Chapter 10

A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below: Year Project S Project L 0 ($2,000) ($2,000) 1 ($ 1,800) ($ 2,000 2 ($2 ,500) ($ 2,500 3 ($2, 20) ($2 ,800 4 ($2, 20) ($ 1,600 The company's cost of capital is 9 percent, and it can get an unlimited amount of capital at that cost. What is the regular IRR of the better project? (Hint: Note that the better project may or may not be the one with the higher IRR.) a. 11.45% b. 11.74% c. 13.02% d. 13.49% e. 12.67%

. b. Put the cash flows into the cash flow register, and then calculate NPV at 9% and IRR: Project S: NPVS = $101.83; IRRS = 13.49%. Project L: NPVL = $172.07; IRRL = 11.74%. Because NPVL > NPVS, it is the better project. IRRL = 11.74%.

Your firm is considering a fast food concession at the World's Fair. The cash flow pattern is somewhat unusual since you must build the stands, operate them for 2 years, and then tear the stands down and restore the sites to their original conditions. You estimate the net cash flows to be as follows: Expected Time Net Cash Flows 0 ($800,000) 1 700,000 2 700,000 3 (400,000) What is the approximate IRR of this venture? a. 5% b. 15% c. 25% d. 35% e. 45%

1. c. Unless you have a calculator that performs IRR calculations, the IRR must be obtained by trial and error or graphically. (Calculator solution: Input CF0 = 800000, CF3 = -400000. Output: IRR = 25.48%.) Note that this project actually has multiple IRRs, with a second IRR at about -53 percent.

1. A firm's _________ ________ outlines its planned expenditures on fixed assets.

1. capital budget

10. If an independent project's _____ is greater than the project's cost of capital, it should be accepted.

10. IRR

27. The ____ shows the "bang per buck."

27. PI

The cost of capital is uncertain at this time, so you construct NPV profiles to assist in the final decision. The profiles for Machines B and O cross at what cost of capital? a. 6% d. 24% b. 10% e. They do not cross in the right hand quadrant. c. 18%

3. b. To solve graphically, construct the NPV profiles: The Y-intercept is the NPV when r = 0%. For B, 4($2,085) - $5,000 = $3,340. For O, $9,677 - $5,000 = $4,677. The X-intercept is the discount rate when NPV = $0, or the IRR. For B, N = 4, PV = -5000, PMT = 2085, FV = 0, which gives I/YR = 24.14, so IRR 24%. For O, N = 4, PV = -5000, PMT = 0, FV = 9677, which gives I/YR = 17.95, so IRR 18%. The graph is an approximation since we are only using two points to plot lines that are curvilinear. However, it shows that there is a crosso-ver point and that it occurs somewhere in the vicinity of r = 10%. (Note that other data points for the NPV profiles could be obtained by calculating the NPVs for the two projects at different discount rates.) Alternatively, Project Year B O (B - O) 0 ($5,000) ($5,000) $7,590) 1 ( 2,085) ($5,000) ( 2,085) 2 ( 2,085) ($5,000) ( 2,085) 3 ( 2,085) ($5,000) ( 2,085) 4 ( 2,085) ($9,677) (7,592) The IRR of Project , 10.00 percent, is the crossover point.

3. The primary advantage of payback analysis is its ____________.

3. simplicity

30. If two mutually exclusive projects have unequal lives, the _____________ _______ method may be used for the analysis.

30. replacement chain (common life)

4. One important weakness of payback analysis is the fact that ______ _______ beyond the payback period are _________.

4. cash flows; ignored

5. The Net Present Value (NPV) method of evaluating investment proposals is a(n) ____________ cash flow technique.

5. discounted

6. A capital investment proposal should be accepted if its NPV is __________.

6. positive

7. If two projects are __________ ___________, the one with the ________ positive NPV should be selected.

7. mutually exclusive; higher

8. In the IRR approach, a discount rate is sought which makes the NPV equal to ______.

8. zero

(The following data apply to the next eight Self-Test Problems.) The director of capital budgeting for Giant Inc. has identified two mutually exclusive projects, L and S, with the following expected net cash flows: Expected Net Cash Flows Year Project L Project S 0 ($100) ($100) 1 10 70 2 60 50 3 80 20 Both projects have a cost of capital of 10 percent. 6. What is the payback period for Project S? a. 1.6 years b. 1.8 years c. 2.1 years d. 2.5 years e. 2.8 years

a. After the first year, there is only $30 remaining to be repaid, and $50 is received in Year 2. Assuming an even cash flow throughout the year, the payback period is 1 + $30/$50 = 1.6 years.

39. Which of the following statements is most correct? a. If a project has an IRR greater than zero, then taking on the project will increase the value of the company's common stock because the project will make a positive contribution to net income. b. If a project has an NPV greater than zero, then taking on the project will increase the value of the firm's stock. c. Assume that you plot the NPV profiles of two mutually exclusive projects with normal cash flows and that the cost of capital is greater than the rate at which the profiles cross one another. In this case, the NPV and IRR methods will lead to contradictory rankings of the two projects. d. For independent (as opposed to mutually exclusive) normal projects, the NPV and IRR methods will generally lead to conflicting accept/reject decisions. e. Statements b, c, and d are all true.

b. Statement b is true; the others are all false. Note that IRR must be greater than the cost of capital; that conflicts arise if the cost of capital is to the left of the crossover rate; and that for some projects with nonnormal cash flows there are two IRRs, so NPV and IRR could lead to conflicting accept/reject decisions, depending on which IRR we examine.

33. Other things held constant, a decrease in the cost of capital (discount rate) will cause an increase in a project's IRR. a. True b. False

b. The computation of IRR is independent of the project's cost of capital.

32. When you find the yield to maturity on a bond, you are finding the bond's net present value (NPV). a. True b. False

b. The yield to maturity on a bond is the bond's IRR.

Plot the NPV profiles for the two projects. Where is the crossover point? a. 6.9% b. 7.8% c. 8.7% d. 9.6% e. 9.9%

c.

Central City Electric is considering two alternative ways to meet demand: It can build a coal-fired plant (Project C) at a cost of $1,000 million. This plant would have a 20-year life and would provide net cash flows of $120 million per year over its life. Alternative-ly, the company can build a gas-fired plant (Project G) that would cost $400 million and would produce net cash flows of $68 million per year for 10 years, after which the plant would have to be replaced. The power will be needed for exactly 20 years; the cost of capital for either plant is 10 percent; and inflation and productivity gains are expected to offset one another so as to leave expected costs and cash flows constant over time. What is the NPV of the better project, that is, how much (in millions) will the better proj¬ect add to Central City's total value? a. $17.83 b. $21.63 c. $20.03 d. $24.70 e. $19.57

d. Project C:

Buckeye Foundries builds railroad cars and then leases them to railroads and shippers. The company has some old boxcars that it plans to convert into specialized carriers. Its analysts foresee demand in two areas—cars to carry coal and cars to carry livestock. Each type of car will cost $50,000 per car to convert. Because of the greater weight they will carry, the coal cars will last only 10 years but will provide an after tax cash flow of $9,500 per year. The livestock cars will last for 15 years, and their annual after tax cash flow is estimated at $8,140. Buckeye's cost of capital is 10 percent. At the end of each car's original life, it can be rebuilt into "like new" condition at a cost expected to equal the original conversion cost. Also, since Buckeye has only a limited number of cars to convert, regard the two types of cars as being mutually exclusive. Using the replace-ment chain method of evaluation, find the adjusted NPV for each alternative. a. $8,373; $11,913 c. $8,373; $16,212 e. $12,846; $14,765 b. $8,373; $14,765 d. $12,846; $11,913

e.

What is Project S's PI? a. 0.875 b. 0.964 c. 1.000 d. 1.100 e. 1.200

e.

22. Wild West Air is considering two alternative planes. Plane A has an expected life of 5 years, will cost $200, and will produce net cash flows of $60 per year. Plane B has a life of 10 years, will cost $245, and will produce net cash flows of $48 per year. Wild West plans to serve the route for 10 years. Inflation in operating costs, airplane costs, and fares is expected to be zero, and the company's cost of capital is 14 percent. Assume all costs are in millions. By how much (in millions) would the value of the company in-crease if it accepted the better project (plane)? a. $12.76 b. $9.78 c. $5.37 d. $6.65 e. $9.09

e. Plane A: Expected life = 5 years; Costs = $200; NCF = $60; WACC = 14%.

11. If two mutually exclusive projects are being evaluated and one project has a higher NPV while the other project has a higher IRR, the project with the higher _____ should be preferred.

11. NPV

12. The process of comparing a project's actual results with its projected results is known as a(n) ______-_______.

12. post audit

13. The objective of the post-audit is to improve ___________, ____________, and identify _____________ and _____________ opportunities.

13. forecasts; operations; abandonment; termination

14. The internal rate of return (IRR) is the __________ rate that equates the present value of the ______ _________ with the present value of the ______ __________.

14. discount; cash inflows; cash outflows (or initial cost)

16. The shorter the payback period, other things held constant, the greater the project's ___________.

16. liquidity

17. The NPV profile crosses the Y-axis at the ______________ NPV, while it crosses the X-axis at the _____.

17. undiscounted; IRR

18. If a(n) _____________ project is being evaluated, then the NPV and IRR criteria always lead to the same accept/reject decisions.

18. independent

19. Two basic conditions can lead to conflicts between NPV and IRR: _______ and ________ differences.

19. scale; timing

(The following data apply to the next four Self-Test Problems.) Toya Motors needs a new machine for production of its new models. The financial vice president has appointed you to do the capital budgeting analysis. You have identified two different machines that are capable of performing the job. You have completed the cash flow analysis, and the expected net cash flows are as follows: Expected Net Cash Flows Year Machine B Machine O 0 ($5,000) ($5,000) 1 2,085 0) 2 2,085 0 3 2,085 0 4 2,085 9,677 2. What is the payback period for Machine B? a. 1.0 year b. 2.0 years c. 2.4 years d. 2.6 years e. 3.0 years

2. c. After Year 1, there is $5,000 - $2,085 = $2,915 remaining to pay back. After Year 2, only $2,915 - $2,085 = $830 is remaining. In Year 3, another $2,085 is collected. Assuming that the Year 3 cash flow occurs evenly over time, then payback occurs $830/$2,085 = 0.4 of the way through Year 3. Thus, the payback period is 2.4 years.

2. The number of years necessary to return the original investment in a project is known as the _________ ________.

2. payback period

20. __________ ______ can result when the IRR criterion is used with a project that has nonnormal cash flows.

20. Multiple IRRs

21. In addition to measuring a project's liquidity, the payback is often used as one indication of a project's ___________.

21. riskiness

22. There is a direct relationship between NPV and _____. NPV is equal to the present value of the project's future ______.

22. EVA; EVAs

23. The ___________ ______ is the discount rate at which the NPV profiles of two projects cross and, thus, at which the projects' NPVs are equal.

23. crossover rate

24. The _______________ _______ shows the relative profitability of any project, or the present value of future cash flows per dollar of initial cost.

24. profitability index (PI)

25. _____ contains information regarding a project's safety margin.

25. IRR

26. _____ gives a direct measure of the dollar benefit of the project to shareholders.

26. NPV

28. A conflict between the NPV and IRR decision rules exist for mutually exclusive projects if the cost of capital is ______ than the crossover rate.

28. less

29. If two projects are _____________, the fact that they have unequal lives will not affect the analysis.

29. independent

9. A net present value profile plots a project's _____ against different __________ _______.

9. NPV; discount rates

34. The IRR method can be used in place of the NPV method for all independent projects. a. True b. False

a. Both the NPV and IRR methods lead to the same accept/reject decisions for independent projects. Thus, the IRR method can be used as a proxy for the NPV method when choosing independent projects.

37. Projects A and B each have an initial cost of $5,000, followed by a series of positive cash inflows. Project A has total undiscounted cash inflows of $12,000, while B has total undiscounted inflows of $10,000. Further, at a discount rate of 10 percent, the two projects have identical NPVs. Which project's NPV will be more sensitive to changes in the discount rate? (Hint: Projects with steeper NPV profiles are more sensitive to discount rate changes.) a. Project A. b. Project B. c. Both projects are equally sensitive to changes in the discount rate since their NPVs are equal at all costs of capital. d. Neither project is sensitive to changes in the discount rate, since both have NPV profiles that are horizontal. e. The solution cannot be determined unless the timing of the cash flows is known.

a. If we were to begin graphing the NPV profiles for each of these projects, we would know two of the points for each project. The Y-intercepts for Projects A and B would be $7,000 and $5,000, respectively, and the crossover rate would be 10 percent. Thus, from this information we can conclude that Project A's NPV profile would have the steeper slope and would be more sensitive to changes in the discount rate.

What is Project L's IRR? a. 18.1% b. 19.7% c. 21.4% d. 23.6% e. 24.2%

a. Input the cash flows into the cash flow register and solve for IRR = 18.1%.

If the cost of capital for both projects is 14 percent at the time the decision is made, which project would you choose? a. Project B; it has the higher positive NPV. b. Project O; it has the higher positive NPV. c. Neither; both have negative NPVs. d. Either; both have the same NPV. e. Project B; it has the higher IRR.

a. Refer to the NPV profiles. When r = 14%, we are to the right of the crossover point and Project B has the higher NPV. You can verify this fact by calcu-lating the NPVs. When r = 14%, NPVB = $1,075 and NPVO = $730. Note that Pro-ject B also has the higher IRR. However, the NPV method should be used when evaluating mutually exclusive projects. Note that had the project cost of capital been 8 percent, then Project O would be chosen on the basis of the higher NPV.

40. Terminating a project before the end of its useful physical life may result in a higher NPV for the project. a. True b. False

a. The NPV of a project may be maximized by terminating it at some point, thus making the economic life of the project shorter than the physical life.

31. The NPV of a project with cash flows that accrue relatively slowly is more sensitive to changes in the discount rate than is the NPV of a project with cash flows that come in more rapidly. a. True b. False

a. The more the cash flows are spread over time, the greater is the effect of a change in discount rate. This is because the compounding process has a greater effect as the number of years increases.

23. Refer to problem 22. Find the equivalent annual annuities of Plane A and B. What is the value of the largest EAA? a. $1.030 b. $1.743 c. $1.945 d. $3.365 e. $3.994

b

The stock of Barkley Inc. and "the market" provided the following returns over the last 5 years: Year Barkley Market 2008 -5% -3% 2009 21 10 2010 9 4 2011 23 11 2012 31 15 Barkley finances only with retained earnings, and it uses the CAPM with a historical be-ta to determine its cost of equity. The risk-free rate is 7 percent, and the market risk premium is 5 percent. Barkley is considering a project which has a cost at t = 0 of $2,000 and which is expected to provide cash inflows of $1,000 per year for 3 years. What is the project's MIRR? a. 23.46% b. 18.25% c. 22.92% d. 20.95% e. 21.82%

b. Put the cash flows into the cash flow register, and then calculate NPV at 9% and IRR: Project S: NPVS = $101.83; IRRS = 13.49%. Project L: NPVL = $172.07; IRRL = 11.74%. Because NPVL > NPVS, it is the better project. IRRL = 11.74%.

38. Which of the following statements is most correct? a. The IRR of a project whose cash flows accrue relatively rapidly is more sensitive to changes in the discount rate than is the IRR of a project whose cash flows come in more slowly. b. There are many conditions under which a project can have more than one IRR. One such condition is where an otherwise normal project has a negative cash flow at the end of its life. c. The phenomenon called "multiple internal rates of return" arises when two or more mutually exclusive projects that have different lives are being compared. d. The modified IRR (MIRR) method has wide appeal to professors, but most business executives prefer the NPV method to either the regular or modified IRR. e. Each of the above statements is false.

b. Statement a is false because the IRR is independent of the discount rate. Statement b is true; the situation identified is that of a project with nonnormal cash flows, which has multiple IRRs. Statement c is false; multiple IRRs occur with projects with nonnormal cash flows, not with mutually exclusive projects with different lives. Statement d is false; business executives tend to prefer the IRR because it gives a measure of the project's safety margin.

What is Project L's PI? a. 0.955 b. 1.050 c. 1.188 d. 1.215 e. 1.346

c.

CDH Worldwide's stock returns versus the market were as follows, and the same rela-tive volatility is expected in the future: Year CDH Market 2010 12% 15% 2011 -6 -3 2012 25 19 2013 18 12 The T-bond rate is 6 percent; the market risk premium is 7 percent; CDH finances only with equity from retained earnings; and it uses the CAPM to estimate its cost of capital. Now CDH is considering two alternative trucks. Truck S has a cost of $12,000 and is expected to produce cash flows of $4,500 per year for 4 years. Truck L has a cost of $20,000 and is expected to produce cash flows of $7,500 per year for 4 years. By how much would CDH's value rise if it buys the better truck, and what is the MIRR of the better truck? a. $803.35; 17.05% d. $1,338.91; 16.06% b. $1,338.91; 17.05% e. $803.35; 14.41% c. $1,896.47; 16.06%

d. First, calculate the beta coefficient. Barkley's stock has been exactly twice as volatile as the market; thus, beta = 2.0. This can be calculated as [21 - (-5)]/[10 - (-3)] = 26/13 = 2.0. (Alternatively, you could use a calculator with statisti-cal functions to determine the beta.) Next, enter the known values in the CAPM equation to find the required rate of re-turn, or the cost of equity capital. Since the company finances only with equity, this is the cost of capital: CAPM = rRF + (rM - rRF)b = 7% + (5%)b = 7% + 5%(2.0) = 17% = rs. 0 17% 1 2 3 | | | | -2,000 1,000 1,000 1,000 1,170.00 1,368.90 TV = $3,538.90 MIRR = ? PV = 2,000 Find TV: N = 3; I = 17; PV = 0; PMT = -1000; FV = $3,538.90. Find MIRR: N = 3; PV = -2000; PMT = 0; FV = 3538.90; I = MIRR = 20.95%.

Assume that your company has a cost of capital of 14 percent and that it is analyzing the following project: 0 14% 1 2 3 4 Project M: | | | | | -250 140 140 170 -100 What are the project's IRR? a. 24.26% d. 24.26% b. 23.12% e. None of the above. c. 23.12%

d. IRR = 24.26%

A firm is considering a project with a cost of $5,000 and operating cash flows of $2,000 for 3 years. The expected abandonment cash flows for Years 0, 1, 2, and 3 are $5,000, $3,500, $2,000, and $0, respectively. If the firm's cost of capital is 10 percent, what should the firm do? a. Do not accept the project. b. Abandon after Year 1; NPV is $0. c. Abandon after Year 2; NPV is $56. d. Abandon after Year 2; NPV is $124. e. Continue the project until the end of its 3-year physical life.

d. Initial Investment & Abandonment

What is Project L's NPV? a. $50.00 b. $34.25 c. $22.64 d. $18.79 e. $10.06

d. NPVL = $100 + $10/1.10 + $60/(1.10)2 + $80/(1.10)3 = $100 + $9.09 + $49.59 + $60.11 = $18.79. Financial calculator solution: Input the cash flows into the cash flow register, I/YR = r = 10, and solve for NPV = $18.78.

If the cost of capital is 14 percent, what is the profitability index for Machine B? a. 0.750 b. 0.995 c. 1.150 d. 1.215 e. 1.333

d. PI= Pv future cash flows / Pv initial cost