8,000

0% 2% 4% 6% 8% 10% 12%

(Page 280) 10-31. For project A:

) = .08(.10) + .92(.15) = .146 E(Rp 2222 )05(.)92(.)02(.)08(. +=pσ = .046 For project B: E(Rp) = .05(.20) + .95(.151) = .1525 σ p = + =(. ) (. ) (. ) (. ) .05 12 95 05 0482 2 2 2

The coefficients of variation for each alternative: Before Adding A or B With A With B .05/.15 = .333 .046/.146= .315 .048/.1525=.315 Both projects have the same effect on CV: a decline of .018 or 1.8%. (Page 287)

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10-32. The NPV and IRR for each project are as follows: Project X Project Y Project Z NPV $588 $1951 $1,015 IRR 19.1% 15.2% 15.9% The ranking based on NPV would be Y, Z, X, but the ranking based on IRR

would be X, Z, Y. When there is a conflict between decision rules, use NPV. Project Y will add the most to firm value. (Page 283)

10-33. A B C Required return 12% 14% 10% IRR 12.38% 14.53% 10.92% NPV $466.87 $637.94 $1,176 If independent, accept A, B, and C. If mutually exclusive, accept C (highest

NPV). If you had not adjusted for risk, Project C would not have been acceptable. (Pages 277 and 282)

10-34 . a. IRR = 22% (Page 280) b. MIRR = 15%:

%151000,8102,16 5

1

=−⎟⎠

⎞⎜⎝

⎛

(Page 277) c. This method assumes that future cash flows from a project are reinvested at a rate of return equal to the cost of capital. The rate of return is often more realistic because it is lower than the expected IRR, since you are reinvesting at your cost of capital as opposed to a higher IRR which realistically may not occur. (Page 284)

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Chapter 11 Estimating Incremental Cash Flows

Overview:

This chapter explains how to determine which cash flows are relevant to proposed capital budgeting projects. Rather than being given cash flow estimates as in the last chapter, the financial manager must estimate the initial investment cash flows necessary to start up a project, the incremental operating cash flows and tax effects, and shut down cash flows.

What You Should Know From This Chapter: 1. Explain the difference between incremental cash flows and sunk costs:

Incremental cash flows are the cash flows that will occur if a capital budgeting project is accepted but will not occur if the investment is rejected. They are the change in the firm’s cash flows due to taking on a particular project. Incremental cash flows may be either positive or negative. Sunk costs are cash flows that have already been spent or promised so that the costs will occur whether a project is accepted or rejected. For example, if a firm used a consultant to determine the feasibility of a project, the management will have to pay the consultant whether or not they decide to do the project. Financial managers must screen out sunk costs from the capital budgeting analysis to prevent distortion in relevant cash flow estimates. Any distortion in these estimates will, in turn, lead to inaccurate NPV or IRR analysis and could result in poor capital budgeting decisions.

2. Identify types of incremental cash flows in a capital budgeting project:

The three main types of incremental cash flows from a proposed capital budgeting project are the initial investment cash flow, the operating cash flows, and the shutdown cash flows. The initial investment cash flow includes: the purchase price, the installation and delivery costs, and any cash flows related to a needed change in net working capital. Incremental operating cash flows include the obvious revenues and expenses and may also include tax changes due to changes in sales, operating expenses, including depreciation expense, opportunity costs, and externalities. The project shutdown cash flows include cash flows from the project’s salvage value, from the reduction of net working capital, and tax-related cash flows from the sale of the used asset.

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The initial investment cash flow (usually at t = 0) is calculated as follows: Purchase Price + Shipping and Installation + Change in Net Working Capital The incremental cash flow statement is usually set up for each period in time as follows: Change in Sales -Change in Expenses -Depreciation Expense =Change in Operating Income -Tax on New Income =Change in Earnings after Taxes +Depreciation Expense =Net Incremental Operating Cash Flow

The shutdown cash flows occur at the end of the project. You must first estimate

the taxable gain from the sale of the asset: Cash from Sale of Old Asset -Book Value of Old Asset (=Original basis – Accum. depreciation) = Taxable Gain (or loss) x Tax Rate = Tax on Gain (Loss) Then, the shutdown cash flows will be: Cash from Sale of Old Asset -Taxes paid +Reduction in net working capital 3. Explain why cash flows associated with project financing are not included in

incremental cash flow estimates:

Incremental operating cash flows are treated separately from incremental financing cash flows. The latter are captured in the discount rate used in the NPV calculation and in the hurdle rate used when applying the IRR decision rule. Financial managers do not include financing costs as incremental operating cash flows to avoid distorting the NPV or IRR calculations in the capital budgeting process due to the double counting that would result if financing costs were reflected in operating cash flows and in the discount rate.

Many projects have options, real options, embedded in them that add to the value

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of the project and, therefore, of the firm. It is a real option because it is related to a real asset such as a piece of equipment or a new plant. The word option indicates that the future alternative does not have to be taken and it will be taken only if it is seen as adding value. The flexibility that is provided by a real option to revise a project at a later date is seen to have value. Traditional NPV and IRR analysis often overlook the value that may come from real options because this value cannot be reduced to incremental cash flow estimates. As a result, the value that real options add to the firm and the increase in the project rates of return they provide are not recognized. The NPV process can be modified, however, to reflect the value that real options add to the firm. This involves computing the traditional NPV and then adding today’s value of any real options that may be present.

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Terminology and Concept Review 11-1. The three main types of incremental cash flows are ___________________ cash

flows, ___________________________ cash flows, and __________________ cash flows.

11-2. The initial investment cash flow includes ______________, _________________,

_________________________, and cash flows associated with a required change in ________________________.

11-3. ___________________________ are the change in a firm’s cash flows due to

taking on a project. 11-4. Cash flows that have already occurred or will occur whether or not a project is

accepted or rejected are called ___________________________. 11-5. A _______________________________ is the change in current assets minus

current liabilities that is due to taking on a project. 11-6. _____________________________ is an expense that is not itself an incremental

cash flow but is considered in the analysis to calculate taxable income and taxes owed.

11-7. ___________________________ are the positive or negative effects that a

proposed project may have on the existing cash flows of the firm’s other projects. 11-8. If a new project will cause the firm to have to forego the benefits of an alternative

not chosen, this represents an ________________________ to the project chosen. 11-9. Shut-down cash flows include those from a proposed project’s

_________________, reduction in net working capital, and taxes tied to the sale of the used asset.

11-10. Accelerated depreciation schedules result in __________________incremental

cash flows than straight line depreciation in the earlier years of the project. 11-11. Interest expense ________________ included as a negative cash flow in

developing incremental cash flow estimates for capital budgeting analysis. 11-12. ___________________ show the different paths a project could take when using

real options.

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Problems and Short-Answer Questions 11-13. Why are sunk costs not considered to be incremental cash flows? 11-14. How does the cash flow analysis of expansion projects differ from the cash flow

analysis of replacement projects? 11-15. Why aren’t financing cash flows such as interest expense considered to be

incremental cash flows to a project? 11-16. Explain how a new project might cause a change in net working capital.

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Use the following information to answer questions 11-17 to 11- 24. Dobie’s Bagel Corporation is considering buying a new oven to expand its bagel

operations. It estimates that the cost of the oven will be $10,000, and there will be $200 in shipping and installation charges. The oven falls under the 3-year MACRS class, and Dobie estimates that it will sell the oven at the end of the third year for an estimated salvage value of $1,500. The expected earnings before depreciation and taxes are $6,000 per year. Dobie’s marginal tax rate is 34%. The additional business is expected to increase inventory by $800 and accounts payable by $300. Assume that the firm begins using the new ovens, January 1, 2011, and sells the ovens, December 31, 2013.

11-17. What is the change in net working capital at the outset of the project? 11-18. What is the initial investment cash flow? 11-19. What are the depreciation deductions for each year? 11-20. What is the total shutdown cash flow assuming that the firm’s current assets and

liabilities will return to their previous level?

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11-21. Provide a complete incremental cash flow statement in the space below. 11-22. If Dobie’s cost of capital is 12%, should they purchase the ovens? Why or why

not? 11-23. If the firm had done a feasibility study at a cost of $500 to determine whether the

new ovens would be justified, how would you incorporate this expense in the cash flow analysis? Explain.

11-24. If the firm borrowed the money to purchase the oven at 10% interest, how would

you incorporate the interest expense in the analysis? Explain.

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11-25. Little Brownie Bakers is planning to replace one of its elf ovens. The existing oven had an original basis of $10,000 and has been depreciated as a 5-year MACRS asset for four years (i.e., there are two years remaining). The new oven will have a depreciable basis of $20,000 and will also be depreciated as a 5-year asset. Calculate the incremental depreciation expenses for the first two years of use for the new oven.

11-26. For the oven in Problem 11-25, assume that Little Brownie Bakers can sell the old

oven for $2,000 at the time that it buys the new oven. What is the net incremental initial investment cash flow if their tax rate is 40%. (Assume no change in NWC.)

Use the following information to answer questions 11-27 to 11-30. Your employer has asked you to evaluate a potential capital budgeting project

which requires the purchase of a new piece of equipment for a price of $50,000. The firm previously paid a consultant $1,000 to estimate the expected revenues that this project would generate. The firm that ships the equipment and installs it in your plant will charge $3,000. The project will not require an increase in net working capital.

The project’s incremental operating cash flows before taxes will be $24,000 per

year for three years. At the end of three years the equipment will be sold for $10,000. The equipment has a three-year useful life and will be depreciated using the three-year MACRS depreciation schedule. (33.3%, 44.5%, 14.8%, 7.4%) The tax rate is 34% and the firm’s cost of capital is 15%.

11-27. a. What is the tax basis for the equipment? b. What are the depreciation deductions for years 1, 2, and 3?

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11-28. What is the after-tax net cash flow from the sale of the asset at the end of year three? 11-29. Calculate the total cash flow for each of the three years. 11-30. Based on your net cash flows that you have calculated in 11-29 above, what is the:

a. payback period

b. net present value

c. internal rate of return Use the following information to answer questions 11-31 and 11-34: The American Beauty Company is considering the purchase of new machines in

order to expand their business. The machines have a useful life of five years. The marginal cost of capital for the expansion is 12%. The company’s tax rate is 40%.

Purchase price of new machines $225,000 Installation charges $ 25,000 Increased revenues from expansion $100,000/year before taxes Residual value at the end of third year $ 88,000

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11-31. a. What is the cash outflow at t = 0?

b. What are the depreciation deductions if the machines fall in the MACRS five-year class?

11-32. What is the book value of machines at the end of year five? 11-33. a. What is the taxable gain/loss from the sale of the machines at the end of the

useful life? (Assume that sale price = residual value) b. What is the terminal year non-operating cash flow (cash proceeds from the

sale)? 11-34. a. What is the payback period? b. What is the net present value?

c. What is the internal rate of return?

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11-35. Ross and Jay are considering establishing a new small engine repair shop which will require an initial investment of $450,000. The probability that the shop will be very successful—35%, moderately successful—45%, and a failure—20%.

If a big success, cash flows will be approximately $50,000 for the first three years, at which point they will consider expanding to another location at a cost of $175,000. After expansion, there is a 45% probability that cash flows will be $75,000, 40% that they will be $50,000, and 15% that they will be $20,000. These cash flow streams would be for years 4-6. If the shop is moderately successful, cash flows will be $35,000 for years 1-6. If the shop fails, losses of $20,000 are expected for each of the years 1-6 and the shop would be closed at the end of year 1. a. Plot the decisions, outcomes, and probabilities associated with the new project on a decision tree similar to Figure 11-3 on page 327 in the text. b. Calculate the NPV and joint probability of each path in the decision tree.

Assume that the pair has a required cost of capital of 8 percent. c. Calculate the NPV of the entire deal assuming an 8 percent cost of capital.

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Answers 11-1. Initial investment; operating; shutdown (Page 316) 11-2. The purchase price; shipping and installation; net working capital (Page 316) 11-3. Incremental cash flows (Page 316) 11-4. Sunk costs (Page 316) 11-5. Change in net working capital (Page 316) 11-6. Depreciation (Page 317) 11-7. Externalities (Page 318) 11-8. Opportunity cost (Page 318) 11-9. Salvage value (Page 322) 11-10. Greater (Page 327) 11-11. Is not (Page 320) 11-12. Decision trees (Page 327) 11-13. Incremental cash flows are the difference between the firm’s cash flows with the

project and without the project. If a firm is obligated to pay the expense whether or not they do the project, it is referred to as “sunk”. Firm cash flows with and without the project will include this cash flow so that the incremental value of the sunk cost is zero. (Page 321)

11-14. There are several differences between the cash flows of an expansion project and

those of a replacement project. In both cases, the manager should consider only incremental cash flows. For an expansion project, this means that the manager must calculate the changes in cash flows before and after replacement. Revenues considered should be only the additional revenues that would be realized from replacing the asset (which in some cases may be zero if the new asset is not better than the old in capabilities). In addition, the after-tax proceeds of the sale of the old asset at the beginning of the new project must be taken into account. Depreciation expenses considered in the replacement analysis should be the difference between depreciation that could have been taken on the old machine and that which can be taken on the new machine. (Pages 321-325)

11-15. Financing cash flows are the outflows that occur as the firm pays interest to

creditors and dividends to stockholders. Since some of these expenses will not occur if a capital budgeting project is not undertaken, they are incremental cash flows. However, these costs are generally not allocated to particular projects when the debt is assumed or when new stock is sold. Instead, they are considered part of the total cost of capital to the firm. As such, they are incorporated in the capital budgeting analysis when the cash flows are discounted to present value or when the hurdle rate is established. If they were also subtracted from cash inflows, we would be double counting these costs. (Page 320)

11-16. Net working capital is defined as the difference between current assets and current

liabilities. When firms expand their operations, they will often need additional short-term assets such as cash and inventory. If they give credit to their

143

customers, higher sales will often imply that accounts receivable will be greater as well. On the liabilities side, the firm’s accruals (to employees and taxing authorities) are likely to rise as they increase their operations. They may also choose to borrow from suppliers to finance some of their inventory which will cause an increase in accounts payable. Additional bank borrowing might also be used. If the increase in current asset accounts is financed to some degree by long-term borrowing or equity, then the current assets may increase to a greater degree than current liabilities which will result in an increase in net working capital. (Page 316)

11-17. Change in net working capital = change in current assets minus change in current

liabilities = $800 - $300 = $500. (Page 316) 11-18. Initial investment cash flow = purchase price + shipping and installation + change

in net working capital = $10,000 + 200 + 500 = $10,700 (Page 316) 11-19. 2011: 33.3% x $10,200 = $3,397; 1999: 44.5% x $10,200 = $4,359; 2000: 14.8%

x $10,200 = $1,510 Remaining basis at the end of 3 years = 7.4% x $10,200 = $755 (Page 322)

11-20. Shutdown cash flow: Cash from sale of asset $1,500 -Book value of asset 755 Taxable Gain 745 Taxes (.34) 253 After-tax cash from sale = $1,500 - 253 = $1,247 CF from reduction in net working capital 500 Total shutdown cash flow = $1,247 + $500 = $1,747 (Page 322) 11-21. Incremental Cash Flows: 2007 2008 2009

Operating Revenue $6,000 $6,000 $6,000 -Depreciation 3,397 4,359 1,510 Taxable Income 2,603 1,641 4,490 -Taxes (34%) 885 558 1,597 After Tax Income 1,718 1,083 2,963 + Depreciation 3,397 4,359 1,510 Net Cash Flow 5,115 5,442 4,473

Initial Investment CF (10,700)

Shutdown CF 1,747

Net Cash Flows (10,700) 5,115 5,442 6,220 (Comprehensive)

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11-22. At a cost of capital of 12%, the NPV = $2,632. Since this is > 0, the firm should do the project. The IRR = 25.4%. (Pages 323 - 325) 11-23. The cost of the feasibility study is a sunk cost and is not incremental to this project. (Page 316) 11-24. The financing costs are incorporated in the analysis through the cost of capital used in the net present value calculation and as a hurdle rate for IRR analysis. (Page 320) 11-25. Year 1 Year 2 Depreciation on new asset ($20k x .2) = $4,000 ($20k x .32) = $6,400 -Depreciation on old asset ($10k x .115) = 1,150 ($10k x .058) = 580 Net depreciation expense 2,850 5,820 (Page 317) 11-26. Remaining basis = $1,150 + 580 = 1,730 Taxable proceeds from sale = $2,000 – 1,730 = $270 Taxes payable = .4 x 270 = 108 Net cash inflow from sale = $2,000 – 108 = $1,892 Cash outflow from purchase of new oven = $20,000 Total incremental initial investment cash flow = $20,000 – $1,892 = $18,108 (Page 322) 11-27. a. $50,000 + 3,000 = $53,000 (Note that consultant fee is a sunk cost).

(Page 310) b. Year 1: $17,649; Year 2: 23,585; $7,844 (Page 322)

11-28. Taxable value = $10,000–(.074)(53,000) = $6,078 Tax paid = .34($6078) = $2,067 After-tax net cash flow from sale of asset = $10,000 – $2,067 = $7,933 (Pages 322) 11-29. Year 1: $24,000 – $17,649 = 6,351 @ 34% = Net income of $$4,192 + 17,649 =

$21,841 Year 2: $24,000 – $23,585= 415 @ 34% = Net income of $274 + $23,585 =

$23,859 Year 3: $24,000 – $7,844 = $16,156 @ 34% = Net income of $10,663 + $7,844 =

$18,507 + cash from sale of $7,933 = $26,440. (Comprehensive) 11-30. a. Payback period = 2.3 years b. NPV = $1,418

145

c. IRR = 16.55% (Comprehensive) 11-31. a. $225,000 + $25,000 = $250,000

b. $50,000, $80,000, $48,000, $28,750, $28,750 (Page 321)

11-32. Book value at end of year 5 = $250,000 x 5.8% = $14,500 (Page 322) 11-33. a. Taxable gain at end of year 5 = $88,000-$14,500 = $73,500

b. Terminal year non-operating cash flow = $88,000 – .4($73,500) = $58,600 (Comprehensive)

11-34. (in thousands) 1 2 3 4 5 Revenue 100 100 100 100 100

Depreciation 50 80 48 28.75 28.75 50 20 52 71.25 71.25 Taxes (40%) 20 8 20.8 28.5 28.5 Net income 30 12 31.2 42.75 42.75 +Deprec 50 80 48 28.75 28.75 Non-Oper. CF Net Operating CF 80 92 79.2 71.5 71.5 Non-Operating CF 58.6 Net CF 80 92 79.2 71.5 130.1

a. Payback = 3 years b. NPV = $70,405

c. IRR = 22.25% (Comprehensive) 11-35 a. Part a:

146

t0 t1 t2 t3 t4 t5 t6

$75,000 $75,000 $75,000 Path 1

$50,000 $50,000 $50,000 -$175,000 $50,000 $50,000 $50,000 Path 2

$20,000 $20,000 $20,000 Path 3

-$450,000 $35,000 $35,000 $35,000 $35,000 $35,000 $35,000 Path 4

-$20,000 -$20,000 -$20,000 -$20,000 -$20,000 Path 5-$20,000

$0 $0 $0 $0 $0 Path 6

Problem 11-35A Real Options Decision Tree

Ross & Jay's Small Engine Repair Shop

A

C

B

P=.35

P=.45

P=.20

P=.45

P=.15

P=0

P=1

P=.40

Parts b & c:

t0 t1 t2 t3 t4 t5 t6

Joint Probability

of Occurrence NPV Product

Path 1 ($450,000) $50,000 $50,000 ($125,000) $75,000 $75,000 $75,000 0.1575 ($250,000) ($39,375)Path 2 ($450,000) $50,000 $50,000 ($125,000) $50,000 $50,000 $50,000 0.14 ($325,000) ($45,500)Path 3 ($450,000) $50,000 $50,000 ($125,000) $20,000 $20,000 $20,000 0.0525 ($415,000) ($21,788)Path 4 ($450,000) $35,000 $35,000 $35,000 $35,000 $35,000 $35,000 0.45 ($240,000) $0Path 5 ($450,000) ($20,000) ($20,000) ($20,000) ($20,000) ($20,000) ($20,000) 0.00 ($570,000) $0Path 6 ($450,000) ($20,000) $0 $0 $0 $0 $0 0.2 ($470,000) ($94,000)

1.0 Exp NPV = ($200,663)

Required rate of return (k) = 8%

|------------------------------------------------------------ Cash Flows -----------------------------|

147

Chapter 12 Business Valuation

Overview: This chapter introduces the techniques and concepts used to determine a

company’s actual worth. It also introduces the techniques used to value both debt and equity instruments. The most common models are discussed, and you have the opportunity to work through various examples of valuations of bonds, common stock, and preferred stock. Discounted cash flow approaches to valuation are discussed. The chapter also introduces balance sheet valuation approaches used by some financial managers.

What You Should Know From This Chapter: 1. Explain the importance of business valuation: The financial manager’s primary goal is to maximize the market value of their

firm and raise capital as necessary. This means that everyone involved needs to be able to assign a value to the business. The general valuation model used for this process includes:

Size of cash flows Timing of cash flows Risk Analysts and investors use a general valuation model to calculate the present

value of future cash flows of a security. This model, the discounted cash flow model, is a basic valuation model for a security that is expected to generate cash payments such as dividends or interest and principal. The DCF model is easy to use if we know the cash flows and discount rate.

ns

n

sss kCF

kCF

kCF

kCF

V)1(

...)1()1()1( 3

32

21

10

++

++

++

+=

where: Vo = Present value of the anticipated cash flows from the asset, its current value

CF1,2,3 and n, = Cash flows expected to be received at the end of periods 1,2,3, and so on up to n periods in the future ks = Required rate of return on the common stock investment 2. Explain the concept of business valuation:

148

The value of a business is the present value of the anticipated cash flows

generated by the business from the asset as seen in the DCF model. In order to accomplish this, the manager must be able to find the net present value of all liabilities, preferred stock, and common stockholders’ equity because this is how the business is financed.

Financial managers need to assess the market value of their bonds and stock to

gauge progress. Accurate bond and stock valuation is also a concern when a corporation contemplates selling securities to raise long-term funds. These firms do not want to undervalue the securities because they want to raise the most money possible. Likewise, would-be purchasers of securities use valuation methods to avoid paying more than the securities are worth.

ns

n

sss kCF

kCF

kCF

kCF

V)1(

...)1()1()1( 3

32

21

10 +

++

++

++

=

3. Compute the market value and the yield to maturity (YTM) of a bond: The market value of a bond is the sum of the present values of the coupon interest

payments plus the present value of the face value to be paid at maturity, given a market’s required rate of return.

The YTM is the average annual rate of return that investors realize if they buy a

bond for a certain price, receive the promised interest payments and principal on time, and reinvest the interest payments at the YTM rate. A bond’s market price and its YTM vary inversely. That is, when the YTM rises, the market price falls, and vice versa. When a bond has a YTM greater than its coupon rate, it sells at a discount to its face value. When the YTM is equal to the coupon rate, the market price equals the face value. When the YTM is less than the coupon rate, the bond sells at a premium over face value.

n

dd

nd

BkM

kk

xINTV)1(

)1(11

++

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡+

−

=

where: VB = Current market value of the bond INT = Dollar amount of each periodic interest payment n = Number of times the interest payment is received kd = Required rate of return per period on the bond debt instrument M = Par value of the bond 4. Calculate the market value and expected yield of preferred stock:

149

The market value of preferred stock is the present value of the stream of preferred stock dividends, discounted at the market’s required rate of return for that investment. Because the dividend cash flow stream is a perpetuity, we adapt the present value of a perpetuity formula to value preferred stock.

The yield on preferred stock represents the annual rate of return that investors

realize if they buy the stock for the current market price and then receive the promised dividend payments on time.

VDkP

P

P

=

where: VP = Current market value of the preferred stock DP = Amount of the preferred stock dividend kP = Required rate of return for this issue of preferred stock 5. Compute the market value per share of common stock: There are several ways to estimate the market value of common stock as

explained below: Find the present value of all the future dividends the stock is expected to pay,

discounted at the market’s required rate of return for that stock: DCF Valuation Model:

ns

n

sss kP

kD

kD

kD

P)1(

...)1()1()1( 3

32

21

10 +

++

++

++

=

where: Po = Present value of the expected dividends, the current price of the common stock D1,D2,D3, = Common stock dividends expected to be received at the end of periods 1,2,3, and so on until the stock is sold Pn = Anticipated selling price of the stock in n periods ks = Required rate of return on the common stock investment

150

Constant Growth Version of the Dividend Valuation Model:

PD

k gs0

1=−

where: P0 = Current price of the common stock D1 = Dollar amount of the common stock dividend expected 1 period from now ks = Required rate of return per period on this common stock investment g = Expected constant growth rate per period of the company’s common stock dividends Nonconstant or Supernormal Growth Model: This presents a problem as high

growth rates cannot be sustained indefinitely. A good example are high-tech companies that have high growth for the first years but gradually the growth must slow down. Thus the constant growth model must be modified.

Step 1: Add the present values of the dividends during the supernormal

growth period. Step 2: Calculate the sum of the present values of the dividends during the

normal growth period

gk

DP

s

s

−=0

where: P0 = Current price of the common stock Ds = Amount of the common stock dividend, a constant amount ks = Required rate of return on this common stock investment gs = Anticipated growth rate of this common stock investment Step 3: Add the present values of the dividends from Steps 1 and 2. The P/E Model for Valuing Common Stock:

The P/E Ratio = Shareper Earnings

Shareper Price

Appropriate Stock Price = Industry P/E Ratio x EPS 6. Compute the market value of total common equity:

151

Different procedures must be used to value total common stockholders’ equity

than are used to value one share of common stock because owners of some large percentage of a corporation’s stock have control over the affairs of the business and can force their will on the remaining shareholders. This makes the value of a controlling-interest of common stock relatively more valuable than a noncontrolling interest. Therefore, to value controlling interests of common stock, or total stockholders’ equity, we must use models that account for this “control premium.”

Estimate the value based on the book value of the firm’s assets as recorded on the

balance sheet: Book Value Book Value of Equity = (Total Assets - Total Liabilities –Pref. Stock) Per share Number of Shares Outstanding Liquidation Value Estimate the value of the firm’s assets if they were liquidated on the open

market and all claims on the firm were paid off. This uses the market value of the assets and, thus, is more realistic than book value but is a worst-case scenario and may provide misleading results for companies that have significant future earning potential.

Free Cash Flow DCF Model: This is similar to the Nonconstant model discussed above, but this model

discounts the total cash flows that would flow to the suppliers of the firm’s capital. This includes:

Cash Revenues - Cash Expenses =Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA) - Depreciation and Amortization = Earnings Before Interest and Taxes (EBIT) - Federal and State Income Taxes = Net Operating Profit After-Tax (NOPAT) + Add Back Depreciation and Amortization - Capital Expenditures - New Net Working Capital = Free Cash Flow Constant Growth Free Cash Flow Valuation Model:

152

( )gk

gFCFV t

fcft −+

=1

where: V fcft = value of future free cash flows at time t FCFt = free cash flow at time t k = the discount rate g = the long-term constant growth rate of free cash flows

7. Compute the yield on common stock: This is done by rearranging the terms of the constant growth model:

gPD

k +=0

1

where: P0 = Current price of the common stock Ds = Amount of the common stock dividend, a constant amount ks = Required rate of return on this common stock investment gs = Anticipated constant growth rate of this common stock investment 8. Compute the yield on common stock:

The Free Cash Flow Model works well for this valuation. Present value of company operations (or enterprise value) + Value of current assets = Complete business value Replacement Value of Assets Method: This is similar to the liquidation method discussed above. According to the concept underlying the model, the market value of a complete

business cannot exceed the amount it would take to buy all of the firm’s assets on the open market. Although it is simple in concept, the replacement value of assets method is not often applied to complete business valuations for two reasons:

a) It is frequently very difficult to locate similar assets for sale on the open market. b) Some of a business’s assets are difficult to define and quantify (how do

you quantify a business’s reputation, for example, or the strength of its brands?).

153

Terminology and Concept Review 12-1. ____________________________ represents the average rate of return on a bond

if all promised interest and principal payments are made on time and if the interest payments are reinvested at the interest rate given the price paid for the bond.

12-2. When interest rates rise, the price of the bond _________________________. 12-3. A bond with a 10% coupon is selling at par. What is the YTM? ___________ 12-4. When the YTM is less than the coupon rate, the bond sells at a ____________. 12-5. The ____________________model is a basic valuation model for a security that

is expected to generate cash payments. 12-6. Show how book value of common stock is calculated.

______________________________________________________________ 12-7. The replacement value of assets method is not often applied to complete business

valuations for two reasons: ___________________;______________________ 12-8. The term kp = Dp/Pp is called _______________________________________. 12-9. The amount each common stockholder would receive if the firm closed, sold all

assets and paid all liabilities and preferred stock and distributed the net proceeds to the common stockholders is the _____________________________________.

12-10. Financial analysts often use a P/E model to estimate common stock value for

private or public corporations. ______________________________________ 12-11. The constant dividend growth model assumes common stock dividends will be

paid ____________________ and grow at a _____________________ rate. 12-12. True/False: Nonconstant growth models are seldom used.

_______________________ 12-13. When a bond has a YTM greater than its coupon rate, it sells at a ___________. 12-14. Free cash flows represent the ________ cash flows from business operations.

12-15. A general valuation model considers three factors that affect future earnings:

_____________________, ____________________, and ________________.

154

Problems and Short-Answer Questions 12-16. Total assets of a firm are $2,000,000, and the total liabilities are $1,000,000.

1,000,000 shares of common stock have been issued and 500,000 shares are outstanding. The market price of the stock is $20, and Net Income for the past year was $300,000.

a. Calculate the book value of the firm. b. Calculate the book value per share. c. Calculate the P/E ratio. 12-17. A firm currently is selling its stock for $15.00 per share. The firm has a required

return of 10% and expects to pay a dividends of $.75 per share one period from now, which will grow at a constant rate for the next several years. What is the growth rate?

12-18. You have an issue of preferred stock which is paying a $4 dividend. A fair rate of

return on this investment is calculated to be 15.0%. What is the value of this stock issue?

12-19. What is the price of a 15-year, 1000 par value bond with a 7% coupon and a 6%

yield to maturity assuming semi-annual coupon payments?

155

12-20. What is the price of a five-year bond with an 8% coupon and a 10% yield to maturity assuming annual coupon payments?

12-21. A three-year bond has a coupon of 8% and a YTM of 7%. Explain why this bond

should sell at a premium. 12-22. A ten-year bond is selling at par. It has a coupon of 7%. What is the YTM?

(Why is no calculation necessary?) 12-23. What is the YTM of an eight-year bond priced at $898 with a 5% coupon

assuming semi-annual coupon payments?

156

12-24. Given the following information, calculate the dividends expected one period from now.

Stock Price $200 Growth Rate 6% Required Return 7% 12-25. Given the following information, calculate the price of the stock. Dividend $3 Required Return 9% Growth Rate 0% 12-26. Explain how financial analysts use the P/E model to estimate common stock

values. 12-27. Explain the inverse relationship between a bond’s price and its YTM. 12-28. Given the following information, calculate the dividend paid. Preferred Stock Price $75 Required Return 10% 12-29. Given the following information, calculate the required return.

157

Stock Price $150 Dividends per share next period $1.50 Growth Rate 5% 12-30. Given the following information, calculate k. Dividends per share next period $2.00 Stock Price 50.00 Growth Rate 7% 12-31. Why is the book value of a firm equal to the net worth? 12-32. Explain why the liquidation value is the worst case scenario for a firm. 12-33. Explain the problems associated with the Discounted Cash-Flow Model. 12-34. Given the following information, calculate the stock price.

158

Dividends per share next period $0.50 Required Return 10% Growth Rate 3% 12-35. Explain why preferred stock is considered to be a perpetuity. 12-36. Suppose Pasta Makers is expected to pay an annual dividend of $4.50 per share

one year from now and that this dividend will grow at the following rates during each of the following five years (to the end of year 6). Year 2, 15%; Year 3, 25%; Year 4, 20%; Year 5, 15%; Year 6, 10%. After this supernormal growth period, the dividend will grow at a sustainable 7% rate each year beyond year 6.

a) What is the present value of the dividends to be paid during the supernormal growth period? Assume that the required rate of return is 12%.

b) What is the present value of the dividends to be paid during the normal growth period (from year 7 through infinity)?

c) What is the total present value of one share of Pasta Makers common stock?

159

12-37. Assume you are the owner of Royal Beemers, Inc., a paint company, and you are interested in acquiring the stock of another company. Selected financial data for the new company is presented below:

Shock-Wave Paint Selected Financial Data for 2001 (in thousands)

Revenue $1,900,000 Cost of Goods Sold 1,140,000 Gross Profit 760,000 Selling & G&A Expenses 360,000 Depreciation 35,000 EBIT 365,000 Capital Expenditures 20,000 Current Assets, Dec 31, 2001 476,000 Current Liabilities, Dec 31, 2001 260,000 Long-Term Debt, Dec 31, 2001 415,000 Prepare a valuation analysis of Shock-Wave Paint total common equity using the

discounted free cash flow model. 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Revenue Growth Factor 15% 18% 20% 25% _30% _25% _20% _15% _10% _ 5% Expected Gross Profit Margin 50% 50% 50% 50% _50% _50% _50% _50% _50% _50% S, G, & A Exp % of Revenue 20% 20% 20% 20% _20% _20% _20% _20% _20% _20% Depr. & Amort. % of Revenue 10% 10% 10% 10% _10% _10% _10% _10% _10% _10% Capital Expend Growth Factor 10% 10% 10% 10% -10% -10% -10% -10% -10% -10% Net Working Cap to Sales Ratio 10% 10% 10% 10% _10% _10% _10% _10% _10% _10% Income tax rate = 35% Assumed long-term sustainable growth rate =6% per year after 2011 Discount rate =15%

160

Answers 12-1. Yield to maturity (Page 345) 12-2. Falls (Page 348) 12-3. 10% (Page 348) 12-4. Premium (Page 348) 12-5. Discounted Cash-Flow Model (Page 340) 12-6. Assets minus Liabilities minus Preferred Stock (Page 355) 12-7. It is frequently very difficult to locate similar assets for sale on the open market;

and some of a business’s assets are difficult to define and quantify. (Page 363) 12-8. Yield on preferred stock (Page 350) 12-9. Liquidation value (Page 356) 12-10. Private (Page 354) 12-11. Regularly; constant (Page 351) 12-12. False (Page 353) 12-13. Discount (Page 348) 12-14. Total (Page 356) 12-15. Size of cash flows, timing of cash flows, and risk (Page 340) 12-16. BV = $1,000,000 BV/Share = $2.00 P/E Ratio = 33.33 (Page 355) 12-17. .1 - [.75/15] = .05 (Page 352) 12-18. 4/.15 = $26.67 (Page 350) 12-19. PVIFA x PMT + par value/PVIF = 19.6 x 35 + 1000/2.427 = $1,098.45 (Page 343) 12-20. PVIFA x PMT + par value/PVIF = 3.79 x 80 + 1000/1.6105 = $924.18 (Page 343) 12-21. The bond should sell at a premium to compensate for the lower investment rate in

the market place. Coupons are being reinvested at a rate lower than the coupon value—more must be invested today to earn the same return. (Page 348)

12-22. 7%. The coupons are being reinvested at the coupon rate; thus the YTM is equal

to the coupon and the bond sells at par. (Page 348) 12-23. 6.65% (Page 345) 12-24. $200 x (.07 - .06) = 2 (Page 352) 12-25. $33.33 = 3/.09 (Page 352)

161

12-26. Analysts compare the P/E ratios of similar companies within an industry to determine an appropriate P/E ratio for companies in that industry. Second, analysts calculate an appropriate stock price for firms in the industry by multiplying each firm’s earnings per share by the industry average P/E ratio. (Page 355)

12-27. As interest rates rise in the market place relative to the coupon of the bond, the

investor does not need as much today to achieve the desired return—coupons are being reinvested at a higher rate. The opposite is true for a falling-interest rate environment. (Page 348)

12-28. $75 x .1 = 7.50 (Pages 349) 12-29. [1.50/$150] + .05 = .06 (Page 352) 12-30. [2/$50] + .07 = .11 (Page 352) 12-31. Net worth is Assets minus Liabilities minus Preferred Stock. Net worth is just

another word for book value. (Page 355) 12-32. A company’s common stock should be worth at least the amount generated per

share at liquidation. Because liquidation value does not consider the earnings and cash flows the firm will generate in the future, it may provide misleading results for companies that have significant future earning potential. (Page 356)

12-33. An estimate of the future selling price of a share of stock is often speculative.

(Page 354) 12-34. $7.14 = .50/(.10 - .03) (Page 352) 12-35. Preferred stock has no maturity date so it has no maturity value. Preferred

stockholders receive dividend payments at regular time intervals for as long as they own the stock. (Page 349)

12-36. a. $4.50 x 1/1.12 = $4.00 5.20 x 1/1.122

= 4.15 6.50 x 1/1.123

= 4.63 7.80 x 1/1.124

= 4.96 8.90 x 1/1.125

= 5.05 9.80 x 1/1.126

= 4.96 $ 27.75

b. 39.106$12.11210$

07.12.5.10

6 ==−

x

162

c. $27.75 + $106. 39 = $134.14 (Page 353) 12-37. (Page 358)

Actual Forecast2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Revenue Growth Factor 15% 18% 20% 25% 25% 25% 20% 10% 5% 5%Expected COGS 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%Expected Gross Profit Margin 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%S, G, & A Exp % Revenue 20% 20% 20% 20% 20% 20% 20% 20% 20% 20%Depreciation 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%Capital Expend growth Factor -20,000 10% 10% 10% 10% -10% -10% -10% -10% -10% -10%Net WorkingCap to Sales Ratio -15,000 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

Income tax rate 35%Growth rate 6%Discount rate 15%

Actual Forecast2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Revenue 125,000 143,750 169,625 203,550 254,438 318,047 397,559 477,070 524,777 551,016 578,567COGS 62,500 93,750 140,625 210,938 316,406 474,609 711,914 1,067,871 1,601,807 2,402,710 3,604,065Gross Profit 62,500 93,750 140,625 210,938 316,406 474,609 711,914 1,067,871 1,601,807 2,402,710 3,604,065

Selling, G & A Expenses 260,000 312,000 374,400 449,280 539,136 646,963 776,356 931,627 1,117,952 1,341,543 1,609,851Depreciation 35,000 38,500 42,350 46,585 51,244 56,368 62,005 68,205 75,026 82,528 90,781EBIT -232,500 -256,750 -276,125 -284,928 -273,973 -228,722 -126,446 68,039 408,829 978,639 1,903,432

Income Taxes -81,375 -89,863 -96,644 -99,725 -95,891 -80,053 -44,256 23,814 143,090 342,524 666,201Net Profit after Taxes -151,125 -166,888 -179,481 -185,203 -178,083 -148,669 -82,190 44,225 265,739 636,115 1,237,231

Add back Depreciation -116,125 -128,388 -137,131 -138,618 -126,839 -92,301 -20,186 112,430 340,764 718,643 1,328,012Subtract Capital Expenditures -20,000 -22,000 -24,200 -26,620 -29,282 -26,354 -23,718 -21,347 -19,212 -17,291 -15,562Subtract new net WC -15,000 -16,500 -18,150 -19,965 -21,962 -24,158 -26,573 -29,231 -32,154 -35,369 -38,906Free Cash Flow -81,097 -89,860 -94,753 -92,005 -75,568 -41,762 30,134 163,036 392,158 771,331 1,382,508

Terminal Value 2011 16,282,871

Present value of FCF -78,139 -92,668 -91,695 -75,529 -41,759 30,134 163,035 392,158 771,331 17,665,379

Total present value 18,642,247Plus current assets 476,000Less current liabiities 260,000Less long-term debt 415,000

Net market value of common equity 18,443,247

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