CHAPTER 10 THE BASICS OF CAPITAL BUDGETING(Difficulty: E = Easy, M = Medium, and T = Tough) Multiple Choice: Conceptual Easy: Ranking methods 1. Answer: b Diff: E Assume a project has normal cash flows (that is, the initial cash flow is negative, and all other cash flows are positive). Which of the following statements is most correct? a. All else equal, a project’s IRR increases as the cost of capital declines. b. All else equal, a project’s NPV increases as the cost of capital declines. c. All else equal, a project’s MIRR is unaffected by changes in the cost of capital. d. Statements a and b are correct. e. Statements b and c are correct. Ranking conflicts 2. Which of the following statements is most correct? a. The NPV method assumes that cash flows will be reinvested at the cost of capital, while the IRR method assumes reinvestment at the IRR. b. The NPV method assumes that cash flows will be reinvested at the riskfree rate, while the IRR method assumes reinvestment at the IRR. c. The NPV method assumes that cash flows will be reinvested at the cost of capital, while the IRR method assumes reinvestment at the risk-free rate. d. The NPV method does not consider the inflation premium. e. The IRR method does not consider all relevant cash flows, particularly, cash flows beyond the payback period. Payback period 3. A major disadvantage of the payback period is that it a. b. c. d. e. Is useless as a risk indicator. Ignores cash flows beyond the payback period. Does not directly account for the time value of money. Statements b and c are correct. All of the statements above are correct. Answer: d Diff: E Answer: a Diff: E Chapter 10 - Page 1 NPV profiles 4. Answer: b Diff: E Projects A and B have the same expected lives and initial cash outflows. However, one project’s cash flows are larger in the early years, while the other project has larger cash flows in the later years. The two NPV profiles are given below: NPV ($) A B k (%) Which of the following statements is most correct? a. Project A has the smaller cash flows in the later years. b. Project A has the larger cash flows in the later years. c. We require information on the cost of capital in order to determine which project has larger early cash flows. d. The NPV profile graph is inconsistent with the statement made in the problem. e. None of the statements above is correct. NPV profiles 5. Answer: d Diff: E Projects A and B both have normal cash flows. In other words, there is an up-front cost followed over time by a series of positive cash flows. Both projects have the same risk and a WACC equal to 10 percent. However, Project A has a higher internal rate of return than Project B. Assume that changes in the WACC have no effect on the projects’ cash flow levels. Which of the following statements is most correct? a. b. c. d. Project A must have a higher net present value than Project B. If Project A has a positive NPV, Project B must also have a positive NPV. If Project A’s WACC falls, its internal rate of return will increase. If Projects A and B have the same NPV at the current WACC, Project B would have a higher NPV if the WACC of both projects was lower. e. Statements b and c are correct. Chapter 10 - Page 2 NPV profiles 6. Answer: e Diff: E Project A and Project B are mutually exclusive projects with equal risk. Project A has an internal rate of return of 12 percent, while Project B has an internal rate of return of 15 percent. The two projects have the same net present value when the cost of capital is 7 percent. (In other words, the “crossover rate” is 7 percent.) Assume each project has an initial cash outflow followed by a series of inflows. Which of the following statements is most correct? a. If the cost of capital is 10 percent, each project will have a positive net present value. b. If the cost of capital is 6 percent, Project B has a higher net present value than Project A. c. If the cost of capital is 13 percent, Project B has a higher net present value than Project A. d. Statements a and b are correct. e. Statements a and c are correct. NPV profiles 7. Answer: e Diff: E Sacramento Paper is considering two mutually exclusive projects. Project A has an internal rate of return (IRR) of 12 percent, while Project B has an IRR of 14 percent. The two projects have the same risk, and when the cost of capital is 7 percent the projects have the same net present value (NPV). Assume each project has an initial cash outflow followed by a series of inflows. Given this information, which of the following statements is most correct? a. If the cost of capital is 13 percent, Project B’s NPV will be higher than Project A’s NPV. b. If the cost of capital is 9 percent, Project B’s NPV will be higher than Project A’s NPV. c. If the cost of capital is 9 percent, Project B’s modified internal rate of return (MIRR) will be less than its IRR. d. Statements a and c are correct. e. All of the statements above are correct. NPV profiles 8. Answer: a Diff: M N O’Leary Lumber Company is considering two mutually exclusive projects, Project X and Project Y. The two projects have normal cash flows (an upfront cost followed by a series of positive cash flows), the same risk, and the same 10 percent WACC. However, Project X has an IRR of 16 percent, while Project Y has an IRR of 14 percent. Which of the following statements is most correct? a. Project X’s NPV must be positive. b. Project X’s NPV must be higher than Project Y’s NPV. c. If Project X has a lower NPV than Project Y, then this means that Project X must be a larger project. d. Statements a and c are correct. e. All of the statements above are correct. Chapter 10 - Page 3 Project X’s MIRR is greater than 19 percent. their NPVs are different. If a project’s internal rate of return (IRR) exceeds the cost of capital. Which of the following statements is most correct? a. b. Project Y has a higher NPV than Project X. Project B will have a higher NPV. If the cost of capital is 10 percent. Statements b and c are correct. Given this information.Page 4 . If the cost of capital is 8 percent. e.NPV profiles 9. None of the statements above is correct. Chapter 10 . If the cost of capital is 16 percent. Statements a and c are correct. b. d. d. All of the statements above are correct. however. Project X will have a higher NPV than Project Y. e. is much larger than the other. Answer: b Diff: E Cherry Books is considering two mutually exclusive projects. c. e. then Project A must also have a higher NPV. the two projects have the same net present value (NPV). NPV and IRR 11. Project X’s IRR is 19 percent. otherwise. The crossover rate between the two projects (that is. Project B will have a higher NPV. the same cost of capital. the point where the two projects have the same NPV) is greater than 10 percent. Project A has an internal rate of return of 18 percent. If Project A has a higher IRR than Project B. and both projects have normal cash flows (an up-front cost followed by a series of positive cash flows). Statements a and b are correct. Project Y’s IRR is 17 percent. If the cost of capital is 12 percent. Which of the following statements is most correct? Answer: a Diff: E a. c. while Project B has an internal rate of return of 30 percent. If the cost of capital is 17 percent. The two projects have the same risk. and the timing of the cash flows is similar. c. Statements a and c are correct. The IRR calculation implicitly assumes that all cash flows are reinvested at a rate of return equal to the cost of capital. Each has an up-front cost followed by a series of positive cash flows. Both projects have the same risk. If the cost of capital is 10 percent. which of the following statements is most correct? a. then the project’s net present value (NPV) must be positive. Answer: a Diff: E N NPV profiles 10. One of the projects. Project B is larger than Project A. d. b. c. None of the statements above is correct. b. while Stock D has a beta of 1. d. Statements a and c are correct. MIRR. The project’s WACC is 12 percent and its net present value is $10. c. All of the statements above are correct. All of the statements above are correct. Project B would have a higher IRR than Project A.000. The expected rates of return of the two stocks should be the same. If the cost of capital were less than 12 percent. e. d. Statements a and b are correct. Which of the following statements is most correct? a. b. The NPV of each stock should equal zero. Answer: e Diff: E Stock C has a beta of 1. e. The project’s internal rate of return is 12 percent and its WACC is 10 percent. The project should be rejected since its return is less than the WACC. Which of the following statements is most correct? a. e. The project’s internal rate of return is greater than 12 percent. Project B has an IRR of 14 percent. The NPV of each stock should equal its expected return. Chapter 10 . c. NPV. Which of the following statements is most correct? a. A proposed project has normal cash flows. d. Both projects have a cost of capital of 12 percent. b.NPV and IRR 12. The project’s payback period is greater than its discounted payback period. Project A must have a higher NPV than Project B.Page 5 . NPV and expected return 15. IRR. and payback 14. and MIRR 13. there is an upfront cost followed over time by a series of positive cash flows. Answer: d Diff: E NPV. Which of the following statements is most correct? a. The project’s modified internal rate of return is less than 12 percent. Assume that the stock market is efficient. In other words.2. IRR. Each stock should have a required rate of return equal to zero. The project’s MIRR is greater than 10 percent but less than 12 percent. Answer: a Diff: E Project A has an internal rate of return (IRR) of 15 percent. e. The required rates of return of the two stocks should be the same.6. Both projects have a positive net present value (NPV). Answer: b Diff: E A project has an up-front cost of $100.000. b. d. The project’s NPV is positive. All of the statements above are correct. c. NPV and project selection 16. Answer: e Diff: E Moynihan Motors has a cost of capital of 10. Statements a and b are correct. while Project B has an internal rate of return of 12. The post-audit is used to Answer: d Diff: E a. d. Project B has an IRR of 18 percent. d. e. b. the NPV of Project B will exceed the NPV of Project A. Statements a and b are correct. Answer: b Diff: E Project A has an IRR of 15 percent. Which of the following statements is most correct? a.25 percent. If the WACC is greater than 18 percent. All of the statements above are correct. Project B will always have a shorter payback than Project A. the IRR of both projects will decline. If the WACC is less than 18 percent. e. Stimulate management to improve operations and bring results into line with forecasts. b. IRR 17.Page 6 . If the projects are mutually exclusive. e. d. and the NPV of Project B will exceed the NPV of Project A. b. Which of the following statements is most correct? a. Project A has an internal rate of return of 14 percent. c. Project B will always have a shorter payback than Project A. Improve cash flow forecasts. Post-audit 18. Chapter 10 . the firm should always select Project A. The firm has two normal projects of equal risk. Project A will have a higher net present value than Project B. Both projects have the same risk. the rate at which the Project’s NPV profiles intersect) is 8 percent. If the WACC is 15 percent. c. Eliminate potentially profitable but risky projects. If the WACC is 10 percent. Both projects have a positive net present value. If the WACC increases. c. If the crossover rate (that is. Statements a and c are correct. both projects will have a positive NPV.25 percent. Which project’s NPV will be more sensitive to changes in the discount rate? a. Which of the following statements is most correct? a. b. NPV profiles 21. Both projects are equally sensitive to changes in the discount rate since their NPVs are equal at all costs of capital. Answer: d Diff: M A company is comparing two mutually exclusive projects with normal cash flows. the two projects have the same NPV. Project L has total. If the WACC is 10 percent. None of the statements above is correct. Further. both projects would have a positive NPV. discount rate of 10 percent. 18 percent. The NPV and IRR methods will select the same project if the cost of capital is greater than 10 percent. Two mutually exclusive projects each have undiscounted cash flows for Project L are cash flows for Project S total $13. Project P has an IRR of 15 percent. Project Q would have a lower NPV than Project P. because it has a higher IRR. for example. Project L should be selected at any cost of capital. c. Project S. Chapter 10 . If the WACC is 12 percent. since both have NPV profiles which are horizontal. b. Project S should be selected at any cost of capital. 8 percent. while Project Q has an IRR of 20 percent. d. the two projects have identical NPVs. d. Neither project is sensitive to changes in the discount rate. e. undiscounted cash inflows of $16. NPV profiles 20. because it has a higher IRR. b. followed by a series of positive cash inflows.000.Page 7 . The NPV and IRR methods will select the same project if the cost of capital is less than 10 percent. d. Project Q would have a higher NPV than Project P. e.000. Which of describes this situation? Answer: a Diff: M a cost of $10. The total.000. c. while S has total undiscounted inflows of $15.000. Answer: b Diff: M Projects L and S each have an initial cost of $10.000. If the WACC is 12 percent. e. for example. If the WACC is 8 percent. The solution cannot be determined unless the timing of the cash flows is known.Medium: NPV profiles 19. at a discount rate of 10 percent. Project L. while the undiscounted Their NPV profiles cross at a the following statements best a.000. $15. c. All of the statements above are correct. To determine if a ranking conflict will occur between the two projects the cost of capital is needed as well as an additional piece of information. Project D’s MIRR is less than its IRR. Project C has a higher IRR. The NPV and IRR rules will always lead to the same decision unless one or both of the projects are “non-normal” in the sense of having only one change of sign in the cash flow stream. the two projects would have the same positive NPV. if the WACC is less than 10 percent. only if the cost of capital is to the left of (or lower than) the discount rate at which the crossover occurs. There will be a meaningful (as opposed to irrelevant) conflict only if the projects’ NPV profiles cross. Chapter 10 . Statements a and c are correct. b. b. None of the statements above is correct. the following statements is most correct? a. NPV profiles 23. b. On the basis of this information. the conflict can always be eliminated by dropping the IRR and replacing it with the MIRR. and Project Y has an IRR equal to 14 percent. and even then. If the WACC were equal to 10 percent. Project C has a higher NPV. Project D has a higher NPV. Statements a and b are correct. Answer: c Diff: M Which of Assume that you are comparing two mutually exclusive projects. Statements a and c are correct. Project X has an IRR equal to 12 percent. The crossover rate in which the two projects have the same NPV is greater than 9 percent and less than 12 percent. which of the following statements is most correct? a. one or more initial cash outflows (the investment) followed by a series of cash inflows. while Project Y will have a positive NPV. d. c. NPV and IRR 24. Project X will have a negative NPV. Project X has a higher net present value than Project Y. regardless of the cost of capital. d. c. If the WACC equals 13 percent. c. If the WACC for both projects equals 9 percent. d. Answer: e Diff: M N Project X and Project Y each have normal cash flows (an up-front cost followed by a series of positive cash flows) and the same level of risk. If the WACC is less than 10 percent. If a conflict exists between the NPV and the IRR.Page 8 .NPV profiles 22. Answer: d Diff: M Project C and Project D are two mutually exclusive projects with normal cash flows and the same risk. Which of the following statements is most correct? a. Project D has a higher IRR. Project X probably has a quicker payback than Project Y. None of the statements above is correct. e. e. All of the statements above are correct. However. If the WACC is less than 10 percent. whereas if the WACC is greater than 10 percent. that is. e. e. NPV. while the NPV method cannot. The modified internal rate of return (MIRR) can never exceed the IRR. If the two projects have the same risk they will have the same NPV. NPV. e. None of the statements above is correct. Assuming a project has normal cash flows. If the multiple IRR problem does not exist. d. Statements a and c are correct. b. Statements a and c are correct. then Project A must also have a higher NPV. All of the statements above are correct. Answer: c Diff: M Answer: a Diff: M Chapter 10 . If the IRR of Project A exceeds the IRR of Project B. c. Answer: e Diff: M Project J has the same internal rate of return as Project K. If the projects have the same size (scale) they will have the same NPV. d. If the two projects have the same size (scale) they will have the same discounted payback. the NPV will be positive if the IRR is less than the cost of capital. If a project with normal cash flows has an IRR that exceeds the cost of capital. even if the two projects have different levels of risk. The MIRR method can overcome the multiple IRR problem. following statements is most correct? Which of the a. e. e. IRR. then the project must have a positive NPV. The MIRR method will always arrive at the same conclusion as the NPV method. b. b. Which of the following statements is most correct? a.NPV and IRR 25. any independent project acceptable by the NPV method will also be acceptable by the IRR method.Page 9 . The MIRR method uses a more reasonable assumption about reinvestment rates than the IRR method. None of the statements above is correct. d. and MIRR 27. IRR. d. The NPV method is not affected by the multiple IRR problem. even if the two projects are of different size. then NPV = 0. and MIRR 28. All of the statements above are correct. NPV can be negative if the IRR is positive. NPV and IRR 26. b. c. even if the two projects have different levels of risk. Which of the following statements is most correct? a. If IRR = k (the cost of capital). c. c. Which of the following statements is incorrect? Answer: a Diff: M a. Which of the following statements is most correct? a. b. e. d. Project Y’s IRR is less than its MIRR. Which of the following statements is most correct? a. Is equal to the annual net cash flows divided by one half of the project’s cost when the cash flows are an annuity. Project X must have a shorter payback than Project Y. All of the statements above are correct. Statements c and d are correct. and payback 30. Chapter 10 . IRR. c. e. Changes when the cost of capital changes. d. If the cost of capital is 8 percent. IRR 31. If the cost of capital is 12 percent. Project X must have a higher net present value. A capital investment’s internal rate of return Answer: e Diff: M a. c. If the cost of capital is 10 percent. Statements b and c are correct. Project X must have a higher net present value than Project Y. d. If the two projects have the same WACC. e.NPV. None of the statements above is correct. Project Y has an internal rate of return of 15 percent. the two Project’s have the same NPV. Specifically. each has an upfront cost followed by a series of positive cash flows. Project X’s IRR is greater than its MIRR. Must exceed the cost of capital in order for the firm to accept the investment. Both projects have normal cash flows.Page 10 . Both projects have a positive net present value. b. Project Y’s IRR is less than 12 percent. Answer: d Diff: M Jurgensen Medical is considering two mutually exclusive projects with the following characteristics: ∑ ∑ ∑ ∑ ∑ The two projects have the same risk and the same cost of capital. b. If the cost of capital is 12 percent. Project X has a lower NPV than Project Y. Project X’s IRR is greater than 12 percent. None of the statements above is correct. Is similar to the yield to maturity on a bond. and MIRR 29. Answer: e Diff: M Project X has an internal rate of return of 20 percent. NPV. IRR. c. Answer: d Diff: M Answer: b Diff: M When comparing two mutually exclusive projects of equal size and equal life. this will favor larger. The project with the higher IRR may not always be the project with the higher MIRR. while in the IRR method the NPV is set equal to zero and the discount rate is found. a NPV/IRR conflict will not occur. Ranking methods 33. c. a project’s discounted payback is normally shorter than its regular payback. Chapter 10 . d. shorter-term alternatives because it is good to earn high rates on larger amounts over longer periods. The NPV and IRR methods use the same basic equation. b. Which of the following statements is most correct? method: Answer: e Diff: M The modified IRR (MIRR) a. longer-term projects over smaller. The project with the higher NPV may not always be the project with the higher IRR. Always leads to the same ranking decision as NPV for independent projects. d. All of the statements above are correct. Because discounted payback takes account of the cost of capital. Overcomes the problem of multiple internal rates of return. If you are choosing between two projects that have the same life. Overcomes the problems of cash flow timing and project size that lead to criticism of the regular IRR method. but in the NPV method the discount rate is specified and the equation is solved for NPV. Which of the following statements is correct? a.MIRR 32. e. If the cost of capital is less than the crossover rate for two mutually exclusive projects’ NPV profiles. e. and if their NPV profiles cross. The project with the higher NPV may not always be the project with the higher MIRR. Statements b and c are correct. b. then the smaller project will probably be the one with the steeper NPV profile. which of the following statements is most correct? a. Compounds cash flows at the cost of capital. If the cost of capital is relatively high. Ranking methods 34. Statements a and c are correct. e.Page 11 . d. c. c. b. The discounted payback method solves all the problems associated with the payback method.000 and generates a net present value of $3. d. Miscellaneous concepts 37. None of the statements above is correct. Project A requires an up-front expenditure of $1. d. e. Miscellaneous concepts 36. b. Project B has a modified internal rate of return of 9. the decision to accept or reject will always be the same using either the IRR method or the NPV method. All of the statements above are correct.7 percent. c. b. None of the projects above should be accepted. Answer: a Diff: M A company estimates that its weighted average cost of capital (WACC) is 10 percent. Which of the following independent projects should the company accept? a.000.5 percent. unless one or both of the projects are “nonnormal” in the sense of having only one change of sign in the cash flow stream. e. For independent projects. b. c.Project selection 35. the discount rate at which the NPV profiles cross).5 percent.000. The IRR method is appealing to some managers because it produces a rate of return upon which to base decisions rather than a dollar amount like the NPV method. The NPV and IRR rules will always lead to the same decision in choosing between mutually exclusive projects. Statements a and c are correct.200. e. d. Answer: d Diff: M Chapter 10 . The discounted payback method overcomes the problems that the payback method has with cash flows occurring after the payback period.Page 12 .000 and generates a positive internal rate of return of 9. Project D has an internal rate of return of 9. Which of the following statements is most correct? a. Project C requires an up-front expenditure of $1. c. The Modified Internal Rate of Return (MIRR) compounds cash outflows at the cost of capital. Conflicts between NPV and IRR rules arise in choosing between two mutually exclusive projects (that each have normal cash flows) when the cost of capital exceeds the crossover rate (that is. Which of the following is most correct? Answer: e Diff: M a. When choosing between mutually exclusive projects. d. Chapter 10 . Project C has a higher net present value if the WACC is less than 12 percent. whereas Project D has a higher net present value if the WACC exceeds 12 percent. Statements a and b are correct. Answer: a Diff: M Normal projects C and D are mutually exclusive. e.Page 13 . Multiple IRRs can occur in cases when project cash flows are normal. c. Which of the following statements is most correct? Answer: a Diff: M a. All of the statements above are correct. payback. b. d. managers should accept all projects with IRRs greater than the weighted average cost of capital. but they are more common in cases where project cash flows are nonnormal. c. correct. Project D has a higher internal Project D is probably larger in Project C probably has a faster Statements a and c are correct.Miscellaneous concepts 38. b. scale than Project C. All of the statements above are rate of return. One of the disadvantages of choosing between mutually exclusive projects on the basis of the discounted payback method is that you might choose the project with the faster payback period but with the lower total return. e. Which of the following statements is most correct? a. Miscellaneous concepts 39. d. irrespective of the relative sizes of the two projects. and modified IRR always lead to the same accept/reject decisions for a given project. if they have identical cash flow patterns. b. If the two projects’ NPV profiles cross once. When dealing with mutually exclusive projects.Page 14 . e. so you do not know which line applies to which project. then the one with the steeper profile probably has the lower initial cost. and if their NPV profiles cross in the lower left quadrant. NPV. Answer: c Diff: T Chapter 10 . IRR. at a discount rate of 40 percent. the NPV and modified IRR methods always rank projects the same. Whenever a conflict between NPV and IRR exist. If one of the projects has a NPV profile that crosses the X-axis twice. this suggests that a NPV versus IRR conflict is not likely to exist. d. your assistant also constructed a graph with NPV profiles for the two projects. at a discount rate of minus 10 percent. e. practical sense (that is. c. a conflict that will affect the actual investment decision). Statements a and c are correct.Tough: NPV profiles 40. To help you with your presentation. discounted payback (using a payback requirement of 3 or less years). which one is most reasonable? a. Of the following statements regarding the profiles. but those rankings can conflict with rankings produced by the discounted payback and the regular IRR methods. You must now take her report to a board of directors meeting and present the alternatives for the board’s consideration. Which of the following statements is most correct? a. b. Multiple rates of return are possible with the regular IRR method but not with the modified IRR method. However. None of the statements above is correct. and if their NPV profiles cross once in the upper right quadrant. your assistant must have made a mistake. However. and MIRR 41. c. and both would be accepted if they were not mutually exclusive. then. hence the project appears to have two IRRs. IRR. and this fact is one reason given by the textbook for favoring MIRR (or modified IRR) over IRR. then there will probably not be a NPV versus IRR conflict. followed by a series of positive cash inflows. Answer: b Diff: T Your assistant has just completed an analysis of two mutually exclusive projects. If the two projects both have a single outlay at t = 0. NPV. When dealing with independent projects. in the upper left quadrant. in any meaningful. If the two projects have the same investment cost. if the two projects have the same initial cost. the one with the steeper NPV profile probably has less rapid cash flows. she forgot to label the profiles. then one of the projects should be accepted. c.NPV. c. $35. and if their NPV profiles cross.000 in Year 10. and the firm’s cost of capital is 10 percent. while Project B has an internal rate of return of 16 percent. A change in the cost of capital would normally change both a project’s NPV and its IRR.86 4. However. that is. b. Assume cash flows occur evenly during the year. Assuming that the two projects have the same scale. Statements b and c are correct. and then we discount the TV at the cost of capital to find the PV. Statements a and b are correct. 1/365th each day. and $40. This investment will cost the firm $150. if the company’s cost of capital (WACC) is 12 percent. and MIRR 42. Which of the following statements is correct? Answer: a Diff: T a. then the project with the higher IRR probably has more of its cash flows coming in the later years. c. Assuming the timing of the two projects is the same. IRR. Multiple Choice: Problems Easy: Payback period 44. The crossover rate for the two projects is less than 12 percent. The NPV and IRR methods both assume that cash flows are reinvested at the cost of capital. Choosing among mutually exclusive projects 43. However.Page 15 . we first compound CFs at the regular IRR to find the TV. There can never be a conflict between NPV and IRR decisions if the decision is related to a normal.23 4. Project B has a higher net present value. Project A is probably of larger scale than Project B. e.35 years years years years years Chapter 10 . 5. NPV will never indicate acceptance if IRR indicates rejection. Answer: b Diff: E The Seattle Corporation has been presented with an investment opportunity that will yield cash flows of $30.12 4. d. independent project.000 per year in Years 5 through 9.000 today. d. Answer: c Diff: T Project A has an internal rate of return of 18 percent. d. What is the payback period for this investment? a. b.00 6. To find the MIRR.000 per year in Years 1 through 4. e. If you are choosing between two projects that have the same cost. e. Which of the following statements is most correct? a. the MIRR method assumes reinvestment at the MIRR itself. b. Project A probably has a faster payback than Project B. d.09 1.00 3.52 3. A project has the following cash flows: Year 0 1 2 3 4 Project Cash Flow -$3. 3. c. b. Answer: e Diff: E Coughlin Motors is considering a project with the following expected cash flows: Year 0 1 2 3 4 Project Cash Flow -$700 million 200 million 370 million 225 million 700 million What is the project’s discounted The project’s WACC is 10 percent. b.000 Answer: d Diff: E Its cost of capital is 10 percent. d. e.62 2.Page 16 .75 years years years years years What is the project’s discounted Chapter 10 .000 1.09 years years years years years Discounted payback 46. c. payback? a.15 4.30 3.000 1.58 3.000 1.000 1.Discounted payback 45. payback period? a. e. 3.75 4. 50 2.57 years years years years years Answer: a Diff: E Project A Cash Flow -$300 100 150 200 50 NPV 48.36 2.000 30.000 Project Z Cash Flow -$100. Answer: e Diff: E N Project A has a 10 percent cost of capital and the following cash flows: Year 0 1 2 3 4 What is Project A’s discounted payback? a. since Z. Neither Project Project Project Project project.000 10.000 50. NPV.43 2. c. since X.000 40. b. e. since it it it it has has has has the the the the higher higher higher higher IRR. 2.000 30.000 60. As the director of capital budgeting for Denver Corporation. which project would you choose? a.Page 17 .25 2. Chapter 10 . since Z. NPV. IRR.000 10. you are evaluating two mutually exclusive projects with the following net cash flows: Year 0 1 2 3 4 Project X Cash Flow -$100. d.Discounted payback 47. X. c.000 40. e. d. b.000 If Denver’s cost of capital is 15 percent. 3% e. e. Neither. IRR 50. 5% d. Find the internal rate of return to the nearest whole percentage point. Answer: c Diff: E The capital budgeting director of Sparrow Corporation is evaluating a project that costs $200. b.625 15.000 0 0 0 0 99.625 Project B Cash Flow -$50.310 at the end of 20 years if you pay premiums of $100 per year at the end of each year for 20 years. d. Project A because it has the higher NPV. d. 11% Chapter 10 . which would be chosen and why? a. c. Answer: a Diff: E Two projects being considered are mutually exclusive and have the following projected cash flows: Year 0 1 2 3 4 5 Project A Cash Flow -$50. 8% 14% 18% -5% 12% Answer: c Diff: E IRR 51. of $44. 9% b. because both have IRRs less than the cost of capital. a. including depreciation.000. c. 7% c.000 15. b.625 15.503 per year.Page 18 . Project A because it has the higher IRR.NPV 49.625 15. what is the project’s IRR? a. If the firm’s cost of capital is 14 percent and its tax rate is 40 percent. Project B because it has the higher IRR.625 15. e. Project B because it has the higher NPV. An insurance firm agrees to pay you $3. is expected to last for 10 years and produce after-tax cash flows.500 If the required rate of return on these projects is 10 percent. payback. What is the regular IRR (not MIRR) of the better project. whose cash flows are shown below: Years 0 | k = 12% 1 | 2 | 350 300 3 | 50 1. Answer: d Diff: E A company is analyzing two mutually exclusive projects.5% e. d.62% 19. 12. 17. and missing cash flow 52. 143. S and L. internal rate of return (IRR)? a.IRR. that is.0% IRR and mutually exclusive projects 53. the project that the company should choose if it wants to maximize its stock price? a. Answer: d Diff: E Oak Furnishings is considering a project that has an up-front cost and a series of positive cash flows. 23. c.1% b. 41.7% d. b.000 0 The company’s cost of capital is 12 percent. e.100 L -1.100 1. The project’s estimated cash flows are summarized below: Year 0 1 2 3 4 Project Cash Flow ? $500 million 300 million 400 million 600 million What is the project’s The project has a regular payback of 2.00% 15.53% 18.Page 19 .46% Chapter 10 . and it can obtain an unlimited amount of capital at that cost.08% 20.9% c.25 years.500 S -1. 33. 510 $15.000 12.43 $291.000 0 k = | -2.50 $481.000 The company’s weighted average cost of capital is 10 percent (WACC = 10%).090 $ 8. d.70 $332.000 10% 1 | 500 2 | 500 2 | 668. How much value will your firm sacrifice if it selects the project with the higher IRR? Project S: 0 k = | -1.15 $535. mutually exclusive projects with the cash flows shown below.200 Chapter 10 . Answer: b Diff: E Your company is choosing between the following non-repeatable.000 20. $243. c.76 4 | 668.76 Project L: 10% 1 | 668.000 Project B Cash Flow -$30.Page 20 .000 10. e. $ 7. e. d.000 18. b.76 a.360 $11. b. equally risky. What is the net present value (NPV) of the project with the highest internal rate of return (IRR)? a.450 $12. projects have the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -$50. Your cost of capital is 10 percent.NPV and IRR 54.000 15.76 3 | 500 3 | 668.000 6.000 12.76 5 | 668. Green Grocers is deciding among two mutually exclusive projects.000 40.13 Answer: e Diff: E The two NPV and IRR 55. c. d.000 Assume that both projects have a 10 percent cost of capital. $260. Braun Industries is following cash flows: Cash Flow -$1. and payback 57.000 400 300 500 400 The company’s WACC is 10 percent. b.000 350.NPV and IRR 56. $ 13.713.62 $107.4.000 Project Y Cash Flow -$500.6. What is the net present value (NPV) of the project that has the highest IRR? a. 21. 2.6.22%.050. 24.12%. Payback Payback Payback Payback Payback = = = = = 2.000 250.000 250.4. NPV NPV NPV NPV NPV = = = = = $600. d.35 $ 16. $260. 21.22%.00 $ 62. Answer: d Diff: E N Projects X and Y have the following expected net cash flows: Year 0 1 2 3 Project X Cash Flow -$500.00 Answer: d considering Year 0 1 2 3 4 an investment project that Diff: E has the NPV. c. 2. and net present value (NPV)? a.438. 2.02 $121. b. IRR IRR IRR IRR IRR = = = = = 10. c. $300.Page 21 . 21.000 350. internal rate of return (IRR). 2. e. e.00%.959. $300. What is the project’s payback. IRR.6.626.000 250.22%. Chapter 10 . 990 15. At what cost of capital would the two projects have the same net present value (NPV)? a.000 50.000 0 0 0 0 100.000 Project B Cash Flow -$200. The cash flows from the projects are summarized below: Year 0 1 2 3 4 Project A Cash Flow -$100.000 The two projects have the same risk. Project A and Project B. 13.000 50.5% 16. Answer: b Diff: E Two projects being considered are mutually exclusive and have the following projected cash flows: Year 0 1 2 3 4 5 Project A Cash Flow -$50.0% The NPV profiles of these two projects do not cross.000 80. 10.990 15.04% c. -24. c. 6. e. b. Hudson Hotels is considering two mutually exclusive projects.990 15.Page 22 .000 25.000 50. d. 15.03% e.000 15.5% 20. Answer: d Diff: E Crossover rate 59.990 Project B Cash Flow -$ 50.5% 11.000 100.90% d.45% Chapter 10 .000 25.Crossover rate 58.990 15.560 At what rate (approximately) do the NPV profiles of Projects A and B cross? a.86% b. 2.000 50. 90% e. Cannot be determined.200 million 900 million 1.000 million 1.135 million 720 million At what cost of capital would the two projects have the same net present value (NPV)? a. e.07% b. The projects have the same risk. is considering two mutually exclusive projects.400 million 1. b.700 million 1.000 700 700 1.51% 26. Answer: a Diff: E Cowher Co. Crossover rate 61. The projects are equally risky and have the following expected cash flows: Year 0 1 2 3 4 Project X Cash Flow -$3. 68.Page 23 . 6.070 million 1.76% 40. d.100 At what cost of capital would the two projects have the same net present value (NPV)? a. Answer: c Diff: E Heller Airlines is considering two mutually exclusive projects.80% c. 8. Below are the cash flows from each project: Year 0 1 2 3 4 Project A Cash Flow -$2.Crossover rate 60. A and B.67% 37.500 300 500 800 1.00% Chapter 10 . 70. c. 45.125 million 700 million Project Y Cash Flow -$3. Project X and Project Y.39% d.55% 4.000 Project B Cash Flow -$1.000 1. Answer: d Diff: E N Bowyer Robotics is considering two mutually exclusive projects with the following after-tax operating cash flows: Year 0 1 2 3 4 Project 1 Cash Flow -$400 175 100 250 175 Project 2 Cash Flow -$500 50 100 300 550 At what cost of capital would these two projects have the same net present value (NPV)? a. c.15% 16.97% 24. b. d. Project A and Project B.33% Answer: d Diff: E N Crossover rate 63. e. c. d.Page 24 .Crossover rate 62. e. b. Company C is considering two mutually exclusive projects. 10.69% 16. The projects are equally risky and have the following cash flows: Year 0 1 2 3 Project A Cash Flow -$300 140 360 400 Project B Cash Flow -$300 500 150 100 At what cost of capital would the two projects have the same net present value (NPV)? a. 10% 15% 20% 25% 30% Chapter 10 .89% 20. 000 40.56 2. What is the approximate payback period? a. What is the project’s regular payback? a. What is the project’s discounted payback? a. Haig Aircraft is considering a project that has an up-front cost paid today at t = 0.000 starting at the end of the second year. b.000 and the building.4793 2.000 a year at the end of each of the next five years.8763 2.35 4.000 The cost of capital is 10 percent. The project’s NPV is $75. d. The land.16 years years years years years Answer: e Diff: M Discounted payback 66. would cost $500. which would be bought immediately (at t = 0).000 50. 6 d. which would be erected at the end of the first year (t = 1). 1. The project will generate positive cash flows of $60. 10 years years years years years Answer: c Diff: M Payback period 65. d.000 25.6380 years years years years years Chapter 10 . 3.22 1.3333 2.Medium: Payback period 64.000 and the company’s WACC is 10 percent. and that this incremental flow would increase at a 10 percent rate annually over the next 10 years. c. e. has a cost of $100. It is estimated that the firm’s after-tax cash flow will be increased by $100. 4 c. 8 e. 2 b.000 100. e.Page 25 . Answer: c Diff: M Michigan Mattress Company is considering the purchase of land and the construction of a new plant. b.000 150.54 2.000. Lloyd Enterprises has a project that has the following cash flows: Year 0 1 2 3 4 5 Project Cash Flow -$200. c.0000 2. 000 40. B only.000 50. The cash flows for the two projects are: Year 0 1 2 3 4 Project A Cash Flow -$100. d.Page 26 .000 per year in Years 1 through 4. b. What is the NPV for this investment? a. $35. A and Project B. Project Neither Project Project A only.67 years years years years years Discounted payback 68. d.11 2.86 2.000 40.146 Chapter 10 . Answer: b Diff: M Polk Products is considering an investment project with the following cash flows: Year 0 1 2 3 4 Project Cash Flow -$100. Project A nor Project B. NPV 69.000 40. d. The corporation uses the discounted payback method to assess potential projects and utilizes a discount rate of 10 percent. b.000 today.984 $ 18. The corporation has an investment policy that requires acceptable projects to recover all costs within 3 years. Answer: d Diff: M The Seattle Corporation has been presented with an investment opportunity that will yield end-of-year cash flows of $30.138 $ 92.000 40.Discounted payback 67. b.000 30.000 per year in Years 5 through 9. c.023 $219. Answer: d Diff: M Davis Corporation is faced with two independent investment opportunities. c. 1.000 30. and the firm’s cost of capital is 10 percent.000 90.000 Project B Cash Flow -$80.49 2. discounted payback? a. $135.000 30. e.000 20.000 0 In which investment project(s) should the company invest? a.000 in Year 10.000 60. and $40. c. e. This investment will cost the firm $150.045 $ 51.67 1.000 What is the project’s The company has a 10 percent cost of capital. 000 a year. e. c.000 40. c.815.000 20. d. The project will generate a positive cash flow of $75.000 When is Project B more lucrative than Project A? That is.000 per year for Years 6-8.937.000.71 Answer: d Diff: M N NPV 71. For all Project Project For all For all values of k B is always A is always values of k values of k less than 7. and the cash flows occur at the end of each year.000 40.000 Answer: d Diff: M NPV profiles 72.27 $21. greater than 6. b.25%.000 Project B Cash Flow -$110. more profitable than Project A.250.000 20.517 $ 560. and $2.000 10.000 60. b. Brown Grocery is considering a project that has an up-front cost of $X. over what range of costs of capital (k) does Project B have a higher NPV than Project A? Choose the best answer.26 $32.00 $52. $3. d.57%.415.000 50.Page 27 .85 $38. a. The project has a 10 percent cost of capital and a 12 percent internal rate of return (IRR). If you require a 14 percent rate of return. $1. The following cash flows are estimated for two mutually exclusive projects: Year 0 1 2 3 4 Project A Cash Flow -$100. Answer: b Diff: M You are considering the purchase of an investment that would pay you $5. $15.309 $ 250. less than 6. e. Assume that these cash flows are paid at the end of each year and that the project will last for 20 years.208 $ 78.57%. then how much should you be willing to pay for this investment? a.000 40.NPV 70.819. e.000 $ 638. d. What is the project’s net present value (NPV)? a. Chapter 10 . b.000 per year for Years 9 and 10. more profitable than Project B. c.000 per year for Years 1-5. 877 Machine B Cash Flow -$2.000 1. e. 24%. c. d. 18%.32 $3. d. Answer: b Diff: M Shannon Industries is considering a project that has the following cash flows: Year 0 1 2 3 4 Project Cash Flow ? $2. 24%. Cash flow analysis indicates the following: Year 0 1 2 3 4 Machine A Cash Flow -$2.91 $1. What is the project’s net present value (NPV)? a.80 $2.049.500 The project has a payback of 2.761. and missing cash flow 73. $ 577. IRRB IRRB IRRB IRRB IRRB = = = = = 20% 20% 16% 24% 26% Chapter 10 .5 years. b.000 0 0 0 3.765. IRR 74.68 $ 765.000 3. 18%. payback.NPV.91 Answer: d Diff: M Genuine Products Inc. b. c. e.000 3.000 832 832 832 832 What is the internal rate of return for each machine? a. requires a new machine. The firm’s cost of capital is 12 percent. and you have been assigned the task of choosing one of the machines. IRRA IRRA IRRA IRRA IRRA = = = = = 16%.Page 28 . Two companies have submitted bids. 000 3.IRR 75. What is the project’s internal rate of return? a. d. A project has the following net cash flows: Year 0 1 2 3 4 5 Project Cash Flow -$ X 150 200 250 400 100 16% 18% 18% 18% 16% and and and and and 14% 10% 20% 13% 13% Answer: e Diff: M N At the project’s WACC of 10 percent. e.38% Chapter 10 .000 Annual Cash Inflows $11. respectively. b. c. e.696 1. are: a.49% 15. Answer: c Diff: M Whitney Crane Inc. 10.800 3.000 12. b.009 Life (Years) 1 2 3 4 IRR 15 13 The IRRs for Projects A and C. d. c.62% 16. IRR 76. has the following independent investment opportunities for the coming year: Project A B C D Cost $10.000 5.00% 12.Page 29 .78. the project has an NPV of $124.075 5.62% 13. 46% 13. and it will provide net cash inflows of $1 million at the end of Year 1. The mine will bring year-end after-tax cash inflows of $2 million at the end of the two succeeding years. c. d.88% 12. you are evaluating construction of a new plant. 14. Your company is planning to open a new gold mine that will cost $3 million to build.09% 12. e. whose cash flows are shown below: Years S L 0 -1.33% 15. and then it will cost $0. c. Answer: a Diff: M A company is analyzing two mutually exclusive projects. d.NPV and IRR 77. S and L. 14.) a. The plant has a net cost of $5 million in Year 0 (today).70% 21. and it can get an unlimited amount of capital at that cost. e.36% 10. c. and $2 million at the end of Years 3 through 5.53% Answer: e Diff: M IRR of uneven CF stream 79. d. What is this project’s IRR? a. b. As the capital budgeting director for Chapel Hill Coffins Company.100 1 900 0 2 350 300 3 50 500 4 10 850 The company’s cost of capital is 12 percent. b.Page 30 .01% 18.53% Answer: d Diff: M IRR of uneven CF stream 78.37% Chapter 10 . with the expenditure occurring at the end of the year three years from today. What is the regular IRR (not MIRR) of the better project? (Hint: Note that the better project may or may not be the one with the higher IRR.50% 17. Within what range is the plant’s IRR? a.00% 17.64% 16.42% 12.5 million to close down the mine at the end of the third year of operation.17% 17. $1.100 -1. b. e. 13.5 million at the end of Year 2. The firm’s management is uncomfortable with the IRR reinvestment assumption and prefers the modified IRR approach.000 and is expected to provide after-tax annual cash flows of $73. a large salmon canning firm operating out of Valdez.45% Chapter 10 . e. 12. and t = 5). b.40% 20. b.64% Answer: c Diff: M Hadl.000 each year for the first two years (t = 1 and t = 2). e. The project has a cost of $275.0% 16.0% 12. What is Project 2’s internal rate of return (IRR)? Answer: d Diff: M Alyeska Salmon Inc.27% 23. Alaska. 44.000 a year for each of the remaining three years (t = 3. d. d. and missing cash flow ∑ 80.Page 31 . The investment will produce cash flows of $25.33% 16. 15. c. You have calculated a cost of capital for the firm of 12 percent..000. c.0% Answer: e Diff: M MIRR 82. payback.IRR.306 for eight years. has a new automated production line project it is considering. Martin Manufacturers is considering a five-year investment that costs $100. What is the project’s MIRR? a.85% 14.73% 17. ∑ Flow o o o o o o ∑ ∑ ∑ ∑ ∑ MIRR 81.00% 18. What is the MIRR of the investment? a.10% 14.com is considering the following two projects: ß Year 0 1 2 3 4 Project 1 Cash Flow -$100 30 50 40 50 Project 2 Cash ? 40 80 60 60 The two projects have the same payback. The company has a weighted average cost of capital of 12 percent.0% 17.25% 19. $50.0% 14. t = 4. the risk-free rate is 7 percent.5 years. 12. e.65% 21. and it has a weighted average cost of capital of 10 percent. d. Answer: d Diff: M R Below are the returns of Nulook Cosmetics and “the market” over a threeyear period: Year 1 2 3 Nulook 9% 15 36 Market 6% 10 24 Nulook finances internally using only retained earnings. b. and the estimated market risk premium is 6 percent.028 and will provide estimated cash inflows of $1.0% 17. What is this project’s MIRR? a. c. The project has an up-front cost and will also generate the following subsequent cash flows: Year 0 1 2 3 Project Cash Flow ? $400 500 200 The project’s payback is 1. What is the project’s modified internal rate of return (MIRR)? a. b. 10.Page 32 .54% 23.5% 20.75% Chapter 10 . c. e. Currently. and it uses the Capital Asset Pricing Model with an historical beta to determine its cost of equity.0% 22. Nulook is evaluating a project that has a cost today of $2.9% Answer: d Diff: M MIRR and missing cash flow 84.4% 16.00% 19. d.MIRR and CAPM 83.82% 14. Belanger Construction is considering the following project.000 at the end of the next 3 years. Project A. What is the sum of the project’s IRR and its MIRR? a. Choose neither. Jones Company’s new truck has a cost of $20.75% 26. because it has a higher IRR.000 Based only on the information given. e. b. c.12% Answer: e Diff: M MIRR and IRR 86.500 Project B Cash Flow -$100.59% Answer: b Diff: M Mutually exclusive projects 87.0 2.11% 34. d. e. What is the project’s modified internal rate of return (MIRR)? a.48% 18.86% 38. b. since the sum of the cash inflows exceeds the initial investment in both cases. c. d.000 39.5 2. d. 15. Indifferent. which of the two projects would be preferred.MIRR. The cost of capital for an average-risk project like the truck is 8 percent.500 39.0 1.000 per year for 5 years. The project’s cost of capital is 12 percent. and why? a. e. and it will produce endof-year net cash inflows of $7. Project B.000 0 0 133.50% 28.500 39.Page 33 . Answer: d Diff: M Tyrell Corporation is considering a project with the following cash flows (in millions of dollars): Year 0 1 2 3 4 Project Cash Flow ? $1. b. Two projects being considered by a firm are mutually exclusive and have the following projected cash flows: Year 0 1 2 3 Project A Cash Flow -$100. payback. 12. since their NPVs are negative.54% 15.5 The project has a regular payback period of exactly two years. because it has a shorter payback period. and missing cash flow 85. because the projects have equal IRRs.000.23% 37. Chapter 10 . c.57% 33. Include both in the capital budget. d.25% 17.000 3. is considering the following mutually exclusive projects: Year 0 1 2 3 4 Project A Cash Flow -$5.) a. The payments (in millions of dollars) he receives under the two contracts are listed below: Year 0 1 2 3 4 Team A Cash Flow $8. At what discount rate would he be indifferent between the two contracts? a. Martin Fillmore is a big football star who has been offered contracts by two different teams.0 4.993 $3. If cash flows are evenly distributed and the tax rate is 40 percent. Answer: b Diff: M Scott Corporation’s new project calls for an investment of $10.0 4.Before-tax cash flows 88.0 4. $1. McCarver Inc.35% 16.000 200 800 3.000 800 200 At what cost of capital will the net present value (NPV) of the two projects be the same? a.49% 19.000.0 8.85% 11. c. what is the annual before-tax cash flow each year? (Assume depreciation is a negligible amount.03% Chapter 10 .15% 16.72% 17. b. d.500 $4.5 4.000 Project B Cash Flow -$5.000 3. e.Page 34 . It has an estimated life of 10 years and an IRR of 15 percent. d.68% 16.983 $5. c. e.019 Answer: b Diff: M Crossover rate 89. e.80% Answer: b Diff: M Crossover rate 90. b.0 Team B Cash Flow $2.321 $1.0 Fillmore is committed to accepting the contract that provides him with the highest net present value (NPV). b.0 8. c. 15.67% 21. 10.0 4.0 4.000 5. 15% Chapter 10 .98% 6.100 Project 2 Cash Flow -$1. b. The projects have the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -$10.900 1. 11.000 1. b.85% 5. c.000 1.000 6.73% 5.Crossover rate 91.84% 13. d.000 6.70% Answer: d Diff: M Crossover rate 92.000 1. d. Answer: b Diff: M Shelby Inc.000 1.000 2.20% 12. 4.Page 35 .100 900 800 600 400 At what weighted average cost of capital would the two projects have the same net present value (NPV)? a.03% 14. is considering two projects that have the following cash flows: Year 0 1 2 3 4 5 Project 1 Cash Flow -$2.000 500 700 800 1.26% 12.000 1. e.000 7. e.000 Project B Cash Flow -$8.000 At what weighted average cost of capital do the two projects have the same net present value (NPV)? a.40% 6. Jackson Jets is considering two mutually exclusive projects. c. 33% 13. -47.000 40.Page 36 .000 80.49% Answer: d Diff: M Crossover rate 94. Robinson Robotics is considering two mutually exclusive projects.000 70.32% e. e. Answer: c Diff: M Midway Motors is considering two mutually exclusive projects. 12.000 25. The projects are of equal risk and have the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -$100.32% d. 9. Project A and Project B. b.000 30.000 55.69% b. c.45% c. 10.21% 25. d.95% 11. 8.96% Chapter 10 . The projects have the following cash flows: Year 0 1 2 3 4 5 Project A Cash Flow -$200 20 30 40 50 60 Project B Cash Flow -$300 90 70 60 50 40 At what weighted average cost of capital would the two projects have the same net present value (NPV)? a.000 40.000 At what WACC would the two projects have the same net present value (NPV)? a. 10.11% 14.000 15. Project A and Project B.Crossover rate 93.000 Project B Cash Flow -$100. Answer: b Diff: M Turner Airlines is considering two mutually exclusive projects.000 30. 58. Answer: b Diff: M Unitas Department Stores is considering the following mutually exclusive projects: Year 0 1 2 3 4 Project 1 Cash Flow -$215 million 20 million 70 million 90 million 70 million Project 2 Cash Flow -$270 million 70 million 100 million 110 million 30 million At what weighted average cost of capital would the two projects have the same net present value (NPV)? a.000 35.000 30.59% c.36% c. 8. Project A and Project B. At what weighted average cost of capital would the two projects have the same net present value (NPV)? a. The projects have the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -$100. 5.85% e.Crossover rate 95.47% Chapter 10 .000 35.37% e.Page 37 .000 40. 3.93% b. 1.25% d. 19.67% Crossover rate 96. 40. 13. 16.000 100. 17.000 40.000 Project B Cash Flow -$190.34% d.000 100.000 The two projects are equally risky.10% b. The projects have the following cash flows (in millions of dollars): Year 0 1 2 3 Project A Cash Flow -$4.7 3. c. d.51 Tough: Multiple IRRs 98.22 -$4.Page 38 . You agree to settle the dispute by analyzing the project cash flows.0 Project B Cash Flow ? $1. e.0 2. There are multiple IRRs of approximately 12. The other analyst calculates an IRR of just under 800 percent. d. b. Chapter 10 .7 percent and 787 percent.0 3.0 5.000 100. There are an infinite number of IRRs between 12. Answer: c Diff: T Two fellow financial analysts are evaluating a project with the following net cash flows: Year 0 1 2 Cash Flow -$ 10.Crossover rate and missing cash flow 97.2 5. What is the cash flow for Project B at t = 0? a.000 -100. Which statement best describes the IRR for this project? a.5 percent and 790 percent that can define the IRR for this project. when the WACC is 9 percent the projects have the same NPV.73 +$4. There is a single IRR of approximately 12.22 -$3.49 -$8. This project has no IRR. Project A and Project B.8 The crossover rate of the two projects’ NPV profiles is 9 percent. Answer: e Diff: M Athey Airlines is considering two mutually exclusive projects. because the NPV profile does not cross the X-axis. e.000 One analyst says that the project has an IRR of between 12 and 13 percent. c. b. -$4.7 percent. but fears his calculator’s battery is low and may have caused an error. This project has two imaginary IRRs. Consequently. You finance only with equity. c. Answer: c Diff: T Returns on the market and Takeda Company’s stock during the last 3 years are shown below: Year 1 2 3 Market -12% 23 16 Takeda -14% 31 10 The risk-free rate is 7 percent. d. c.Page 39 . and the required return on the market is 12 percent. b. and the required return on the market is 11 percent.12 Answer: c Diff: T Returns on the market and Company Y’s stock during the last 3 years are shown below: Year 1 2 3 Market -24% 10 22 Company Y -22% 13 36 The risk-free rate is 5 percent.NPV 99. You are considering a low-risk project whose market beta is 0.42 $12. The project has a cost of $500 million. d. $20. all of which comes from retained earnings.10 $ 9.75 Chapter 10 . and it is expected to provide cash flows of $100 million per year at the end of Years 1 through 5 and then $50 million per year at the end of Years 6 through 10. and it is expected to provide cash flows of $20 million per year at the end of Years 1 through 5 and then $30 million per year at the end of Years 6 through 10. The project has a cost of $100 million.5 less than the company’s overall corporate beta. NPV 100.2 to the company’s overall corporate beta. What is the project’s NPV (in millions of dollars)? a. $ 7.55 $23.10 $15. b.26 $10. Takeda is considering a project whose market beta was found by adding 0. all of which comes from retained earnings. What is the project’s NPV (in millions of dollars)? a.89 $22.11 $25. e. e. Takeda finances only with equity.76 $28. Your company is considering two mutually exclusive projects. c. 9%.00% 11. You must make a recommendation.000 200 600 800 1.000 2. Answer: c Diff: T MIRR and NPV 102.Page 40 . e. 11%. d. at at at at k k k k ª ª ª ª 7%.59% 12. Yes. Answer: b Diff: T As the director of capital budgeting for Raleigh/Durham Company.NPV profiles 101. you are evaluating two mutually exclusive projects with the following net cash flows: Year 0 1 2 3 4 Project X Cash Flow -$100 50 40 30 10 Project Z Cash Flow -$100 10 30 40 60 Is there a crossover point in the relevant part of the NPV profile graph (the northeast. quadrant)? a. Yes. Yes. What is the MIRR of the better project? a.46% 13. X and Y. c. or upper right. d. and the firm’s cost of capital is 12 percent. e. b. b.73% Chapter 10 . 13%. and you must base it on the modified IRR (MIRR).400 Project Y Cash Flow -$2. 12.89% 15. Yes.000 200 100 75 Year 0 1 2 3 4 The projects are equally risky. whose costs and cash flows are shown below: Project X Cash Flow -$2. No. 68 -$262.000. 13. 11. at t = 2 is an outflow (that is. Answer: a Diff: T Florida Phosphate is considering a project that involves opening a new mine at a cost of $10.000.000 operating cash inflow and an outflow of -$6.000 at t = 0. However.000 at the end of the second year.22% d. What is the difference between the project’s MIRR and its regular IRR? a. e. X. that the cash flow.Page 41 . X < 0).000.65 -$237.51% b. c. 12.65% c. The company’s weighted average cost of capital is 15 percent. at the end of Year 2 there will be a $5.000 at the end of each of the next 4 years.55% e.92 -$318. Project C has a 10 percent cost of capital and a 12 percent modified internal rate of return (MIRR). Thus. the facility will have to be repaired at a cost of $6.95 -$246.000. The project is expected to have operating cash flows of $5.MIRR and IRR 103. 9. -$196.78% MIRR and missing cash flow 104.13 Chapter 10 .000. d. b. 0.000 for repairs. Project C has the following net cash flows: Year 0 1 2 3 4 Project C Cash Flow -$500 200 -X 300 500 Answer: b Diff: T N Note. What is the project’s cash outflow at t = 2? a. 000 200. b.000 2.000 The project has a payback of two years and a weighted average cost of capital of 10 percent. b.12% Chapter 10 .000 200.89% 13.34% 16.74% 13.500 1.000 What is the modified internal rate of return (MIRR) of the project with the highest NPV? a. MIRR 106.37% 17.000 5.74% 12. e.01% 18. d.000 5. c.67% Answer: e Diff: T Mooradian Corporation estimates that its weighted average cost of capital is 11 percent.66% 16.25% 20.000 -1.000 -100. What is the project’s modified internal rate of return (MIRR)? a. d. Answer: b Diff: T Diefenbaker Inc. The company is considering two mutually exclusive projects whose after-tax cash flows are as follows: Year 0 1 2 3 4 Project S Cash Flow -$3.Page 42 .MIRR and missing cash flow 105. e.500 1. 5.500 -500 Project L Cash Flow -$9. c. 11.000 5. is considering a project that has the following cash flows: Year 0 1 2 3 4 Project Cash Flow ? $100. 000 50. b.78% 24. e.56% 13.68% 23. Answer: d A company is considering a project with the following cash flows: Year 0 1 2 3 4 Project Cash Flow -$100. c. b.28% 14.000 50.000 Diff: T The project’s weighted average cost of capital is estimated to be 10 percent. project’s modified internal rate of return (MIRR)? a. c. 11.Page 43 . 16. d. d. What is the modified internal rate of return (MIRR)? a.000 12.000 -10.82% 21.93% Chapter 10 .000 7.34% Answer: d Diff: T Javier Corporation is considering a project with the following cash flows: Year 0 1 2 3 4 Project Cash Flow -$13.000 50.500 What is the The firm’s weighted average cost of capital is 11 percent. e.000 -1.25% 11.000 8.90% 25.25% 20. MIRR 108.MIRR 107. 000 200 -300 900 -700 600 What is the project’s modified internal Chapter 10 .MIRR 109.52% MIRR 110.14% e. and the tax rate is 30 percent. The company’s stock has a beta = 1. The equity will be financed with retained earnings.68% 6. The company is considering a project with the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -$50.Page 44 .000 43. d. b. rate of return (MIRR)? a. Answer: c Diff: T Conrad Corp. 9. 20.76% b. 2.000 -40.000 35. 10. 6. e.1.95% 5. 16.83% Project Cash Flow -$1. c.000 What is the project’s modified internal rate of return (MIRR)? a.26% c.20% 3. the market risk premium is 5 percent. The risk-free rate is 6 percent.78% d.63% 3. Answer: e Diff: T Taylor Technologies has a target capital structure that consists of 40 percent debt and 60 percent equity.000 60. has an investment project with the following cash flows: Year 0 1 2 3 4 5 The company’s WACC is 12 percent. The company’s bonds have a yield to maturity of 10 percent. e. what is the project’s MIRR? (Hint: Think carefully about the MIRR equation and the treatment of cash outflows.26% 25.Page 45 . The company’s weighted average cost of capital is 12 percent.28% 28.81% d. d.4% 11.5% 11. repairs that will cost $1.52% Answer: e Diff: T Project Cash Flow -$700 400 -200 600 500 What is the project’s modified internal rate MIRR 112.75% b. 9. and it expects to sell the property and net $1 million at the end of Year 6. Capitol City Transfer Company is considering building a new terminal in Salt Lake City. of return (MIRR)? a.7% Answer: b Diff: T MIRR 113.000.) a. c.000. Answer: b Diff: T Simmons Shoes is considering a project with the following cash flows: Year 0 1 2 3 4 Simmons’ WACC is 10 percent. However.000 for repairs. Houston Inc. at the end of Year 10 there will be a $500. 12.10% 18. 11. What is the project’s modified IRR (MIRR)? a. Thus.000 at the end of each of the next 20 years. b.17% c.000.45% e. If the company goes ahead with the project.MIRR 111.33% Chapter 10 . b.93% 29. is considering a project that involves building a new refrigerated warehouse that will cost $7.9% 12.5 million at the end of Years 2-5. 11.000 operating cash inflow and an outflow of -$1. c.000 must be incurred at the end of the 10th year. All cash inflows and outflows are after taxes. 7. It will then receive net cash flows of $0. it must spend $1 million immediately (at t = 0) and another $1 million at the end of Year 1 (t = 1). 8. If Houston’s weighted average cost of capital is 12 percent. d.0% 11.000 at t = 0 and is expected to have operating cash flows of $500. 17. and it uses the modified IRR criterion for capital budgeting decisions. e. MIRR 114. Answer: b Diff: T Acheson Aluminum is considering a project with the following cash flows: Year 0 1 2 3 4 Acheson’s WACC is 10%. return (MIRR)? a. b. c. d. e. 17.95% 16.38% 14.90% 15.23% 12.86% Answer: e Diff: T Cash Flow -$200,000 125,000 140,000 -50,000 100,000 What is the project’s modified internal rate of MIRR 115. Mississippi Motors is considering a project with the following cash flows: Year 0 1 2 3 Project Cash Flow -$150,000 -50,000 200,000 50,000 What is the project’s modified The project has a WACC of 9 percent. internal rate of return (MIRR)? a. b. c. d. e. 7.72% 29.72% 11.62% 12.11% 11.02% Chapter 10 - Page 46 MIRR 116. Answer: e Diff: T Walnut Industries is considering a project with the following cash flows (in millions of dollars): Year 0 1 2 3 Project Cash Flow -$300 -200 500 700 What is The project has a weighted average cost of capital of 10 percent. the project’s modified internal rate of return (MIRR)? a. b. c. d. e. MIRR 117. Kilmer Co. is considering the following project: Year 0 1 2 3 4 Project Cash Flow -$150 100 50 -50 150 26.9% 15.3% 33.9% 49.4% 37.4% Answer: c Diff: T The company’s weighted average cost of capital is 10 percent. project’s modified internal rate of return (MIRR)? a. b. c. d. e. 4.01% 24.15% 16.34% 14.15% 17.77% What is the Chapter 10 - Page 47 MIRR 118. Answer: e Diff: T N Arrington Motors is considering a project with the following cash flows: Time period 0 1 2 3 The project has a 12 percent WACC. rate of return (MIRR)? a. b. c. d. e. 68.47% 51.49% 48.58% 37.22% 52.49% Answer: e Diff: T Cash Flows -$200 +120 -50 +700 What is the project’s modified internal MIRR 119. Ditka Diners is considering a project with the following expected cash flows (in millions of dollars): Year 0 1 2 3 4 The project’s WACC is 10 percent. rate of return (MIRR)? a. b. c. d. e. 36.95% 18.13% 27.35% 26.48% 23.93% Answer: c Diff: T Project Cash Flow -$300 -100 70 125 700 What is the project’s modified internal PV of cash flows 120. After getting her degree in marketing and working for 5 years for a large department store, Sally started her own specialty shop in a regional mall. Sally’s current lease calls for payments of $1,000 at the end of each month for the next 60 months. Now the landlord offers Sally a new 5-year lease that calls for zero rent for 6 months, then rental payments of $1,050 at the end of each month for the next 54 months. Sally’s cost of capital is 11 percent. By what absolute dollar amount would accepting the new lease change Sally’s theoretical net worth? a. b. c. d. e. $2,810.09 $3,243.24 $3,803.06 $4,299.87 $4,681.76 Chapter 10 - Page 48 Chapter 10 . b. is considering a project that has the following after-tax operating cash flows (in millions of dollars): Year 0 1 2 3 4 Project Cash Flow -$300 125 75 200 100 Woodgate Inc. c. d.83% 18.00% 21. Answer: c Diff: M N What is the internal rate of return (IRR) of the project that has the highest NPV? a.30% 21.) Woodgate Inc. e.’s finance department has concluded that the project has a 10 percent cost of capital. 14.) Warrick Winery is considering two mutually exclusive projects. e.30% 24. 10.00% 0.24% 10. Project Red and Project White. IRR 121.Page 49 .Multiple part: (The information below applies to the next two problems. b.04% 14. At what weighted average cost of capital would the two projects have the same net present value? a. d.000 700 400 200 100 Assume that both projects have a 10 percent WACC. The projects have the following cash flows: Year 0 1 2 3 4 Project Red Cash Flows -$1.96% Answer: d Diff: E N Crossover rate 122. c.000 100 200 600 800 Project White Cash Flows -$1.96% (The following information applies to the next five problems.00% 20. What is the project’s discounted payback period? a. b. c.65 2.50 2. b.00 2. b.77% 19. e. b. e.83 3. d.00 2. e. d. c. IRR 125.12% 23.64% Diff: M N Chapter 10 .12% 27.42% 26.00 years years years years years Answer: b Diff: E N Discounted payback 124. d. d.65 2. c.64% 10. What is the project’s net present value (NPV)? a.00 years years years years years Answer: d Diff: E N Answer: d Diff: E N Answer: c Diff: E N Answer: c What is the project’s modified internal rate of return (MIRR)? a.88 $ 40.53% 17.83 3. MIRR 127.Payback period 123. b.73 million million million million million 10. e. $ 25. NPV 126. What is the project’s internal rate of return (IRR)? a. c. 7. What is the project’s payback period? a.18 $137.83% 19. e.Page 50 .32% 2.91 $ 94.56 $198. d.50 2.00% 16. c. 2. MIRR 130.(The following information applies to the following four problems.31 Answer: d Diff: E N Project A Cash Flow -$300 100 150 200 50 Answer: d Diff: E N Chapter 10 . What is Project A’s net present value (NPV)? a.32 $ 66. What is Project A’s internal rate of return (IRR)? a.40% 12.00 $ 99.54% Answer: e What is Project A’s modified internal rate of return (MIRR)? a. b.29 $112.Page 51 . 13. d.49% 15. c. c. d. 7. c. e.79% 26. e.44% 16.15% 14. b.15% Diff: M N $ 21.16% 18. b.92% 24.54% 18. IRR 129. d.) Project A has a 10 percent cost of capital and the following cash flows: Year 0 1 2 3 4 NPV 128.26 $ 83. e. 63% 13.0% 18. c.000 The project has a cost of capital of 10 percent. e. Answer: c Diff: M N In addition to Project A.6% 18.273 $1.776 Answer: c What is the project’s modified internal rate of return (MIRR)? a.6% Diff: T N Answer: b Diff: E N Chapter 10 . d. 16.000 $2.03% 13. the firm has a chance to invest in Project B.) Company A is considering a project with the following cash flows: Year 0 1 2 3 Project Cash Flow -$5.157 $1. b.0% 17. e.6% 17. 11. d.23% 12. Project B has the following cash flows: Year 0 1 2 3 4 Project B Cash Flow -$200 150 100 50 50 At what cost of capital would Project A and Project B have the same net present value (NPV)? a.Page 52 .19% 12. c. c. e. What is the project’s net present value (NPV)? a. $1.000 3.Crossover rate 131. NPV 132.000 5. d.818 $2.000 -1. MIRR 133. b. b.27% (The following information applies to the next two problems. IRR. c.Page 53 Answer: d Diff: E N .08 $27.86 46. $179.11 $279. e.) Bell Corporation is considering two mutually exclusive projects. and NPV 134. 30.54 $37.00 $18. c. NPV 136.11 Answer: c Diff: M N Missing cash flow. What is Project A’s net present value (NPV)? a. instead assume that the project has an internal rate of return (IRR) of 15 percent. c. b. $ 0. payback period. b. What is the project’s net present value (NPV)? a. Given this assumption. d. Project Cash Flow X 175 175 300 Answer: a Diff: M N Assume that the project has a regular payback period of 2 years and a cost of capital of 10 percent.13 57.(The following information applies to the next two problems. b. d. d. e. Project A and Project B.01 Chapter 10 . Now instead of making an assumption about the payback period.11 $229. and NPV 135.12 34. what would be the project’s net present value (NPV) if the WACC equals 12 percent? a.30 $47.36 (The following information applies to the next four problems.11 $204.) Company B is considering a project with the following cash flows: Year 0 1 2 3 Missing cash flow.78 62. The projects have the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -500 150 200 250 100 Project B Cash Flow -500 300 300 350 -300 Both projects have a 10 percent cost of capital.11 $254. e. d. e. c. e.37% 14. b.83% Chapter 10 . c.88% Answer: c Diff: T N Crossover rate 139.15% 8.32% 15. MIRR 138.95% 13.05% 12.IRR 137. Diff: M N At what discount rate would the two projects have the same net present value? a. d. d.Page 54 .36% 7.01% 14.50% 5.04% 16. e. 15.68% 17. 12. b. What is Project A’s internal rate of return (IRR)? a.01% Answer: a Diff: E N Answer: b What is Project B’s modified internal rate of return (MIRR)? a.82% 16. b. c. 4.72% 6. CHAPTER 10 ANSWERS AND SOLUTIONS 1. while a project’s MIRR is dependent on the cost of capital since the terminal value in the MIRR equation is compounded at the cost of capital.) Statement a is false.Page 55 . Project B could have a higher NPV at some WACC if the NPV profiles cross. 4. the IRR is unaffected by the WACC. Statement c is false. Statement b is false. NPV ($) A B k (%) 0 10% IRRB IRRA Chapter 10 . 2. Ranking conflicts Payback period NPV profiles NPV profiles Answer: a Answer: d Answer: b Answer: d Diff: E Diff: E Diff: E Diff: E You can draw the NPV profiles to get an idea of what is happening. A project’s IRR is independent of its cost of capital. (See the diagram below. Statement d is the correct choice. 5. Ranking methods Answer: b Diff: E A project’s NPV increases as the cost of capital declines. 3. Project B could have a negative NPV when A’s NPV is positive. Therefore. the cost of capital is less than the crossover rate and Project A has a higher NPV than B. When IRR is used. both will have a positive NPV. At 6 percent. statement c is true. If B’s cost of capital is 9 percent. NPV profiles Answer: a Diff: M N The correct answer is statement a. existing information would suggest that Project X was the smaller project. NPV profiles NPV ($) Answer: e Diff: E A B k (%) 0 7% 12% 15% Since both projects have an IRR greater than the 10% cost of capital. the lower NPV could be the product of the timing of cash flows or the length of the project’s life. Since statements a. Statement c is also incorrect. the project has a positive net present value. b. 7. The IRR of Project X exceeds its weighted average cost of capital. if anything. then the cost of capital is greater than the crossover rate and B would have a higher NPV than A. Chapter 10 . NPV profiles NPV ($) Answer: e Diff: E A B k (%) 0 7% 12% 14% Statement a is true because at any point to the right of the crossover point B will have a higher NPV than A. the correct choice is statement e. In addition. we do not know where the crossover point is (if one exists) for these two projects. therefore. at any point to the right of the crossover point. Statement b is true for the same reason that statement a is true. If the cost of capital is 13 percent. B will have a higher NPV than A. the MIRR assumes reinvestment of the cash flows at 9 percent. and c are true. Therefore. the IRR calculation assumes that cash flows are reinvested at the IRR (which is higher than the cost of capital). Statement c is true. statement e is the correct choice.Page 56 . statement b is false. statement a is true.6. Therefore. 8. Statement b is incorrect. Since statements a and c are both true. Therefore. So. 11. so statement a is correct. Project Y has a higher NPV for any cost of capital less than the crossover point (which we know is greater than 10%). you can see that the crossover rate is greater than 10%. Project B will have a higher NPV than Project A. To see this. draw the projects’ NPV profiles from the information given in the problem. In order for statement c to be true. At a 17 percent cost of capital. Chapter 10 . so statement b is incorrect. NPV profiles Answer: a Diff: E N The correct answer is statement a. 10. then the NPV of the projects would be the simple sum of all the cash flows. If the projects are mutually exclusive. X’s MIRR is between the cost of capital and X’s IRR (making it less than 19%). IRR is calculated assuming cash flows are reinvested at the IRR. So. From the diagram we see that this is clearly incorrect. the other statements are false. If the cost of capital were 0. B’s NPV at a 0 cost of capital would have to be higher than A’s. NPV and IRR Answer: a Diff: E Statement a is true. Since these are normal projects. statement c is incorrect.Page 57 . statement c is false. statement b is true. Therefore. then project B may have a higher NPV even though Project A has a higher IRR. statement a is false. It is clear that Project A will have a higher NPV when the cost of capital is 12 percent. The profiles look like this: NPV ($) Y X 0 10% 17% 19% Discount rate (%) From this diagram. not the cost of capital. NPV profiles NPV ($) A B Answer: b Diff: E 0 16% 17% 18% 30% Discount rate (%) Draw the NPV profiles using the information given in the problem.9. then MIRR > WACC. IRR is independent of the discount rate. draw the NPV profiles. IRR Answer: b Diff: E The correct statement is b. We cannot determine this without knowing the NPVs of the projects. If the stock is correctly priced. The IRRs of both projects exceed the cost of capital. Since Project A’s IRR is 15%. and payback Answer: d Diff: E Statement a is true because the IRR exceeds the WACC. Statement b is false. 16. the NPV of this project should be zero. Statement a is false. NPV. c. 17. For a normal project. IRR. which is less than the IRR. the other statements are false. NPV and project selection Answer: e Diff: E Statement a is true. we can’t conclude which project’s NPV is going to be greater at a cost of capital of 10%.e.Page 58 . Statement c is false because the IRR is independent of the cost of capital. i. the other statements are false. Therefore. 20. the stock market is efficient. 14. IRR. however. Since we are given no details about each project’s cash flows we cannot conclude anything about payback. Therefore. Post-audit NPV profiles NPV profiles Answer: d Answer: b Answer: a Diff: E Diff: M Diff: M Chapter 10 . Statement b is also true because the MIRR assumes that the inflows are reinvested at the WACC. NPV. statement e is the correct answer. Statement b is false because you know nothing about the relative magnitudes of the projects.12. if NPV > 0. at a WACC of 15% NPVA = 0. Given the information in a. statement d is the correct answer. 13. Statement e is correct because you can think of a firm as a big project. So. Project B would still have a positive NPV. To see why. 18. 19. and d are false. IRR stays the same no matter what the WACC is. Statement c is true. Finally. projects with IRRs greater than the cost of capital will have a positive NPV. that is. the correct choice is statement a. MIRR. NPV and IRR Answer: a Diff: E Statement a is true. 15. if the NPV > 0. and MIRR Answer: b Diff: E Statement b is true. Statement d is false. Statement c is false. NPV and expected return Answer: e Diff: E Statements a.. b. the discounted payback is always longer than the regular payback because it takes longer for the discounted cash flows to cover the purchase price. Statement c is false. then the return must be > 12%. From the diagram drawn. statement d is the correct choice. 22. Therefore. Chapter 10 .21. D’s MIRR will be somewhere between the cost of capital and the IRR. Statement c is true. When WACC is less than 10 percent. Statement a is true. so C’s NPV profile is above D’s NPV profile to the left of the crossover point (10%). the correct choice is statement d. IRR is always independent of the cost of capital. Statement b is false. we can see that D’s IRR is to the right of C’s where the two lines cross the X-axis.Page 59 . NPV profiles NPV ($) Answer: d Diff: M C D 0 10% k (%) First. Make sure the profiles cross at 10 percent because the projects have the same NPV at a cost of capital of 10 percent. NPV profiles NPV ($) P Answer: d Diff: M Q k (%) 0 10% 15% 20% The diagram above can be drawn from the statements in this question. draw the NPV profiles as shown above. b. statements a. and c are true. C has a higher NPV. and from the diagram above. therefore. IRR is independent of the cost of capital. and from the diagram C’s IRR is always lower than D’s. which is 12%). If WACC < IRR. NPV does not suffer from the multiple IRR problem. then its NPV must be positive. IRR. NPV. NPV and IRR Answer: c Answer: a Diff: M Diff: M NPV is positive if IRR is greater Answer: e Diff: M Statement a is false. and MIRR Answer: c Diff: M Statement c is correct. Statement b is false. statement a is correct. If a project’s IRR exceeds the firm’s cost of capital. The profiles look like this: NPV $ X Y l l k (discount rate) 9% 12% 14% Recall if WACC > IRR. the other statements are false. the other statements are false. 28. and MIRR Answer: a Diff: M The correct answer is a. To see this. then the project has a positive NPV. 26. MIRR and NPV can conflict for mutually exclusive projects if the projects differ in size. statement e is the correct choice. draw the projects’ NPV profiles from the information given in the problem. 27. Chapter 10 . So. 25.23. NPV and IRR NPV and IRR Statement a is the incorrect statement. then the crossover rate must be between 9% and the lowest IRR (the IRR of X. yet the IRRX < IRRY. Think about the NPV of a $3 project versus the NPV of a $3 million project. 24. NPV. Statement c is false. Therefore. The projects could easily have different NPVs based on different cash flows and costs of capital. NPV is dependent upon the size of the project. So. statement c is correct. the project has a negative NPV. A lower IRR is usually associated with a longer payback. the correct choice is statement e.Page 60 . since NPV is calculated using the firm’s cost of capital to discount project cash flows. IRR. statement b is incorrect. than the cost of capital. NPV is dependent on a project’s risk. Thus. So. Since Project X has a higher NPV at 9% than Project Y. NPV profiles Answer: e Diff: M N The correct answer is statement e. The IRR is the discount rate at which a project’s NPV is zero. Statement a is false. IRR. Statement b is false. therefore. and MIRR NPV ($) Answer: d Diff: M Y X Crossover k (%) 0 10% IRRY 12% IRRX If IRRX is greater than MIRRX. NPV. Due to reinvestment rate assumptions.29. statement d is the correct choice. statement b must be true. Consequently. 33. Y could have a higher NPV. NPV. the other statements are false. if the two projects’ NPV profiles cross. (Remember that the MIRR will be somewhere between the cost of capital and the IRR. IRR. 31. Therefore.Page 61 . then its IRR must be greater than the cost of capital. At a cost of capital of 10 percent they have the same NPV. then its IRR must be less than the cost of capital. b. if IRRY is less than MIRRY.) Therefore. Statement c is false. statement a must be true. Therefore. the two projects’ NPV profiles could cross. so to the right of the crossover rate NPVX will be larger than NPVY. 34. consequently. IRR MIRR Ranking methods Answer: e Answer: e Answer: b Diff: M Diff: M Diff: M This statement reflects exactly the difference between the NPV and IRR methods. 30. Chapter 10 . NPV and IRR can lead to conflicts. so this is the crossover rate. there will be no conflict between NPV and MIRR if the projects are equal in size (which is one of the assumptions in this question). Ranking methods Answer: d Diff: M Both statements a and c are correct. and c are all true. 32. Similarly. the correct choice is statement d. a higher IRR doesn’t guarantee a higher NPV. statement c is also true. and payback Answer: e Diff: M Statement e is correct. however. Since statements a. From statements a and b we know that IRRX must be greater than IRRY. we don’t have enough information. to the left of the crossover rate NPVX must be smaller than NPVY. Miscellaneous concepts Statement a is true. while cash inflows are compounded at the cost of capital. The project with chosen. D has the higher IRR. IRR can lead to conflicting decisions with NPV even with normal cash flows if the projects are mutually exclusive. Miscellaneous concepts Answer: a Diff: M other statements are false. 40. 41. The discounted payback method still ignores cash flows that occur after the payback period. the other statements are false. 36. So C would have a slower payback than D. Multiple IRRs can with nonnormal cash flows. but it still does not consider cash flows that occur beyond the payback period. Sketch the profiles. IRR. therefore. Cash outflows are discounted at the cost of capital with the MIRR method. statement d is the correct choice. 38. and MIRR Answer: b Answer: c Diff: T Diff: T Chapter 10 . Project selection Answer: a Diff: M This is the only project with either a positive NPV or an IRR that exceeds the cost of capital.35. this implies that more of the cash flows are coming later on. Mutually exclusive one project should be chosen. NPV profiles NPV. 37. Miscellaneous concepts Answer: e Diff: M Statement e is true. As C’s NPV declines more rapidly with an increase in rates.Page 62 . From the information given. Miscellaneous concepts Answer: d Diff: M Statements a and c are true. The project’s scale cannot be determined from the information given. Answer: a Diff: M Statement a is true. the occur only for projects projects imply that only the highest NPV should be 39. The discounted payback method corrects the problem of ignoring the time value of money. Conflicts between NPV and IRR arise when the cost of capital is less than the crossover rate. the other statements are false. 3. then one project must have a higher NPV at k = 0 than the other project. The only way the profiles can cross is for the project with more total cash inflows to get a relatively high percentage of those inflows in distant years. and its IRR would also be higher. it would dominate the other project--its NPV would be higher at all discount rates. because it has the higher NPV when cash flows are not discounted. 4. 5.Page 63 . If WACC < IRR. To see this. But in that case. 44.42.86 years.86 of Year 5: $30 Payback = 4 + = 4. Choosing among mutually exclusive projects Answer: c Diff: T Draw out the NPV profiles of these two projects. sketch out a NPV profile for a normal. the project will completely recover the initial investment after $30/$35 = 0. and MIRR Answer: a Diff: T Statement a is true. which is the situation if k = 0. independent project. $35 Chapter 10 . their vertical axis intercepts will be different. NPV > 0. so the profiles would not cross. Project A has a faster payback than Project B. that is. then IRR says accept. If the project with more total cash inflows also had its cash flows come in earlier. One can sketch out two NPV profiles on a graph to see that these three conditions are indeed required. Payback period Answer: b Diff: E Time line (in thousands): 0 k = 10% 1 2 30 -90 3 30 -60 4 30 -30 5 35 5 6 35 7 35 8 35 9 35 10 Yrs. The project with the higher NPV at k = 0 must have more cash inflows. 2. this implies that more of the cash flows are coming later on. For the NPV profiles to cross. so NPV will also say accept. Statement d is false. Here is the reasoning: 1. As B’s NPV declines more rapidly with an increase in discount rates. Therefore. NPV. Most students either grasp this intuitively or else just guess at the question! 43. 40 CFs -150 30 Cumulative CFs -150 -120 Using the even cash flow distribution assumption. A second condition for NPV profiles to cross is that one have a higher IRR than the other. so that their PVs are low when discounted at high rates. IRR. The third condition necessary for profiles to cross is that the project with the higher NPV at k = 0 will have the lower IRR. which means that only one NPV profile will appear on the graph. Page 64 .000 1.00 -209.57 years. the discounted payback is 3. the discounted payback is 3.0000 -518.000 1.0907 through the year.000.31 683.000.10) = 90. we calculate $43.8182 305.3509 434.0000 181.00 -2.91 150/(1.10)2 = 123.000 Discounted Cash Flow @ 10% -$3.01 Answer: d Diff: E Cumulative PV -$3.264.10)4 = 34.15 169.000 1. Discounted payback Year 0 1 2 3 4 Cash Flow -$300 100 150 200 50 Discounted Cash Flow @ 10% -$300. Therefore.86 After Year 3.45. or 2.10)3 = 150. Therefore.090. 47. the initial outlay is recovered in 2 + $85. So.01 = 0.45 751.26 50/(1.0458 478. We assume that the $150.7851 169.15 Answer: e Diff: E N Cumulative PV -$300.26 is received evenly throughout the third year.3509/$478.09 826.75.15/$683.46 -513.14 From the cumulative cash flows we can see that the discounted payback is somewhere between 2 and 3 years. To find the portion that you need.091 years. 46.1094 = 0. you can see that you won’t need all of Year 4 cash flows to break even.12/$150.09 -85.1094 Cumulative PV -$700. Discounted payback Year 0 1 2 3 4 Cash Flow -$3.91 -1.00 100/(1.00 909. calculate $513.7585 The payback occurs somewhere in Year 4.12 65. Chapter 10 .000 1.26. To find the discounted payback you need to keep adding cash flows until the cumulative PVs of the cash inflows equal the PV of the outflow: Year 0 1 2 3 4 Cash Flow -$700 million 200 million 370 million 225 million 700 million Discounted Cash Flow @ 10% -$700. Discounted payback Answer: e Diff: E The PV of the outflows is -$700 million. To find out exactly where.75 years.97 200/(1.3967 -43.1818 -212. 15) (1. Project Z: Inputs: Output: CF0 = -100. CF1 = 10. 000 + Financial calculator solution (in thousands): Project X: Inputs: CF0 = -100.014. CF1 = 50. I = 15.15) (1. NPVZ = -8. 000 $10 . 014.48. CF3 = 30.15) -832. 000 $40 . At a cost of capital of 15%. both would be rejected. 000 NPVX -$100 . 014. thus. CF2 = 40. -$100 . NPV Time line: Project X (in thousands): 0 k = 15% Answer: a Diff: E 1 50 2 40 3 30 4 10 Years CFX -100 NPVX = ? Project Z (in thousands): 0 1 k = 15% 2 30 3 40 4 60 Years CFZ -100 NPVZ = ? 10 Numerical solution: $50 . CF4 = 10. CF4 = 60. 000 + + + + 2 3 4 1.833 = -$833.15) (1.15) (1. 000 $60 .014 = -$8.15 ) -$8 . 000 $40 . Output: NPVX = -0. 000 $30 .19 ª -$8 .15 (1. Chapter 10 . 000 + + + 2 3 4 1. I = 15. both projects have negative NPVs and. NPVZ $10 . CF2 = 30.15 (1. CF3 = 40. 000 $30 .Page 65 .97 ª -$833. CF1 = -100.500 Financial calculator solution: Project A: Inputs: CF0 = -50000. Diff: E -100 -100 Financial calculator solution: Inputs: CF0 = 0.310 Output: IRR = 5. 50.231. payback.49% ª 33. CF1 = 15625. Nj = 5. Nj = 19. CF4 = 600. IRR. IRR Output: IRR = 18%.625 4 15. Step 2: Chapter 10 . Calculate the IRR: CF0 = -900.625 3 15.25 years.000 NPVA = ? CFB -50. I = 10.781.503 ∑ ∑ ∑ 10 Years 44. CF2 = 3210. Nj = 10.625 99. Choose Project B. CF1 = 0. $11.Page 66 . CF2 = 300.625 2 15. CF1 = 44503.49. Project B: Inputs: CF0 = -50000.25($400)] = -$900. CF1 = 500. 51. IRR Answer: c Diff: E Time line: 0 -200. 52. Output: NPV = $11.231.67 > $9. CF3 = 400.67. NPV Answer: a Diff: E Time line: 0 1 k = 10% CFA -50. I = 10.04. NPVB > NPVA. CF2 = 99500.781.000 NPVB = ? 15.0%.503 2 44. Output: NPV = $9.503 Financial calculator solution: Inputs: CF0 = -200000. and missing cash flow Step 1: Answer: d Determine the cash outflow at t = 0: The payback is 2. so the cash flow will be: CF0 = -[CF1 + CF2 + 0.625 5 Years 15. Answer: c Diff: E Time line: 0 IRR = ? 1 2 ∑ ∑ ∑ 20 Years -100 FV = 3.25(CF3)] = -[$500 + $300 + 0. Nj = 4. and then solve for IRR = 33.04.000 k = 14% 1 44.5%. 08%. Outputs: $243. CF2 = 350. $535.13 . CF1 = 500. CF2 = 12000.53. Time line: 0 S 1 1. its IRR = 19.092. CF3 = 50. CF2 = 300. CF4 = 12000. IRR = 19.73 ≈ $7. so the answer is $15.83. 54. Answer: e Diff: E Diff: E Value sacrificed: 55. I = 12. Outputs: NPV = $15.08%.46. IRR = 19.091. CF3 = 1500. Project A has the highest IRR. CF1 = 10000. CF1 = 6000.13.100 Inputs: CF0 = -1100. Time line: 0 L 1 0 2 300 3 1. Chapter 10 . Outputs: NPV = $206. Project L is the “better” project because it has the higher NPV. Outputs: NPV = $107. the project with the higher positive NPV is the “better” project. CF1 = 0.46%.200. Project B: Inputs: CF0 = -30000. I = 10.43 = $291.000 2 350 3 50 k = 12% -1.76. CF3 = 40000. Inputs: CF0 = -2000.500 k = 12% -1. IRR = 20. CF1 = 1000. IRR = 23. IRR and mutually exclusive projects Answer: d Diff: E Because the two projects are mutually exclusive.Page 67 . Outputs: NPV = $7. Nj = 5.38%. Outputs: $535. CF1 = 668.43. CF4 = 20000.46 ≈ $15. CF2 = 15000. IRR = 21.38%. I = 10. I = 12.200. NPV and IRR Enter the cash flows for each project into the cash flow register on the calculator as follows: Project A: Inputs: CF0 = -50000. IRR = 20%. CF3 = 18000. I = 10.70.200. I = 10. Nj = 3.28%.100 Inputs: CF0 = -1100.$243. NPV and IRR Project S: Project L: Answer: b Inputs: CF0 = -1000. 43 ª $260. Since Project Y has the higher IRR. CF2 = 350000.438. calculate the NPV and IRR as follows: Inputs: CF0 = -1000.38%. and payback Answer: d Diff: E Payback = 2 + $300/$500 = 2. 57.02. and then solve for NPV = $107. CF1 = 350000. CF4 = 400. and then solve for IRR = 25. use its data to solve for its NPV as follows: CF0 = -500000. NPV and IRR Answer: d Diff: E N Use your financial calculator to solve for each project’s IRR: Project X: Project Y: CF0 = -500000. and then solve for IRR = 23. CF2 = 250000. Outputs: NPV = $260. CF1 = 350000. Using the cash flow register. I/YR = 10.Page 68 . NPV. Chapter 10 . CF3 = 500. IRR.6 years.22%.56. I = 10. CF1 = 400. CF1 = 250000. CF2 = 350000. CF2 = 300.69%. IRR = 21. CF3 = 250000. CF0 = -500000. 570 Financial calculator solution: Solve for IRRA: Inputs: CF0 = -50000.5% 29. Crossover rate Answer: b Diff: E NPV ($) 50.990 4 15. CFA-B Inputs: CF0 = 0. Crossover rate Answer: d Diff: E Find the crossover rate.49%.0%. CF2 = 100560.03%. which is the IRR of the difference in each year’s cash flow from the two projects.560 Project B’s NPV profile Crossover rate = 11.990 5 Years CFA -50. Output: IRR = 15.990 15. CF4 = 50000. CF3 = 30000.000 CFB -50. Nj = 4. The crossover rate is 11.990 0 15.990 3 15. Nj = 5. CF1 = 0. Solve for IRRB: Inputs: CF0 = -50000. Nj = 4.990 100.58.0%. CF2 = 25000. CF2 = -84570. Output: IRR = 18. CF1 = 15990.950 Project A’s NPV profile Cost of Capital (%) IRRB = 15% IRRA = 18% Time line: 0 IRRA = ? IRRB = ? 1 2 15.990 0 15.990 0 15.Page 69 .990 0 15. CF1 = 15990. Solve for crossover rate using the differential project CFs.000 CFA-B 0 15. 59. and then solve for IRR = 10.49%.560 -84. Chapter 10 . The differences of the cash flows (CFB CFA) are entered into the calculator: CF0 = -100000. Output: IRR = 11. CF1 = 25000. Answer: c Diff: E 61.125 700 Project Y Cash Flow -$3. we must find the difference in the 2 projects’ cash flows for each year. Crossover rate Step 1: Determine the differential cash flows between Projects A and B: Year 0 1 2 3 4 Project A Cash Flow -$2. CF1 = 500.400 1.100 DCFs A . Year 0 1 2 3 4 Project 1 Cash Flow -$400 175 100 250 175 Project 2 Cash Flow -$500 50 100 300 550 DCFs 1 . CF4 = -20. CF1 = 400. CF4 = -100. CF2 = 70.97%.073%.60.000 Project B Cash Flow -$1. CF1 = 125. Crossover rate Step 1: Answer: a Diff: E Determine the differential cash flows (in millions of dollars) between Projects X and Y: Year 0 1 2 3 4 Project X Cash Flow -$3.070 1. CF2 = 0. Crossover rate First.200 900 1.135 720 DCFs X . and then solve for IRR = 8.000 700 700 1. CF3 = 200. Chapter 10 . CF2 = 200.000 1.Page 70 . enter these data into the cash flow register on your calculator and solve for IRR: CF0 = 100.67%.2 $100 125 0 -50 -375 Then.000 1.Y $-500 500 70 -10 -20 Step 2: Calculate the IRR of the differential cash flows: Enter the following data in the calculator: CF0 = -500. CF3 = -10. Answer: d Diff: E N 62.500 300 500 800 1. CF3 = -50.700 1. and then solve for IRR = 20. and then solve for IRR = 26. CF4 = -375.B -$500 400 200 200 -100 Step 2: Calculate the IRR of the differential cash flows: Enter the following data in the calculator: CF0 = -500. Output: PV = -$227.9 = 5.928 years ª 6 years. FV =0.447. Calculate the regular payback: Year CF Cumulative CF 0 -$152. $60.21 ≈ $227. = -$152. CF2 = 210.553 So the payback is 2 + X or CF0 Step 2: Step 3: $32. Calculate the Year 0 outflow: The outflow at t = 0 is X where $227.X = $75. Payback period Time line (in thousands): 0 CF Cumulative NCF -100 -100 1 -500 -600 2 100 -500 3 110 -390 4 121 -269 5 133.447 -$152. enter the D cash flows in the cash flow register: CF0 = 0.B $0 -360 210 300 To find the crossover rate.000 -92.000 87. $146.447.447 = 2. CF1 = -360.9 ∑ ∑ ∑ 146.41 10.00%.447 2 60.63. and then solve for IRR = 25.51 6 10 Years Answer: c Diff: M Payback = 5 + 65.447.1 -135. Crossover rate Answer: d Diff: E N This is simply asking for the crossover rate of these two projects. PV of cash flows = $227.553 5 60.54 years. Here.553 4 60.000 Chapter 10 . The first step to finding the crossover rate is to take the difference of the two projects’ cash flows.000 27. 64.447 1 60.000. Payback period Step 1: $135. PMT = 60000.41 Answer: c Diff: M Calculate the PV of the cash flows: Inputs: N = 5. CF3 = 300.447 .21.000 -32.000 147.447 3 60.447. we subtracted the second column from the first: Year 0 1 2 3 Project A Cash Flow -$300 140 360 400 Project B Cash Flow -$300 500 150 100 DCFs A .Page 71 . I = 10. 40 68. $74.000 100.59 20.22 27.454.363.454.052. Discounted payback Year 0 1 2 3 4 $71.796.000 40.380.380.644.000 60.000 Discounted Cash Flow @ 10% -$200.52 4.00 36.000.000.000.000 30.86 years.363.82 40. Discounted payback Year 0 1 2 3 4 5 Cash Flow -$200.92 4.539.000 Discounted Cash Flow @ 10% -$100.539.636.980.000 30.92 19.00 36.636.00 -63.44 40.66.900.000 50. so it would not be accepted.00 45.25 74.000.000 150.97 Payback period = 2 years + 67.93 22.54 15.000 30.000 40.82 = 2.17 Answer: d Diff: M Cash Flow -$100.64 74.490.57 Project A’s discounted payback period exceeds 3 years.Page 72 .116.900.00 -63.49 Cumulative PV -$100.000.000 0 Discounted Cash Flow @ 10% -$80.36 -30.528.000.545.000.55 82.06 Discounted Payback = 1 + 68.743.000 40.00 -34.45 -18.64 33.000 20.55 16.03 Answer: e Diff: M Cumulative PV -$200.264.000 40.51 -525.000. Project B: Year 0 1 2 3 4 Cash Flow -$80.17 22.057.63 112.00 45.000 25.000 40.522.81 33.578. $112.92 You can see that in Year 3 the cumulative cash flow becomes positive so the project’s payback period is less than 3 years.00 -154.44 0 Cumulative PV -$80.94 83.545.697.36 = 1.2 2 Answer: b Cash Flow -$100.000 Discounted Cash Flow @ 10% -$100.320.697.016.639. Chapter 10 .636.45 -71.36 10.283.964.522.000 50.523.000 90.85 30. Discounted payback Project A: Year 0 1 2 3 4 $63.638 years.81 Diff: M Cumulative PV -$100. cash flow by solving for NPV the placeholder. Then solve for NPV = $78. Output: NPV = $51. CF2 = 35.27. Step 2: Calculate the net present value of the project at its cost of capital of 10 percent: Enter the following data as inputs in your calculator: CF0 = -560208. Step 1: Answer: d Diff: M N X (the up-front cash flow in this project). IRR need to reinvest the cash flows for NPV to equal is 12 percent. Nj = 3. CF1 = 75000.Page 73 .309.208. Calculate the value of the initial at a 12 percent cost of capital: You don’t have CF0.138. so that initial cash flow must be –$560. Chapter 10 .309. I = 14.208.01 ª $78. Nj = 4. Nj = 5.93726 = $21. CF3 = 2. CF3 = 40.24 ª $51. NPV Answer: d Diff: M Time line (in thousands): 0 k = 10% 1 2 30 3 30 4 30 5 35 6 35 7 35 8 35 9 35 10 Yrs. 71.27. so use 0 as following data as inputs in your 75000. 40 -150 NPV = ? 30 Financial calculator solution (in thousands): Inputs: CF0 = -150. Output: NPV = 21.937.138. Enter the calculator: CF0 = 0. Nj = 20. and I/Yr = 12. CF1 = solve for NPV = $560.26. NPV Time line (in thousands): 0 k = 14% 1 5 2 5 3 5 4 5 5 5 6 3 7 3 8 3 9 2 10 Yrs.27. so if you invest all the project’s you should have an NPV of zero. CF1 = 30.13824 = $51. Then This is the NPV when the initial cash flow is missing.69. Nj = 2. I = 10. NPV First. 2 PV = ? Answer: b Diff: M Financial calculator solution (in thousands): Inputs: CF0 = 0. Nj = 5. find the value of is the rate at which you $0. The NPV when the cash flow is added must be $0. and I/Yr = 10. Nj = 20. CF2 = 3. CF1 = 5. In this case the IRR cash flows at 12 percent. 70. 000 $3. Machine B: Inputs: CF0 = -2000.500. CF1 = 0. 74.57%.996% ª 18%. IRR Answer: d Diff: M $2. PMT = 5696. this implies t = 0 cash flow must be -$2. CF2 = 3877.5 years.000 + (0. Thus. Answer: c Diff: M 75.12) (1. solve for the crossover rate. For lower discount rates. PV = -10000. then Project B has a higher NPV than Project A. If payback = 2. If you subtract the cash flows (CFs) of Project A from the CFs of Project B. Output: IRR = 17. Output: IRR = 24.$3.01% ª 24%.500 + = $765.72. I = 19. CF2 = 0.12) (1. If the cost of capital is less than 6. PMT = 0.12 (1.Page 74 .12) Time line: IRRA = ? 0 IRR = ? B CFA CFB -2.877 832 Years Financial calculator solution: Machine A: Inputs: CF0 = -2000. and CF4 = 40000. NPV. PV = -12000.99% ª 20% = IRRC.500 + + + 2 3 4 1.000 = -$6. 73.91.57%. find the missing t = 0 cash flow. Output: I = 18% = IRRA. IRR Financial calculator solution: Project A: Inputs: N = 1. NPV = -$6. FV = 11800. since Project B’s cash inflows come comparatively later in the project life. CF1 = 832.000 $1. and missing cash flow Answer: b Diff: M First. then Projects A and B have the same NPV.5)$3.000 -2. FV = 0. Entering these CFs and solving for IRR/YR yields a crossover rate of 6.000 $3.57%. CF1 = -40000. Chapter 10 . CF3 = 20000. Project B’s NPV is not penalized as much for having large cash inflows farther in the future than Project A.000 1 0 832 2 0 832 3 0 832 4 3. Project C: Inputs: Output: N = 3. then the differential CFs are CF0 = -10000. if the cost of capital is 6. NPV profiles Answer: d Diff: M First. payback.000 . Nj = 4. Nj = 3. 100 NPVS = ? Cash flows L -1. I = 12.0.5. Chapter 10 .Page 75 . and then solve for NPV = $824. CF5 = 100.24. Nj = 3. IRRL = 13.000 Financial calculator solution (in millions): Inputs: CF0 = -3.000.000. Inputs: Project L: Project L has the higher NPV and its IRR = 13. CF4 = 10. CF3 = 50. CF4 = 850. CF1 = 150. CF1 = 900. NPV and IRR Answer: a Diff: M Time line: 0 k = 12% 1 900 IRRS = ? 0 IRRL = ? 2 350 300 3 50 500 4 10 850 Years Cash flows S -1. 78.78 = -$700).76. we can enter all the cash flows and solve for the project’s IRR.0.78.5 Financial calculator solution (in millions): Inputs: CF0 = -5.09%.000 2.78 . CF3 = 500. 77.699% ª 12. Outputs: NPVS = $24. CF3 = 250. CF0 = -1100. CF1 = 2. CF4 = 400. CF3 = 250. Output: IRR = 12. 79. I = 12. IRRS = 13.5. CF2 = 1.53. CF1 = 150.88%. This means that the initial cash flow must be –700 ($124. CF5 = 100.09%. CF4 = 400. CF1 = 1. CF2 = 200. CF0 = -700.000 2.000. I = 10. CF3 = 2.$824. Output: IRR = 18.000 -500. IRR of uneven CF stream Time line (in millions): 0 1 2 IRR = ? Answer: e 3 2 4 2 5 2 Years Diff: M -5 1 1. CF1 = 0. CF2 = 200. Outputs: NPVL = $35.70%. IRR of uneven CF stream Time line: 0 1 2 3 4 5 Answer: d 6 Diff: M IRR = ? Years -3. CF2 = 300. IRR Answer: e Diff: M N Using your financial calculator find the NPV without the initial cash flow: CF0 = 0.100 NPVL = ? Project S: Inputs: CF0 = -1100. Nj = 2.37%. CF2 = -0. Now.38%. CF2 = 350. and then solve for IRR = 16. 5 years: Initial outlay = -[CF1 + CF2 + (0.Page 76 . PMT = 0. FV = 901641.80. Answer: d 1 2 73.31. PV = -275000. CF1 = 40.5)(CF3)] = -[$40 + $80 + (0.000 8 Diff: M Years 73.85%. Chapter 10 . IRR. CF4 = 60. Calculate Project 2’s IRR: Enter the following data in the calculator: CF0 = -150. Output: I = 16.5 years projects’ paybacks are equal.5 years. I = 12.641. MIRR Inputs: N = 8.5)($60)] = -$150.306 73.306 ∑ ∑ ∑ Step 3: 81. PV = 0. because we’re told the two Project 2’s payback = 2. MIRR Time line: 0 k = 12% -275. Step 2: Calculate Project 2’s initial outlay. Output: FV = -$901. payback. PMT = 73306. and then solve for IRR = 20. CF3 = 60. CF2 = 80.31.0%. given its payback = 2.306 Financial calculator solution: TV Inputs: N = 8.306 3 73. and missing cash flow Step 1: Find Project 1’s payback: Year 0 1 2 3 4 Project 1 Cash Flow -100 30 50 40 50 1 Answer: c Diff: M Cumulative Cash Flow -100 -70 -20 20 70 PaybackProject = 2 + $20/$40 = 2. 18 Answer: e Diff: M Alternatively.000 ¥ (1.16)2 Diff: M R ¥ 1.00 Future Value = $243.000 1.000)(1. PMT = 0.337.Page 77 Step 2: Step 3: Step 4: . PV = -2028.00 ( 50. PMT = 0.181.82.123. Item(3) = 24 INPUT.5. FV = 243181. PV = 0.505.53. I = 16.345.181.000)(1.000)(1.5 = 16. Calculate cost of equity using CAPM and beta and given inputs: ke = kRF + (RPM)Beta = 7. CF0 = 0.0%.000.60 3.028 1.720. Graphical/numerical method: Slope = Rise/Run = (36% . use linear model. Calculate MIRR: Inputs: N = 3. MIRR and CAPM Time line: 0 1 | k = 16% | -2. Calculate TV of inflows: Inputs: N = 3. Output: m or slope = 1. Item(2) = 10 INPUT. and then solve for I = MIRR = 19. Item(2) = 15 INPUT.5. Item(3) = 36 INPUT.987.01 = MIRR ª 20%.50.98 ( 25. Beta = 1.00 1.0% + (6%)1.12) = 56.6%) = 27%/18% = 1. and then solve for NPV = $137.000 3 Years | 1. N = 5.18. PV = -137987. Chapter 10 . Output: I = 20. Enter X-list: Inputs: Item(1) = 6 INPUT. Step 2: Find the MIRR.16 -2. PV = -100000.9%)/(24% . FV = 3505.18.60.12)2 = 62. Answer: d 2 | 1.160.505.60 83.00 0 ( 50. Output: FV = -$3. PMT = 1000. and then solve for FV = $243. CF3-5 = 50000.12) = 50. I = 12.000.20 ( 50. Enter Y-list: Inputs: Item(1) = 9 INPUT.45%. CF1-2 = 25000. I = 12. PMT = 0.60.53. with a financial calculator you can find the FV of the cash inflows by first finding the NPV of these inflows and then finding the FV of their NPV.000)(1.000)(1.12)4 = $ 39. which is the discount rate that equates the cash inflows and outflows: N = 5. MIRR Step 1: Find the FV of cash inflows: ($25.12)3 = 35.028 MIRR = 20% Step 1: Calculate the historical beta: Regression method: Financial calculator: Different calculators have different list entry procedures and key stroke sequences. 50 + ($2. Sum = 22.000 IRRT = 22.21.026530. FV = 41066. PMT = 7000.00)(1.86%. 5 7.066. PV = -20000. and missing cash flow Step 1: Step 2: Answer: d Diff: M Solve for the CF0 by knowing the payback is exactly 2. PV = -650. MIRR and missing cash flow The up-front cost can be calculated using the payback: $400 + ($500)(0.85881% ª 33. PMT = 0. Answer: d Diff: M Use your calculator to obtain the MIRR: Enter N = 3. PV = 0.59%.50)(1.000 Diff: M 7.00)(1.82%. PV = -2.000 Calculate MIRRT: Find TV of cash inflows: N = 5. The terminal value of the cash inflows are: ($400)(1. Find FV = = = the FV of the cash inflows: $2.0: The CF0 for the project is $1 + $1.88160 + $1. PMT = 0. PMT = 0. and then solve for MIRR = I = 23. MIRR. payback.1) + $200 = $1.12)1 + ($1. Find MIRRT = 15.40493 $8.5 = $2.12)3 $2.11% + 15. I = 8.5. FV = 1234. MIRR and IRR Time line: 0 k = 8% -20.84.12)2 + ($1. Chapter 10 . and then solve for I = MIRR = 33. and then solve for FV = TV = $41.21. and then solve for I = MIRR = 15.1)2 + ($500)(1. FV = 8.50 + $2.48% = 37. Step 3: Solve for the MIRR: Enter the following input data in the calculator: N = 4.026530 million. Answer: e 1 ∑ ∑ ∑ 86.48%.5 million.Page 78 .24 + $1.11%.234.48%: N = 5.5) = $650. 85. CF4 = 400. CF4 = 4.992% ª 9.500 0 3 Years -100.0%. find the differential CFs by subtracting Team A CFs from Team B CFs as follows: CF0 = -5. CF3 = 0. CF4 = 4800.000 -100.972% ª 10. 91.992. PV = -10000. Project B is preferred.000 . CF2 = 0. Crossover rate Answer: b Diff: M First.52.992. Nj = 3.0%. CF1 = 200 . Crossover rate Answer: b Diff: M Subtract Project 2 cash flows from Project 1 cash flows: CF0 = -100. CF2 = -200. CF2 = 133000. CF0 = -5. CF5 = 700.87 ª $3.52/0.CFB). 90.87. The firm’s cost of capital is not given in the problem. 89. Before-tax cash flows Time line: 0 1 IRR = 15% -10. Crossover rate Answer: b Diff: M Find the differences between the two projects’ respective cash flows as follows: (CFA . Output: PMT = $1.Page 79 . I = 15.15%. Enter Chapter 10 .6 = $3. Before-tax CF = $1. Output: IRRA = 8. CF1 = 0.000 = -2800.000 39. 88. these in the cash flow register and then solve for IRR = 5.5. IRRB = 9. CF1 = -600. Since IRRB > IRRA.000 PMT = ? 2 PMT 3 PMT 4 ∑ ∑ ∑ Answer: b Diff: M 10 Years PMT PMT Financial calculator solution: Inputs: N = 10. Nj = 2. and then solve for IRR = 11.(-5. Project B: Inputs: Output: CF0 = -100000.85%.500 133.321. CF2 = -2200. Mutually exclusive projects Answer: b Diff: M Time line: 0 CFA CFB IRRA = ? IRRB = ? 1 39. FV = 0. CF3 = 4. CF1 = 39500. CF3 = 2200. which is the crossover rate. Enter these CFs and find the IRR = 16.500 0 2 39.35%. CF1 = 0.000 Financial calculator solution: Project A: Inputs: CF0 = -100000. so use the IRR decision rule.3.320.000) = 0. CF1 = 0. subtract CFB from CFA: -$100. 95. Chapter 10 .000 40. $70. CF2 = 1000.32 percent.21%. CF0 = -2000.000.000) = 0.000 0 0 60.000 .000 . Crossover rate Step 1: Calculate the differential cash flows: Year 0 1 2 3 4 Step 2: Project A Cash Flow -$100.A -$100 70 40 20 0 -20 Input the cash flows into your calculator’s cash flow register and solve for the IRR to obtain the crossover rate of 9.000 .000 .000 40. Enter these into your CF register and then solve for IRR = 11. Crossover rate Answer: d Diff: M Find the differential cash flows to compute the crossover rate. $25. To find the crossover rate.000 = -$10.$55. Enter these cash flows and then solve for IRR = crossover rate = 13.$30.000 60.000 DCFs B – A -$90. CF4 = 5000.000 30.000 100. CF2 = 0.000. Subtracting Project A cash flows from Project B cash flows.Page 80 . Crossover rate Answer: c Diff: M The crossover rate is the point where the two projects will have the same NPV.000 Answer: b Diff: M Determine the crossover rate: Enter the following inputs in the calculator: CF0 = -90000.000 100. CF3 = 5000.000 . and then solve for IRR = 8. $40.000.92.000 = -$15.000 35.000 = $10.$80.000 Project B Cash Flow -$190.000 30. 93.(-$100. 94.5931%.$15. CF4 = 60000.000. CF1 = -6000. CF3 = 60000.000 = $10. we obtain the following differential cash flows: Year 0 1 2 3 4 5 DCFs B . $40.000 35. Crossover rate Answer: d Diff: M Find the differential cash flows by subtracting B’s cash flows from A’s cash flows for each year.03%. CF0 .09 + $3. NPVA .22082 million. NPVA = $4. CF3 = -20.73167 million.09 + $3/(1. CF4 = 40.73167 million.$8.NPVB = 0.22082 CF0 = -$4.51085 million.73167 = 0 -CF0 = $8. Chapter 10 .22082 million.7/1.Page 81 .09)2 + $5.55963 + $2.83486 + $2. for IRR = the IRR of the DCFs: following data (in millions) in the calculator: CF1 = -50.09)3 + $1. Determine rate: NPVB = CF0 = CF0 = CF0 the PV of cash inflows for Project B at the crossover + $1.$4.52504 + $3.73167 . Crossover rate and missing cash flow Step 1: Determine the NPV of Project A at the crossover rate: NPVA = -$4 + $2/1.22082 .96. Crossover rate Step 1: Answer: b Diff: M Calculate the difference in the cash flows of the 2 projects: Year 0 1 2 3 4 Project A Cash Flow -$215 million 20 million 70 million 90 million 70 million Project B Cash Flow -$270 million 70 million 100 million 110 million 30 million DCFs B – A $55 million -50 million -30 million -20 million 40 million Step 2: Calculate Enter the CF0 = 55.09)3 = -$4 + $1. and then solve 19.86092 = $4.2/(1. NPVA = NPVB.09)2 + $5/(1. NPVB = CF0 + $8. CF2 = -30. Answer: e Diff: M 97.36%. $4.8/(1.47866 + $8. Step 2: Step 3: Determine the cash outflow at t = 0 for Project B: At the crossover rate.69338 + $4. 100. there are multiple IRRs.000/1.111.234.5% = -10. we find that there are two IRRs. The first claim appears to be correct.46.000/(1 + 8)2 = -10.000 + 100.000.Page 82 .125 .7% IRR2 ª 787% By randomly selecting various costs of capital and calculating the project’s NPV at these rates.5% and 13.57 = -123.000.11 .91 6.94 72.8)2 = -10.0 800.67) (123.0 400.13)2 = 180.000 + 11.32 = 72.0 12.000/(1 + 7.1.000 + 100.100. Chapter 10 . The IRR of the project appears to be between 12.7 percent.32 IRR1 ª 12.0 25.0 780.00 6. Thus.98.000 1 100.7 13. since the NPVs are approximately equal to zero at these values of k.1. The second claim also appears to be correct.02) 180. Multiple IRRs Time line: 0 -10.000/(1. Below is a table of various discount rates and the corresponding NPVs.64 .100.125)2 = -123. The IRR of the project flows also appears to be above 780% but below 800%.32.0%. NPVk = 12.363. Investigate second claim: Try k = 800% and k = 780% NPVk = 800% = -10.000 Answer: c Diff: T IRR = ? Numerical solution: This problem can be solved numerically but requires an iterative process of trial and error using the possible solutions provided in the problem.0 ($ NPV 433.291.46) (1.8 .000 2 -100.000/(1.000 + 11. NPVk = 780% = -10. Discount rate (%) 12.46.000 + 100.46) 2.13 .00 (123. Investigate first claim: Try k = IRR = 13% and k = 12.91.0 787. one at about 787 percent and the other at about 12.5% NPVk = 13% = -10.000/9 .5 12.000/1.000 + 100.100.000/8. 3633 = 13. which is its WACC because it uses no debt: ks = WACC = 7% + (12% .8165% ª 13.7102 = 9. Now find the project’s NPV (inputs are in millions): CF0 = -500.2102. The project beta is thus 1. NPV Step 1: Step 2: Step 3: Run a regression to find the corporate beta. Now find NPV (in millions): CF0 = -100.2 to the corporate beta.3633. Beta is 1. Answer: c Diff: T Step 4: 100.5 from the corporate beta. CF1-5 = 20. CF6-10 = 30.26%.1633. I = 13. and then solve for NPV = $10. and then solve for NPV = $23. Market returns are the X-input values.42 million.26%. I = 9. CF6-10 = 50.99.2102 . Find the project’s estimated beta by subtracting 0. CF1-5 = 100.5%)0. Find the company’s cost of equity. Find the project’s cost of equity.7%)1.0. Find the project’s estimated beta by adding 0. NPV Step 1: Run a regression to find the corporate beta. Answer: c Diff: T It is 1.82. while Y’s returns are the Y-input values. The project beta is thus 1.82%. which is its WACC because it uses no debt: ks = WACC = 5% + (11% .11 million.Page 83 . Step 2: Step 3: Step 4: Chapter 10 .7102.5 = 0. CF2 = 30.167 ª 7.489% ª 14. The crossover rate is the graph.Z Inputs: CF0 = 0. IRR = 14. NPVX. Project Z has the higher NPV at k 7. CF4 = 10.17%.Page 84 . IRR = 11. NPVZ. CF4 = 60. that is. CF1 = 50. Calculate the IRR of the differential project.79%. Output: IRR = 7. Solely using the calculator we can determine point in the relevant part of an NPV profile higher IRR. Chapter 10 . ProjectX IRRX . Calculate the NPVs of the projects at k = 0 discount rate.49%. CF2 = 40. CF1 = 40. CF1 = 10.k = 0% = -$100 + $10 + $30 + $40 + $60 = $40. CF3 = -10.17% and occurs in the upper right quadrant of Z that there is a crossover graph.k = 0% = -$100 + $50 + $40 + $30 + $10 = $30. NPV profiles Answer: b Diff: T Time line: CFX CFZ CFX 0 -100 -100 0 Inputs: Output: Inputs: Output: 1 50 10 40 2 40 30 10 3 30 40 -10 4 10 60 -50 Years . CF3 = 30. CF0 = -100. CF4 = -50. CF3 = 40.101. CF2 = 10. Project X has the = 0.Z Project X: Project Z: CF0 = -100. (Also note that since the 2 projects are of equal size that the project with the higher MIRR will also be the project with the higher NPV.64 3 ¥(1.59%.89% 4 Years | 75.63 Time line for Project Y: k 0 MIRR | -2.12)3 2.59% 3 4 Years | | 800 ¥(1.12)2 752. CF1 = 2000.000 2 | 200 -2.00 ¥(1.12) 1.809.04.) Chapter 10 . I = 12.400.000 = 12% = ? 1 | 2. CF4 = 1400.102. I = 12.12) Calculate NPV of Projects: Project X: Inputs: CF0 = -2000. Note that the better project is X because it has a higher NPV.12) 280.000 = 12% = ? Answer: c Diff: T 1 | 200 2 | 600 -2. CF2 = 200.86 Terminal Value (TV) = 3. Its corresponding MIRR = 13. CF3 = 100. Project Y: Inputs: CF0 = -2000. CF3 = 800.Page 85 . Output: NPVY = $63. CF1 = 200.247.74 3 | 100 ¥(1.99 Terminal Value (TV) = 3. MIRR and NPV Find the MIRR of the Projects.329.88 ¥(1. Output: NPVX = $116.00 896.99. Time line for Project X: k 0 MIRR | -2.12)2 250.000 MIRRX = ? 13. CF2 = 600.00 112.00 ¥(1.000 MIRRY = ? 12. CF4 = 75. I = 12.000 Diff: T Step 1: Calculate IRR by inputting the following into a calculator: CF0 = -10000000. Find the PV of the future value of cash inflows using the MIRR.48. The PV of all cash outflows is -$500 + -X/(1.67. Nj = 2. Calculate the difference between the project’s MIRR and its IRR: MIRR .95 = X.X/(1.000 2 5. and then solve for NPV = $10. PMT = 0.51%.000 -1. I = 15. CF2 = -1000000.10)2 -$196. and then solve for IRR = 13.103. and then solve for PV = $696. MIRR and missing cash flow Step 1: Determine the PV of cash outflows and the FV of cash inflows.21 -$237. CF2 = 0.67. Step 2: Step 3: Chapter 10 .20 = $1. -$696.65 = -X/1. b. Calculate MIRR: a.95 = -X $237. I = 15. Calculate MIRR: N = 4. Determine the value of the missing cash outflow. CF1 = 5000000.1) + $200(1.000 Answer: a 4 5.78% = 0.000 -6. FV = 1096. CF1 = 5000000. CF1 = 0.Page 86 .10)2. Calculate PV of the outflows: CF0 = -10000000.29% . CF3-4 = 5000000.000 5. Answer: b Diff: T N Step 2: Step 3: 104. Calculate FV of the inflows: CF0 = 0.29%.13. CF2 = -1000000.1)3 = $500 + $330 + $266.20.173. PV = -10756143. c.65 = -$500 .494.000 3 5.756. CF4 = 5000000. PMT = 0.143. MIRR and IRR Time line (in thousands): 0 k = 15% 1 -10.20. N = 4. and then solve for NPV = -$10. FV = 18354375.78%.096. and then solve for I = MIRR = 14.65. The FV of all cash inflows is $500 + $300(1.IRR = 14. Enter the following inputs in the calculator: N = 4. -CF0 = CF1 + CF2. and then solve for MIRR = I = 20.237. PV = -3329. N = 4. Since NPVS > NPVL we need to calculate MIRRS.37. Answer: e Diff: T 106. CF2 = 200000. MIRR Use cash flow registers to determine the NPV of each project: NPVS = $1.7448% ª 12. and then solve for FV = $595. FV = 6932.Page 87 . Step 2: Step 3: Step 4: Calculate the MIRR: Enter the following inputs in the calculator: N = 4.82. CF0 = -($100. I = 11.3455. I = 10. and then solve for NPV = -$3.11. I = 11. I = 10. Chapter 10 .12%.100. CF4 = 0. Calculate the TV of cash inflows: First find the cumulative PV. CF2 = 0.000 + $200. PV = -368301. Calculate the present value of the cash outflows: Enter the following inputs in the calculator: CF0 = -300000. I = 11.566.106. CF1-3 = 0. MIRR and missing cash flow Step 1: Answer: b Diff: T Determine the missing cash outflow: The payback is 2 years so the project must have cash inflows through t = 2 that equal its cash outflow. I = 10. CF1 = 0. and then solve for NPV = -$368.3455. PMT = 0. CF4 = -500. PMT = 0. and then solve Calculate MIRR: N = 4.47. and then solve for NPV = $406.000.105.74%. CF3 = 200000. NPVL = $1. and then solve for I = MIRR = 12.329. then take forward as a lump sum to find the TV. CF4 = -100000. Calculate the PV of cash outflows: CF0 = -3000. Calculate TV or FV: for FV = $6. CF1 = 2500. CF0 = -$300. and then solve for NPV = $4.000). PV = -406461. PMT = 0. CF1 = 100000. PMT = 0. Calculate PV: CF0 = 0. FV = 595100.23. CF2 = 1500. CF3 = 0.3073.23.47.461. CF3 = 1500. Calculate the future value of the cash inflows: Enter the following inputs in the calculator: CF0 = 0. PV = -4566.932.301.37.3073. enter N = 4. Add -$100. FV = 182050. Solve for MIRR: N = 4.620.771.10.5%. Thus. Solve for Second. PMT = 0.038.13. PMT = 0.115) = 0. PV = -113086. Second. I = 9. PMT = 0. Use the TVM keys to calculate the future value of this present value.086. CF2 = 50000.7.05(1. PMT = 0.60. I/YR = 10. I = 11. PMT = 0.115 or 11.7. CF3 = 60000.13. find the company’s weighted average cost of capital: We’re given the before-tax cost of debt.0. Solve for NPV of costs = -$77. I = 9. 108. the PV of all cash outflows can be calculated as follows: CF0 = -50000.342. CF1-3 = 0. CF4 = -1500. Solve for NPV = $124. find the terminal value of the project at t = 4: CF0 = 0. PV = -106830.988.90%. CF3 = 7000.60. FV = 10000. FV = 34038. Solve for FV = $163. calculate the present value of costs: N = 4.10)(1 . CF1 = 12000. and then solve for I = MIRR = 24.13.050.13. and then solve for I = MIRR = 14.62.7%. Solve for FV = $182. PV = -13988. Chapter 10 . CF4 = 0. Finally. find the PV at t = 4 of all cash inflows: CF0 = 0.62. MIRR Answer: e Diff: T First. kd = 10%. To find the MIRR.Page 88 .25%.3) + 0. PMT = 0. -$6. Solve for NPV = $113.6(0. Solve for FV = $34.76.830. Answer: d Diff: T Solve for NPV = -$13. FV = 163771. PMT = 0. calculate the MIRR: N = 4. the WACC is: k = 0.37. MIRR First. We can find the cost of equity as follows: ks = 0. I = 10.37. Use the TVM keys to calculate the future value of this present value.52%. CF4 = -40000. I = 11. find PV of all cash outflows: CF0 = -13000.422.1) = 0.000 + -$6. CF2 = 43000. CF1 = 50000.76. and then solve for I = MIRR = 20. CF2 = 8000. N = 4. CF4 = 0. NPV = $22.4(0. Third. 109.097 or 9.13 = -$106.48.107.10. N = 4.06 + 0. PV = -22422. PV = -124342.13. I = 10. I = 11. CF1-3 = 0. CF4 = 0. Answer: d Diff: T and then solve for PV = Find the terminal value of inflows: CF0 = 0.830. CF3 = 50000. Use the TVM keys to calculate the future value of this present value. I = 9. PV = -77620.7. CF1 = 35000. MIRR First.48. N = 4.830. 684. CF4 = -700.68.40.1)3 + $600(1.5 5 . Output: NPV = $1. CF3 = 1000000.14.26%. PMT = 0. FV = 1692.5 3 .5 4 . Calculate PV of costs: Inputs: CF0 = -1000000.423.2593% ª 18.0208.110. Nj = 4. CF2 = -1000000. CF1 = 0. CF3 = 0.1)2 = -$865.65. CF1 = 200. Answer: e Diff: T Answer: b Diff: T Solve 112. FV = 2043.6995% ª 11. I = 12. 111. for NPV = $1.68.857. N = 5.70%. Solve for FV = $2. CF5 = 0.1) + $500 = $1. Find MIRR: N = 4.0208. Inputs: N = 6.6639. and then solve for MIRR = I = 3. Output: NPV = -$1. MIRR There are three steps to getting the MIRR.2893. CF3 = 900.676.14.590. I = 12.5 6 Yrs 1.9471% ª 3. PV = -1159.6298. Solve for NPV of costs = -$1.862. I = 12. and then solve for I = MIRR = 18. CF1 = 0. PV = -1862590.65.Page 89 . Calculate MIRR: Inputs: N = 6. MIRR Time line (in millions): 0 -1 k = 12% MIRR = ? 1 2 . Chapter 10 . Find FV of inflows: $400(1. CF2 = 0. PV = -865.40. Step 1: Step 2: Step 3: Find PV of outflows: -$700 + -$200/(1. PMT = 0. I = 12. PMT = 0. Find the future value of the inflows: CF0 = 0.043. CF2 = 500000. PV = -1892857. Output: FV = $3. PMT = 0.159. PMT = 0. CF4 = 0.95%.6298. Use the TVM keys to calculate the future value of this present value. CF2 = -300. I = 12.6639. FV = 3676423. MIRR Answer: c Diff: T Find the present value of the outflows: CF0 = -1000.692.892. PV = -1684.0 -1 Calculate TV (Terminal value) of inflows: Inputs: CF0 = 0. Output: I = MIRR = 11. Then find the MIRR: N = 5.2893. I = 12. CF5 = 600. 30.473. CF1 = 0. less than WACC = 12%. CF10 = -500. PV = -3573. Next.30. PMT = 0.587. 12. I = 12. 114. PV = -7161.38%.74. PMT = 0.640.161 = PV of outflows 500 TV of inflows: Calculation of PV of outflows: CF0 = -7000.74. Calculation of TV of inflows: CF0 = 0. Compound this number 4 years into the future to get the TV: ($297.775. Calculation of MIRR: N = 20.52% and NPV = -$3. CF3 = 0. Step 2: Step 3: Chapter 10 .10)4 = $435. CF4 = 0.113. CF11-20 = 500.74.251. and then solve for NPV = $297. find the MIRR: N = 4.30 -7. CF1-9 = 0. I/YR = 10. FV = 34473. FV = 435775.640.74.573.17%. I = 12. Solve for FV = $34. CF10 = 0. CF2 = 0. Then. and then solve for I = MIRR = 16. and then solve for I = MIRR = 8. MIRR Step 1: Both are consistent with MIRR Answer: b Diff: T Find the terminal value (TV) of the inflows with your calculator as follows: CF0 = 0. find the PV of the outflows: CF0 = -200000.160.473. I/YR = 10. MIRR Time line (in thousands): 0 1 10 k = 12% ∑ ∑ ∑ Answer: b Diff: T 11 ∑ ∑ ∑ 20 500 34. CF1 = 125000. CF4 = 100000.565.000 500 -500 -161 -7.1885)(1. PMT = 0. CF1-9 = 500. Note: IRR = 2. and then solve for NPV = -$7. I = Use TVM to calculate the future value of the present value. PV = -237565.1885. and then solve for NPV = $237.161.Page 90 .99 ª -$7. CF3 = -50000. $3. Solve for NPV = N = 20. CF2 = 140000. MIRR Answer: e Diff: T The MIRR is the discount rate that equates the FV of the inflows with the PV of the outflows. Answer: e Diff: T 116.34%.60. MIRR Step 1: Step 2: Step 3: Chapter 10 . Answer: c Calculate the present value of the cash outflows: PV = -$150 + -$50/(1. we need the PV of the cash outflows and the FV of the inflows. Calculate the FV of the inflows: FV = ($200.82.8182 ª -$481.02%. Diff: T for NPV = Step 2: Step 3: 117. MIRR Remember that in order to solve for MIRR.10)1 + $700 = $550 + $700 = $1.000)(1. Calculate the MIRR: MIRR is the discount rate that equates the PV of the outflows with the future value of the inflows: N = 4.01657% ª 11. CF1 = -200. PV = -481.10)2 + $150 = $133.57 = -$187.115.871. FV = 268000. PMT = 0.000/1.56.000 = $268. The MIRR is the discount rate that equates the two.57.4%.57.10)3 + $50(1. Calculate the MIRR: N = 3. and then solve for I = MIRR = 11. PMT = 0. and then solve for I = MIRR = 37. PMT = 0.000 + (-$50.000.09) = -$195. FV = 1250.09) + $50. FV = 343. Step 1: Calculate the present value of the outflows: Enter the following input data in the calculator: CF0 = -300. Calculate the future value (terminal value) of the cash inflows: FV = $100(1. PV = -195871. and then solve -$481.60.250. PV = -187.50 + $150 = $343. I = 10.56. and then solve for I = MIRR = 16. Calculate the future value of the cash inflows: FV = $500(1.82.10)3 = -$150 .00. Calculate the MIRR: Enter the following data into the calculator: N = 3. Step 1: Step 2: Step 3: Calculate the PV of the outflows: PV = -$150.4069% ª 37.10 + $60.Page 91 .$37. 49%.10 = -$390.00 137.70 922. PV = -239.Page 92 .8597.118. MIRR Step 1: Step 2: Answer: e Find the PV of the cash outflows (in millions of dollars): PV = -$300 + -$100/1.70 + $137. and then solve for I = MIRR = 23.5 + $700 $922.8597 1 2 | | 120 -50 ¥ (1.50 84.9091 -390.10)2 + $125(1. PMT = 0.528 850.528. Then solve for I = MIRR = 52. FV = 922.528 Using your financial calculator.93% Chapter 10 .4908% ª 52.93%.8597 -239.12)2 1 ¥ 2 (1.9091 2 | 70 3 | 125 4 | 700. 119. PMT = 0.20 MIRR = 23.9091.20. MIRR Time line: 0 12% | -200 Answer: e Diff: T N -39.10) + $700 $84. PV = -390. enter the following data as inputs: N = 3.20. Find FV = = = the FV of the cash inflows (in millions of dollars): $70(1.9091.12 ) MIRR = ? 3 | 700 150. Diff: T Step 3: Find the MIRR: N = 4. Time line: 0 1 | k = 10% | -300 -100 -90. and FV = 850. CF4 = 800.189.000 PMT 0 FV -45.189. Then.993.9167% 1 0 2 0 3 0 4 0 5 0 6 0 7 ∑ ∑ ∑ 60 Months 1. CF1-6 = 0.24%. and I/Yr = 10. Project White: Using your financial calculator.03 .97 = $3. Find the NPV and IRR of both projects: Project Red: Using your financial calculator. CF2 = 400.803.000 3 ∑ ∑ ∑ Diff: T 60 Months 1.120. Sally should accept the new lease because it would raise her theoretical net worth by $3. the PV of payments under the proposed lease would be less than the PV of payments under the old lease by $45. Then. Therefore. CF4 = 100.06.06.97. enter the following data as inputs: CF0 = -1000. IRR Answer: c Diff: M N The project with the highest NPV will add the most value for shareholders.9167.8346% ª 21.5065 ª $185. enter the following data as inputs: CF0 = -1000. solve for NPV = $253. CF3 = 600.83%.050 1.398 ª $253. and then solve for NPV = -$42.9167 I/YR PV 1.000 60 N 11/12= 0. Project Red has the higher NPV. 121. CF3 = 200. CF2 = 200.2354% ª 18. CF1 = 700. solve for NPV = $185. Chapter 10 .050 CF0 = 0.51 and IRR = 21. I = 11/12 = 0.$42.803.40 and IRR = 18.Page 93 .03 New lease: 0 0. and I/Yr = 10. PV of cash flows Current lease: 0 11%/12 = 0.24%.993.9167% Answer: c 1 1. CF7-60 = 1050. CF1 = 100.000 2 1. and its IRR is 18.000 1. 122. Crossover rate Answer: d Diff: E N Find the difference between the two projects’ cash flows, enter differences as your cash flows, and solve for the IRR of project D. Year 0 1 2 3 4 Project White Cash Flow -$1,000 700 400 200 100 Project Red Cash Flow -$1,000 100 200 600 800 DCFs White – Red $ 0 600 200 -400 -700 the Using your financial calculator, enter the following data as inputs: CF0 = 0; CF1 = 600; CF2 = 200; CF3 = -400; and CF4 = -700. Then, solve for IRR = 14.2978% ª 14.30%. 123. Payback period Answer: b Diff: E N Remember, payback is calculated by determining how long it takes for a firm to recoup its initial investment. Year 0 1 2 3 4 Project Cash Flow -$300 125 75 200 100 Cumulative Cash Flow -$300 -175 -100 100 200 Therefore, the project has a payback of 2 + $100/$200 = 2.5 years. 124. Discounted payback Answer: d Diff: E N Remember, discounted payback is calculated by determining how long it takes for a firm to recoup its initial investment using discounted cash flows. We must find the present values of the cash flows using the firm’s 10% cost of capital. Year 0 1 2 3 4 Cash Flow -$300 125 75 200 100 Discounted Cash Flow @ 10% -$300.00 125/1.10 = 113.64 75/(1.10)2 = 61.98 200/(1.10)3 = 150.26 100/(1.10)4 = 68.30 Cumulative PV -$300.00 -186.36 -124.38 +25.88 +94.18 $124.38 = 2.83 years. $150.26 Therefore, the project’s discounted payback is 2 + Chapter 10 - Page 94 125. IRR Answer: d Diff: E N For this problem, you simply need to enter the cash flows and then solve for IRR. CF0 = -300; CF1 = 125; CF2 = 75; CF3 = 200; CF4 = 100; and then solve for IRR = 23.42%. 126. NPV Answer: c Diff: E N Here, you just need to enter the cash flows, supply a discount rate (10%), and then solve for NPV. CF0 = -300; CF1 = 125; CF2 = 75; CF3 = 200; CF4 = 100; I/YR = 10; and solve for NPV = $94.18. Note that the cash flows are in millions of dollars. 127. MIRR Answer: c Diff: M N To calculate the MIRR, we need to find the present value of all the outflows and the future value of all the inflows. The discount rate that equates the two is the modified internal rate of return. PV of inflows -$300 $125 $ 75 $200 $100 FV of outflows ¥ 1.103 = $166.375 ¥ 1.102 = 90.750 ¥ 1.101 = 220.000 ¥ 1.100 = 100.000 $577.125 Now we just enter these values into a financial calculator, along with the number of years and solve for I to get the MIRR. N = 4; PV = -300; PMT = 0; FV = 577.125; and then solve for I = MIRR = 17.77%. 128. NPV Answer: d Diff: E N Using your financial calculator, enter the following input data: CF0 = -300; CF1 = 100; CF2 = 150; CF3 = 200; CF4 = 50; I = 10; and then solve for NPV = $99.29. 129. IRR Answer: d Diff: E N Using your financial calculator, enter the following input data: CF0 = -300; CF1 = 100; CF2 = 150; CF3 = 200; CF4 = 50; and then solve for IRR = 24.79%. Chapter 10 - Page 95 130. MIRR 0 | -300 10% 1 | 100 2 | 150 3 | 200 Answer: e 4 | 50.0 220.0 181.5 133.1 584.6 Diff: M N ¥ 1.1 ¥ (1.1)2 ¥ (1.1)3 -300 MIRR = ? All the of all problem equates cash outflows are discounted back to the present. The future value cash inflows are compounded to Year 4. Then, this becomes a TVM for the calculator to determine the interest rate (MIRR) that the two values. Enter the following data in your calculator: N = 4; PV = -300; PMT = 0; FV = 584.60; and then solve for I = MIRR = 18.15%. 131. Crossover rate Year 0 1 2 3 4 Project A Cash Flow -$300 100 150 200 50 Project B Cash Flow -$200 150 100 50 50 Answer: c DCFs A - B -$100 -50 50 150 0 Diff: M N Entering these values into your financial calculator’s cash flow register, you can calculate the delta project’s IRR, 12.63%. This is the discount rate where the two projects’ NPVs are equal. 132. NPV Answer: b Diff: E N Enter all the cash flows into the cash flow register as follows: CF0 = -5000; CF1 = 5000; CF2 = 3000; CF3 = -1000; I/YR = 10; and then solve for NPV = $1,273.48 ª $1,273. 133. MIRR Step 1: Step 2: Step 3: The PV of all cash outflows is: -$5,000 + -$1,000/(1.10)3 = -$5,751.3148. The FV of all cash inflows is: $5,000(1.10)2 + $3,000(1.10) = $9,350.00. Now calculate the MIRR as follows: N = 3; PV = -5751.3148; PMT = 0; FV = 9350.00; and then solve for I = 17.58% ª 17.6% = MIRR. Answer: c Diff: T N Chapter 10 - Page 96 134.54. the NPV with a WACC of 12% is calculated as follows: NPV = –$481. I = 10. CF3 = 250. the NPV at 15% is zero. and NPV Answer: c Diff: M N Numerical solution: To have an IRR of 15%. I = 15.12)2 + $300/(1. Answer: d Diff: E N 136. CF1 = 150.7539.10) + $175/(1. CF3 = 250.7539. CF2 = 200. Missing cash flow. 135. Step 2: Calculate the NPV at a WACC of 12%: CF0 = -481. Missing cash flow. So: -X + $175/(1. 137.10)3 = $179. Numerical solution: The NPV is –$350 + $175/(1.32%. I = 10.12)3 = $27. and then solve for NPV = $57. CF4 = 100. CF1 = 150. Financial calculator solution: Enter the following data in your calculator: CF0 = -350. and then solve for NPV = $27. CF2 = 175. NPV The project NPV can be calculated by using the cash flow registers of your calculator as follows: CF0 = -500.15)2 + $300/(1. IRR Answer: a Diff: E N The project IRR can be calculated by using the cash flow registers of your calculator as follows: CF0 = -500. IRR.7539 + $175/(1. and NPV Answer: a Diff: M N If the project has a payback period of 2 years. or X = $481. CF2 = 175. CF3 = 300. CF4 = 100. and then solve for NPV = $481.11. CF2 = 200. CF3 = 300. CF1 = 175.10)2 + $300/(1. payback period.5391 ª $27. CF1 = 175. and then solve for NPV = $179.54.5391 ª $27. then X = 2 ¥ $175 = $350.78. Financial calculator solution: Step 1: Find the missing cash flow by entering the following data in your calculator: CF0 = 0. and then solve for IRR = 15. CF1 = 175. I = 12.15)3 = 0. CF2 = 175. So.11. CF3 = 300.15) + $175/(1.Page 97 .12) + $175/(1. Chapter 10 .7539. you need to enter the differences in cash flows between the two projects. and then solve for I = MIRR = 12.10)1 = $1. you need to determine the difference in the 2 projects’ cash flows. find the MIRR using these two values by entering the following data into your financial calculator: N = 4.147. CF4 = +400. Crossover rate Answer: c Diff: M N First.10)2 + $350 ¥ (1. find the PV of all cash outflows: PV = -$500 + -$300/(1. Finally.90.B 0 -150 -100 -100 400 Then.10)3 + $300 ¥ (1. and calculate the IRR: CF0 = 0. Chapter 10 .10)4 = -$704. CF1 = -150.90. CF3 = -100. and then solve for IRR = 6. Answer: b Diff: T N Second. CF2 = -100.36%. PV = -704. Time 0 1 2 3 4 Project A Cash Flow -500 150 200 250 100 Project B Cash Flow -500 300 300 350 -300 DCFs A . find the FV of all cash inflows: FV = $300 ¥ (1. PMT = 0.138. MIRR First.95%.30.30. 139.Page 98 . FV = 1147.
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