CHAPTER 11 THE BASICS OF CAPITAL BUDGETING (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) We point out to our students that some of the questions can best be analyzed by sketching out a NPV profile graph and then thinking about the question in relation to the graph. Please see the preface for information on the AACSB letter indicators (F, M, etc.) on the subject lines. Multiple Choice: True/False (11-1) Capital budget F I Answer: b EASY . A firm should never accept a project if its acceptance would lead to an increase in the firm's cost of capital (its WACC). a. True b. False (11-2) PV of cash flows F I Answer: b EASY . Because "present value" refers to the value of cash flows that occur at different points in time, a series of present values of cash flows should not be summed to determine the value of a capital budgeting project. a. True b. False (11-2) NPV F I Answer: b EASY . Assuming that their NPVs based on the firm's cost of capital are equal, the NPV of a project whose cash flows accrue relatively rapidly will be more sensitive to changes in the discount rate than the NPV of a project whose cash flows come in later in its life. a. True b. False (11-2) NPV and IRR F I Answer: b EASY . A basic rule in capital budgeting is that If a project's NPV exceeds its IRR, then the project should be accepted. a. True b. False (11-2) Mutually exclusive projects F I Answer: a EASY . Conflicts between two mutually exclusive projects occasionally occur, where the NPV method ranks one project higher but the IRR method puts the other one first. In theory, such conflicts should be resolved in favor of the project with the higher NPV. a. True b. False (11-2) Mutually exclusive projects F I Answer: b EASY . Conflicts between two mutually exclusive projects occasionally occur, where the NPV method ranks one project higher but the IRR method puts the other one first. In theory, such conflicts should be resolved in favor of the project with the higher IRR. a. True b. False (11-3) IRR F I Answer: a EASY . The internal rate of return is that discount rate that equates the present value of the cash outflows (or costs) with the present value of the cash inflows. a. True b. False (11-3) IRR F I Answer: b EASY . Other things held constant, an increase in the cost of capital will result in a decrease in a project's IRR. a. True b. False (11-4) Multiple IRRs F I Answer: a EASY . Under certain conditions, a project may have more than one IRR. One such condition is when, in addition to the initial investment at time = 0, a negative cash flow (or cost) occurs at the end of the project's life. a. True b. False (11-4) Multiple IRRs F I Answer: b EASY . The phenomenon called "multiple internal rates of return" arises when two or more mutually exclusive projects that have different lives are being compared. a. True b. False (11-5) Reinvestment rate assumption F I Answer: a EASY . The NPV method is based on the assumption that projects' cash flows are reinvested at the project's risk-adjusted cost of capital. a. True b. False (11-5) Reinvestment rate assumption F I Answer: b EASY . The IRR method is based on the assumption that projects' cash flows are reinvested at the project's risk-adjusted cost of capital. a. True b. False (11-5) Reinvestment rate assumption F I Answer: a EASY . The NPV method's assumption that cash inflows are reinvested at the cost of capital is generally more reasonable than the IRR's assumption that cash flows are reinvested at the IRR. This is an important reason why the NPV method is generally preferred over the IRR method. a. True b. False (11-6) Modified IRR F I Answer: a EASY . For a project with one initial cash outflow followed by a series of positive cash inflows, the modified IRR (MIRR) method involves compounding the cash inflows out to the end of the project's life, summing those compounded cash flows to form a terminal value (TV), and then finding the discount rate that causes the PV of the TV to equal the project's cost. a. True b. False (11-6) Modified IRR F I Answer: b EASY . Both the regular and the modified IRR (MIRR) methods have wide appeal to professors, but most business executives prefer the NPV method to either of the IRR methods. a. True b. False (11-6) Modified IRR F I Answer: b EASY . When evaluating mutually exclusive projects, the modified IRR (MIRR) always leads to the same capital budgeting decisions as the NPV method, regardless of the relative lives or sizes of the projects being evaluated. a. True b. False (11-8) Payback period F I Answer: a EASY . One advantage of the payback method for evaluating potential investments is that it provides information about a project's liquidity and risk. a. True b. False (11-2) Mutually exclusive projects F I Answer: b MEDIUM . When considering two mutually exclusive projects, the firm should always select the project whose internal rate of return is the highest, provided the projects have the same initial cost. This statement is true regardless of whether the projects can be repeated or not. a. True b. False (11-5) NPV vs. IRR F I Answer: b MEDIUM . The primary reason that the NPV method is conceptually superior to the IRR method for evaluating mutually exclusive investments is that multiple IRRs may exist, and when that happens, we don't know which IRR is relevant. a. True b. False (11-5) NPV vs. IRR F I Answer: b MEDIUM . The NPV and IRR methods, when used to evaluate two independent and equally risky projects, will lead to different accept/reject decisions and thus capital budgets if the projects' IRRs are greater than their cost of capital. a. True b. False (11-5) NPV vs. IRR F I Answer: b MEDIUM . The NPV and IRR methods, when used to evaluate two equally risky but mutually exclusive projects, will lead to different accept/reject decisions and thus capital budgets if the cost of capital at which the projects' NPV profiles cross is greater than the projects' cost of capital. a. True b. False (11-5) NPV vs. IRR F I Answer: a MEDIUM . No conflict will exist between the NPV and IRR methods, when used to evaluate two equally risky but mutually exclusive projects, if the projects' cost of capital exceeds the rate at which the projects' NPV profiles cross. a. True b. False (11-7) NPV profiles F I Answer: a MEDIUM . Project S has a pattern of high cash flows in its early life, while Project L has a longer life, with large cash flows late in its life. Neither has negative cash flows after Year 0, and at the current cost of capital, the two projects have identical NPVs. Now suppose interest rates and money costs decline. Other things held constant, this change will cause L to become preferred to S. a. True b. False (11-8) Discounted payback F I Answer: b MEDIUM . The regular payback method is deficient in that it does not take account of cash flows beyond the payback period. The discounted payback method corrects this fault. a. True b. False (11-9) Ranking methods F I Answer: a MEDIUM . In theory, capital budgeting decisions should depend solely on forecasted cash flows and the opportunity cost of capital. The decision criterion should not be affected by managers' tastes, choice of accounting method, or the profitability of other independent projects. a. True b. False (11-9) Ranking methods F I Answer: b MEDIUM . If you were evaluating two mutually exclusive projects for a firm with a zero cost of capital, the payback method and NPV method would always lead to the same decision on which project to undertake. a. True b. False (11-10) Small business practices F I Answer: a MEDIUM . Small businesses make less use of DCF capital budgeting techniques than large businesses. This may reflect a lack of knowledge on the part of small firms' managers, but it may also reflect a rational conclusion that the costs of using DCF analysis outweigh the benefits of these methods for very small firms. a. True b. False (Comp.) NPV and IRR F I Answer: b MEDIUM . An increase in the firm's WACC will decrease projects' NPVs, which could change the accept/reject decision for any potential project. However, such a change would have no impact on projects' IRRs. Therefore, the accept/reject decision under the IRR method is independent of the cost of capital. a. True b. False (11-7) NPV profiles F I Answer: b HARD . The IRR of normal Project X is greater than the IRR of normal Project Y, and both IRRs are greater than zero. Also, the NPV of X is greater than the NPV of Y at the cost of capital. If the two projects are mutually exclusive, Project X should definitely be selected, and the investment made, provided we have confidence in the data. Put another way, it is impossible to draw NPV profiles that would suggest not accepting Project X. a. True b. False (11-7) NPV profiles F I Answer: b HARD . Normal Projects S and L have the same NPV when the discount rate is zero. However, Project S's cash flows come in faster than those of L. Therefore, we know that at any discount rate greater than zero, L will have the higher NPV. a. True b. False (11-7) NPV profiles F I Answer: b HARD . If the IRR of normal Project X is greater than the IRR of mutually exclusive (and also normal) Project Y, we can conclude that the firm should always select X rather than Y if X has NPV > 0. a. True b. False Multiple Choice: Conceptual (11-2) NPV C I Answer: c EASY . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. A project’s NPV is found by compounding the cash inflows at the IRR to find the terminal value (TV), then discounting the TV at the WACC. b. The lower the WACC used to calculate it, the lower the calculated NPV will be. c. If a project’s NPV is less than zero, then its IRR must be less than the WACC. d. If a project’s NPV is greater than zero, then its IRR must be less than zero. e. The NPV of a relatively low-risk project should be found using a relatively high WACC. (11-3) IRR C I Answer: e EASY . Which of the following statements is CORRECT? a. One defect of the IRR method is that it does not take account of cash flows over a project’s full life. b. One defect of the IRR method is that it does not take account of the time value of money. c. One defect of the IRR method is that it does not take account of the cost of capital. d. One defect of the IRR method is that it values a dollar received today the same as a dollar that will not be received until sometime in the future. e. One defect of the IRR method is that it assumes that the cash flows to be received from a project can be reinvested at the IRR itself, and that assumption is often not valid. (11-3) IRR C I Answer: e EASY . Which of the following statements is CORRECT? a. One defect of the IRR method versus the NPV is that the IRR does not take account of cash flows over a project’s full life. b. One defect of the IRR method versus the NPV is that the IRR does not take account of the time value of money. c. One defect of the IRR method versus the NPV is that the IRR does not take account of the cost of capital. d. One defect of the IRR method versus the NPV is that the IRR values a dollar received today the same as a dollar that will not be received until sometime in the future. e. One defect of the IRR method versus the NPV is that the IRR does not take proper account of differences in the sizes of projects. (11-3) IRR C I Answer: d EASY . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. A project’s regular IRR is found by compounding the cash inflows at the WACC to find the terminal value (TV), then discounting this TV at the WACC. b. A project’s regular IRR is found by discounting the cash inflows at the WACC to find the present value (PV), then compounding this PV to find the IRR. c. If a project’s IRR is greater than the WACC, then its NPV must be negative. d. To find a project’s IRR, we must solve for the discount rate that causes the PV of the inflows to equal the PV of the project’s costs. e. To find a project’s IRR, we must find a discount rate that is equal to the WACC. (11-3) IRR C I Answer: d EASY . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. A project’s regular IRR is found by compounding the initial cost at the WACC to find the terminal value (TV), then discounting the TV at the WACC. b. A project’s regular IRR is found by compounding the cash inflows at the WACC to find the present value (PV), then discounting the TV to find the IRR. c. If a project’s IRR is smaller than the WACC, then its NPV will be positive. d. A project’s IRR is the discount rate that causes the PV of the inflows to equal the project’s cost. e. If a project’s IRR is positive, then its NPV must also be positive. (11-4) Normal vs. nonnormal CFs C I Answer: e EASY . Which of the following statements is CORRECT? a. If a project has “normal” cash flows, then its IRR must be positive. b. If a project has “normal” cash flows, then its MIRR must be positive. c. If a project has “normal” cash flows, then it will have exactly two real IRRs. d. The definition of “normal” cash flows is that the cash flow stream has one or more negative cash flows followed by a stream of positive cash flows and then one negative cash flow at the end of the project’s life. e. If a project has “normal” cash flows, then it can have only one real IRR, whereas a project with “nonnormal” cash flows might have more than one real IRR. (11-4) Normal vs. nonnormal CFs C I Answer: a EASY . Which of the following statements is CORRECT? a. Projects with “normal” cash flows can have only one real IRR. b. Projects with “normal” cash flows can have two or more real IRRs. c. Projects with “normal” cash flows must have two changes in the sign of the cash flows, e.g., from negative to positive to negative. If there are more than two sign changes, then the cash flow stream is “nonnormal.” d. The “multiple IRR problem” can arise if a project’s cash flows are “normal.” e. Projects with “nonnormal” cash flows are almost never encountered in the real world. (11-8) Payback C I Answer: d EASY . Which of the following statements is CORRECT? a. The regular payback method recognizes all cash flows over a project’s life. b. The discounted payback method recognizes all cash flows over a project’s life, and it also adjusts these cash flows to account for the time value of money. c. The regular payback method was, years ago, widely used, but virtually no companies even calculate the payback today. d. The regular payback is useful as an indicator of a project’s liquidity because it gives managers an idea of how long it will take to recover the funds invested in a project. e. The regular payback does not consider cash flows beyond the payback year, but the discounted payback overcomes this defect. (11-8) Payback C I Answer: b EASY . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. The longer a project’s payback period, the more desirable the project is normally considered to be by this criterion. b. One drawback of the payback criterion for evaluating projects is that this method does not properly account for the time value of money. c. If a project’s payback is positive, then the project should be rejected because it must have a negative NPV. d. The regular payback ignores cash flows beyond the payback period, but the discounted payback method overcomes this problem. e. If a company uses the same payback requirement to evaluate all projects, say it requires a payback of 4 years or less, then the company will tend to reject projects with relatively short lives and accept long-lived projects, and this will cause its risk to increase over time. (11-8) Payback C I Answer: b EASY . Which of the following statements is CORRECT? a. The shorter a project’s payback period, the less desirable the project is normally considered to be by this criterion. b. One drawback of the payback criterion is that this method does not take account of cash flows beyond the payback period. c. If a project’s payback is positive, then the project should be accepted because it must have a positive NPV. d. The regular payback ignores cash flows beyond the payback period, but the discounted payback method overcomes this problem. e. One drawback of the discounted payback is that this method does not consider the time value of money, while the regular payback overcomes this drawback. (Comp.) Ranking methods C I Answer: b EASY . Assume a project has normal cash flows. All else equal, which of the following statements is CORRECT? a. A project’s IRR increases as the WACC declines. b. A project’s NPV increases as the WACC declines. c. A project’s MIRR is unaffected by changes in the WACC. d. A project’s regular payback increases as the WACC declines. e. A project’s discounted payback increases as the WACC declines. (Comp.) Ranking methods C I Answer: d EASY . Which of the following statements is CORRECT? a. The internal rate of return method (IRR) is generally regarded by academics as being the best single method for evaluating capital budgeting projects. b. The payback method is generally regarded by academics as being the best single method for evaluating capital budgeting projects. c. The discounted payback method is generally regarded by academics as being the best single method for evaluating capital budgeting projects. d. The net present value method (NPV) is generally regarded by academics as being the best single method for evaluating capital budgeting projects. e. The modified internal rate of return method (MIRR) is generally regarded by academics as being the best single method for evaluating capital budgeting projects. (11-4) Normal vs. nonnormal CFs C I Answer: d EASY/MEDIUM . Which of the following statements is CORRECT? a. An NPV profile graph shows how a project’s payback varies as the cost of capital changes. b. The NPV profile graph for a normal project will generally have a positive (upward) slope as the life of the project increases. c. An NPV profile graph is designed to give decision makers an idea about how a project’s risk varies with its life. d. An NPV profile graph is designed to give decision makers an idea about how a project’s contribution to the firm’s value varies with the cost of capital. e. We cannot draw a project’s NPV profile unless we know the appropriate WACC for use in evaluating the project’s NPV. (11-2) NPV C I Answer: e MEDIUM . Which of the following statements is CORRECT? a. The NPV method was once the favorite of academics and business executives, but today most authorities regard the MIRR as being the best indicator of a project’s profitability. b. If the cost of capital declines, this lowers a project’s NPV. c. The NPV method is regarded by most academics as being the best indicator of a project’s profitability, hence most academics recommend that firms use only this one method. d. A project’s NPV depends on the total amount of cash flows the project produces, but because the cash flows are discounted at the WACC, it does not matter if the cash flows occur early or late in the project’s life. e. The NPV and IRR methods may give different recommendations regarding which of two mutually exclusive projects should be accepted, but they always give the same recommendation regarding the acceptability of a normal, independent project. (11-2) NPV C I Answer: b MEDIUM . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. A project’s NPV is generally found by compounding the cash inflows at the WACC to find the terminal value (TV), then discounting the TV at the IRR to find its PV. b. The higher the WACC used to calculate the NPV, the lower the calculated NPV will be. c. If a project’s NPV is greater than zero, then its IRR must be less than the WACC. d. If a project’s NPV is greater than zero, then its IRR must be less than zero. e. The NPVs of relatively risky projects should be found using relatively low WACCs. (11-4) Multiple IRRs C I Answer: d MEDIUM . Which of the following statements is CORRECT? a. For a project to have more than one IRR, then both IRRs must be greater than the WACC. b. If two projects are mutually exclusive, then they are likely to have multiple IRRs. c. If a project is independent, then it cannot have multiple IRRs. d. Multiple IRRs can only occur if the signs of the cash flows change more than once. e. If a project has two IRRs, then the smaller one is the one that is most relevant, and it should be accepted and relied upon. (11-5) NPV and IRR C I Answer: a MEDIUM . Which of the following statements is CORRECT? a. The NPV method assumes that cash flows will be reinvested at the WACC, while the IRR method assumes reinvestment at the IRR. b. The NPV method assumes that cash flows will be reinvested at the risk-free rate, while the IRR method assumes reinvestment at the IRR. c. The NPV method assumes that cash flows will be reinvested at the WACC, while the IRR method assumes reinvestment at the risk-free rate. d. The NPV method does not consider all relevant cash flows, particularly cash flows beyond the payback period. e. The IRR method does not consider all relevant cash flows, particularly cash flows beyond the payback period. (11-5) NPV and IRR C I Answer: e MEDIUM . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. If Project A has a higher IRR than Project B, then Project A must have the lower NPV. b. If Project A has a higher IRR than Project B, then Project A must also have a higher NPV. c. The IRR calculation implicitly assumes that all cash flows are reinvested at the WACC. d. The IRR calculation implicitly assumes that cash flows are withdrawn from the business rather than being reinvested in the business. e. If a project has normal cash flows and its IRR exceeds its WACC, then the project’s NPV must be positive. (11-5) NPV vs. IRR C I Answer: d MEDIUM . Assume that the economy is in a mild recession, and as a result interest rates and money costs generally are relatively low. The WACC for two mutually exclusive projects that are being considered is 8%. Project S has an IRR of 20% while Project L's IRR is 15%. The projects have the same NPV at the 8% current WACC. However, you believe that the economy is about to recover, and money costs and thus your WACC will also increase. You also think that the projects will not be funded until the WACC has increased, and their cash flows will not be affected by the change in economic conditions. Under these conditions, which of the following statements is CORRECT? a. You should reject both projects because they will both have negative NPVs under the new conditions. b. You should delay a decision until you have more information on the projects, even if this means that a competitor might come in and capture this market. c. You should recommend Project L, because at the new WACC it will have the higher NPV. d. You should recommend Project S, because at the new WACC it will have the higher NPV. e. You should recommend Project S because it has the higher IRR and will continue to have the higher IRR even at the new WACC. (11-5) NPV vs. IRR C I Answer: c MEDIUM . Assume that the economy is enjoying a strong boom, and as a result interest rates and money costs generally are relatively high. The WACC for two mutually exclusive projects that are being considered is 12%. Project S has an IRR of 20% while Project L's IRR is 15%. The projects have the same NPV at the 12% current WACC. However, you believe that the economy will soon fall into a mild recession, and money costs and thus your WACC will soon decline. You also think that the projects will not be funded until the WACC as decreased, and their cash flows will not be affected by the change in economic conditions. Under these conditions, which of the following statement is CORRECT? a. You should reject both projects because they will both have negative NPVs under the new conditions. b. You should delay a decision until you have more information on the projects, even if this means that a competitor might come in and capture this market. c. You should recommend Project L, because at the new WACC it will have the higher NPV. d. You should recommend Project S, because at the new WACC it will have the higher NPV. e. You should recommend Project L because it will have both a higher IRR and a higher NPV under the new conditions. (11-5) NPV vs. IRR C I Answer: e MEDIUM . Suppose a firm relies exclusively on the payback method when making capital budgeting decisions, and it sets a 4-year payback regardless of economic conditions. Other things held constant, which of the following statements is most likely to be true? a. It will accept too many short-term projects and reject too many long-term projects (as judged by the NPV). b. It will accept too many long-term projects and reject too many short-term projects (as judged by the NPV). c. The firm will accept too many projects in all economic states because a 4-year payback is too low. d. The firm will accept too few projects in all economic states because a 4-year payback is too high. e. If the 4-year payback results in accepting just the right set of projects under average economic conditions, then this payback will result in too few long-term projects when the economy is weak. (11-7) NPV profiles C I Answer: a MEDIUM . Projects A and B have identical expected lives and identical initial cash outflows (costs). However, most of one project’s cash flows come in the early years, while most of the other project’s cash flows occur in the later years. The two NPV profiles are given below: Which of the following statements is CORRECT? a. More of Project A’s cash flows occur in the later years. b. More of Project B’s cash flows occur in the later years. c. We must have information on the cost of capital in order to determine which project has the larger early cash flows. d. The NPV profile graph is inconsistent with the statement made in the problem. e. The crossover rate, i.e., the rate at which Projects A and B have the same NPV, is greater than either project’s IRR. (11-7) NPV profiles C I Answer: b MEDIUM . Projects S and L both have an initial cost of $10,000, followed by a series of positive cash inflows. Project S’s undiscounted net cash flows total $20,000, while L’s total undiscounted flows are $30,000. At a WACC of 10%, the two projects have identical NPVs. Which project’s NPV is more sensitive to changes in the WACC? a. Project S. b. Project L. c. Both projects are equally sensitive to changes in the WACC since their NPVs are equal at all costs of capital. d. Neither project is sensitive to changes in the discount rate, since both have NPV profiles that are horizontal. e. The solution cannot be determined because the problem gives us no information that can be used to determine the projects’ relative IRRs. (11-7) NPV profiles C I Answer: a MEDIUM . Projects C and D are mutually exclusive and have normal cash flows. Project C has a higher NPV if the WACC is less than 12%, whereas Project D has a higher NPV if the WACC exceeds 12%. Which of the following statements is CORRECT? a. Project D probably has a higher IRR. b. Project D is probably larger in scale than Project C. c. Project C probably has a faster payback. d. Project C probably has a higher IRR. e. The crossover rate between the two projects is below 12%. (11-8) Payback C I Answer: d MEDIUM . Four of the following statements are truly disadvantages of the regular payback method, but one is not a disadvantage of this method. Which one is NOT a disadvantage of the payback method? a. Lacks an objective, market-determined benchmark for making decisions. b. Ignores cash flows beyond the payback period. c. Does not directly account for the time value of money. d. Does not provide any indication regarding a project’s liquidity or risk. e. Does not take account of differences in size among projects. (Comp.) NPV, IRR, and MIRR C I Answer: a MEDIUM . Which of the following statements is CORRECT? a. If a project with normal cash flows has an IRR greater than the WACC, the project must also have a positive NPV. b. If Project A’s IRR exceeds Project B’s, then A must have the higher NPV. c. A project’s MIRR can never exceed its IRR. d. If a project with normal cash flows has an IRR less than the WACC, the project must have a positive NPV. e. If the NPV is negative, the IRR must also be negative. (Comp.) NPV, IRR, and MIRR C I Answer: c MEDIUM . Which of the following statements is CORRECT? a. The MIRR and NPV decision criteria can never conflict. b. The IRR method can never be subject to the multiple IRR problem, while the MIRR method can be. c. One reason some people prefer the MIRR to the regular IRR is that the MIRR is based on a generally more reasonable reinvestment rate assumption. d. The higher the WACC, the shorter the discounted payback period. e. The MIRR method assumes that cash flows are reinvested at the crossover rate. (Comp.) NPV, IRR, and MIRR C I Answer: c MEDIUM . Which of the following statements is CORRECT? a. The NPV, IRR, MIRR, and discounted payback (using a payback requirement of 3 years or less) methods always lead to the same accept/reject decisions for independent projects. b. For mutually exclusive projects with normal cash flows, the NPV and MIRR methods can never conflict, but their results could conflict with the discounted payback and the regular IRR methods. c. Multiple IRRs can exist, but not multiple MIRRs. This is one reason some people favor the MIRR over the regular IRR. d. If a firm uses the discounted payback method with a required payback of 4 years, then it will accept more projects than if it used a regular payback of 4 years. e. The percentage difference between the MIRR and the IRR is equal to the project’s WACC. (Comp.) NPV, IRR, and MIRR C I Answer: e MEDIUM . Which of the following statements is CORRECT? a. For a project with normal cash flows, any change in the WACC will change both the NPV and the IRR. b. To find the MIRR, we first compound cash flows at the regular IRR to find the TV, and then we discount the TV at the WACC to find the PV. c. The NPV and IRR methods both assume that cash flows can be reinvested at the WACC. However, the MIRR method assumes reinvestment at the MIRR itself. d. If two projects have the same cost, and if their NPV profiles cross in the upper right quadrant, then the project with the higher IRR probably has more of its cash flows coming in the later years. e. If two projects have the same cost, and if their NPV profiles cross in the upper right quadrant, then the project with the lower IRR probably has more of its cash flows coming in the later years. (Comp.) Ranking methods: NPV C I Answer: b MEDIUM . Which of the following statements is CORRECT? a. One advantage of the NPV over the IRR is that NPV takes account of cash flows over a project’s full life whereas IRR does not. b. One advantage of the NPV over the IRR is that NPV assumes that cash flows will be reinvested at the WACC, whereas IRR assumes that cash flows are reinvested at the IRR. The NPV assumption is generally more appropriate. c. One advantage of the NPV over the MIRR method is that NPV takes account of cash flows over a project’s full life whereas MIRR does not. d. One advantage of the NPV over the MIRR method is that NPV discounts cash flows whereas the MIRR is based on undiscounted cash flows. e. Since cash flows under the IRR and MIRR are both discounted at the same rate (the WACC), these two methods always rank mutually exclusive projects in the same order. (Comp.) Miscellaneous concepts C I Answer: a MEDIUM . Which of the following statements is CORRECT? a. The IRR method appeals to some managers because it gives an estimate of the rate of return on projects rather than a dollar amount, which the NPV method provides. b. The discounted payback method eliminates all of the problems associated with the payback method. c. When evaluating independent projects, the NPV and IRR methods often yield conflicting results regarding a project's acceptability. d. To find the MIRR, we discount the TV at the IRR. e. A project’s NPV profile must intersect the X-axis at the project’s WACC. (11-7) NPV profiles C I Answer: a MEDIUM/HARD . Projects S and L are equally risky, mutually exclusive, and have normal cash flows. Project S has an IRR of 15%, while Project L’s IRR is 12%. The two projects have the same NPV when the WACC is 7%. Which of the following statements is CORRECT? a. If the WACC is 10%, both projects will have positive NPVs. b. If the WACC is 6%, Project S will have the higher NPV. c. If the WACC is 13%, Project S will have the lower NPV. d. If the WACC is 10%, both projects will have a negative NPV. e. Project S’s NPV is more sensitive to changes in WACC than Project L's. (11-7) NPV profiles C I Answer: e MEDIUM/HARD . Westchester Corp. is considering two equally risky, mutually exclusive projects, both of which have normal cash flows. Project A has an IRR of 11%, while Project B's IRR is 14%. When the WACC is 8%, the projects have the same NPV. Given this information, which of the following statements is CORRECT? a. If the WACC is 13%, Project A’s NPV will be higher than Project B’s. b. If the WACC is 9%, Project A’s NPV will be higher than Project B’s. c. If the WACC is 6%, Project B’s NPV will be higher than Project A’s. d. If the WACC is greater than 14%, Project A’s IRR will exceed Project B’s. e. If the WACC is 9%, Project B’s NPV will be higher than Project A’s. (11-7) NPV profiles C I Answer: b MEDIUM/HARD . You are considering two mutually exclusive, equally risky, projects. Both have IRRs that exceed the WACC. Which of the following statements is CORRECT? Assume that the projects have normal cash flows, with one outflow followed by a series of inflows. a. If the two projects' NPV profiles do not cross, then there will be a sharp conflict as to which one should be selected. b. If the cost of capital is greater than the crossover rate, then the IRR and the NPV criteria will not result in a conflict between the projects. One project will rank higher by both criteria. c. If the cost of capital is less than the crossover rate, then the IRR and the NPV criteria will not result in a conflict between the projects. One project will rank higher by both criteria. d. For a conflict to exist between NPV and IRR, the initial investment cost of one project must exceed the cost of the other. e. For a conflict to exist between NPV and IRR, one project must have an increasing stream of cash flows over time while the other has a decreasing stream. If both sets of cash flows are increasing or decreasing, then it would be impossible for a conflict to exist, even if one project is larger than the other. (11-7) NPV profiles C I Answer: b MEDIUM/HARD . Project X’s IRR is 19% and Project Y’s IRR is 17%. The projects have the same risk and the same lives, and each has constant cash flows during each year of their lives. If the WACC is 10%, Project Y has a higher NPV than X. Given this information, which of the following statements is CORRECT? a. The crossover rate must be less than 10%. b. The crossover rate must be greater than 10%. c. If the WACC is 8%, Project X will have the higher NPV. d. If the WACC is 18%, Project Y will have the higher NPV. e. Project X is larger in the sense that it has the higher initial cost. (11-4) Multiple IRRs C I Answer: c HARD . You are on the staff of Camden Inc. The CFO believes project acceptance should be based on the NPV, but Steve Camden, the president, insists that no project should be accepted unless its IRR exceeds the project’s risk-adjusted WACC. Now you must make a recommendation on a project that has a cost of $15,000 and two cash flows: $110,000 at the end of Year 1 and -$100,000 at the end of Year 2. The president and the CFO both agree that the appropriate WACC for this project is 10%. At 10%, the NPV is $2,355.37, but you find two IRRs, one at 6.33% and one at 527%, and a MIRR of 11.32%. Which of the following statements best describes your optimal recommendation, i.e., the analysis and recommendation that is best for the company and least likely to get you in trouble with either the CFO or the president? a. You should recommend that the project be rejected because its NPV is negative and its IRR is less than the WACC. b. You should recommend that the project be rejected because, although its NPV is positive, it has an IRR that is less than the WACC. c. You should recommend that the project be accepted because (1) its NPV is positive and (2) although it has two IRRs, in this case it would be better to focus on the MIRR, which exceeds the WACC. You should explain this to the president and tell him that that the firm’s value will increase if the project is accepted. d. You should recommend that the project be rejected because (1) its NPV is positive and (2) it has two IRRs, one of which is less than the WACC, which indicates that the firm’s value will decline if the project is accepted. e. You should recommend that the project be rejected because, although its NPV is positive, its MIRR is less than the WACC, and that indicates that the firm’s value will decline if it is accepted. (11-6) MIRR C I Answer: e HARD . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one cash outflow at t = 0 followed by a series of positive cash flows. a. A project’s MIRR is always greater than its regular IRR. b. A project’s MIRR is always less than its regular IRR. c. If a project’s IRR is greater than its WACC, then its MIRR will be greater than the IRR. d. To find a project’s MIRR, we compound cash inflows at the regular IRR and then find the discount rate that causes the PV of the terminal value to equal the initial cost. e. To find a project’s MIRR, the textbook procedure compounds cash inflows at the WACC and then finds the discount rate that causes the PV of the terminal value to equal the initial cost. (11-7) NPV profiles C I Answer: e HARD . Projects S and L both have normal cash flows, and the projects have the same risk, hence both are evaluated with the same WACC, 10%. However, S has a higher IRR than L. Which of the following statements is CORRECT? a. Project S must have a higher NPV than Project L. b. If Project S has a positive NPV, Project L must also have a positive NPV. c. If the WACC falls, each project’s IRR will increase. d. If the WACC increases, each project’s IRR will decrease. e. If Projects S and L have the same NPV at the current WACC, 10%, then Project L, the one with the lower IRR, would have a higher NPV if the WACC used to evaluate the projects declined. (11-7) NPV profiles C I Answer: c HARD . Which of the following statements is CORRECT? Assume that all projects being considered have normal cash flows and are equally risky. a. If a project’s IRR is equal to its WACC, then, under all reasonable conditions, the project’s NPV must be negative. b. If a project’s IRR is equal to its WACC, then under all reasonable conditions, the project’s IRR must be negative. c. If a project’s IRR is equal to its WACC, then under all reasonable conditions the project’s NPV must be zero. d. There is no necessary relationship between a project’s IRR, its WACC, and its NPV. e. When evaluating mutually exclusive projects, those projects with relatively long lives will tend to have relatively high NPVs when the cost of capital is relatively high. (11-7) NPV profiles C I Answer: d HARD . A company is choosing between two projects. The larger project has an initial cost of $100,000, annual cash flows of $30,000 for 5 years, and an IRR of 15.24%. The smaller project has an initial cost of $50,000, annual cash flows of $16,000 for 5 years, and an IRR of 16.63%. The projects are equally risky. Which of the following statements is CORRECT? a. Since the smaller project has the higher IRR, the two projects’ NPV profiles cannot cross, and the smaller project's NPV will be higher at all positive values of WACC. b. Since the smaller project has the higher IRR, the two projects’ NPV profiles will cross, and the larger project will look better based on the NPV at all positive values of WACC. c. If the company uses the NPV method, it will tend to favor smaller, shorter-term projects over larger, longer-term projects, regardless of how high or low the WACC is. d. Since the smaller project has the higher IRR but the larger project has the higher NPV at a zero discount rate, the two projects’ NPV profiles will cross, and the larger project will have the higher NPV if the WACC is less than the crossover rate. e. Since the smaller project has the higher IRR and the larger NPV at a zero discount rate, the two projects’ NPV profiles will cross, and the smaller project will look better if the WACC is less than the crossover rate. (11-7) NPV profiles C I Answer: c HARD . McCall Manufacturing has a WACC of 10%. The firm is considering two normal, equally risky, mutually exclusive, but not repeatable projects. The two projects have the same investment costs, but Project A has an IRR of 15%, while Project B has an IRR of 20%. Assuming the projects' NPV profiles cross in the upper right quadrant, which of the following statements is CORRECT? a. Each project must have a negative NPV. b. Since the projects are mutually exclusive, the firm should always select Project B. c. If the crossover rate is 8%, Project B will have the higher NPV. d. Only one project has a positive NPV. e. If the crossover rate is 8%, Project A will have the higher NPV. (11-7) NPV profiles C I Answer: c HARD . Projects A and B are mutually exclusive and have normal cash flows. Project A has an IRR of 15% and B's IRR is 20%. The company’s WACC is 12%, and at that rate Project A has the higher NPV. Which of the following statements is CORRECT? a. The crossover rate for the two projects must be less than 12%. b. Assuming the timing pattern of the two projects’ cash flows is the same, Project B probably has a higher cost (and larger scale). c. Assuming the two projects have the same scale, Project B probably has a faster payback than Project A. d. The crossover rate for the two projects must be 12%. e. Since B has the higher IRR, then it must also have the higher NPV if the crossover rate is less than the WACC of 12%. (11-6) MIRR C I Answer: c VERY HARD . Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. A project’s MIRR is always greater than its regular IRR. b. A project’s MIRR is always less than its regular IRR. c. If a project’s IRR is greater than its WACC, then the MIRR will be less than the IRR. d. If a project’s IRR is greater than its WACC, then the MIRR will be greater than the IRR. e. To find a project’s MIRR, we compound cash inflows at the IRR and then discount the terminal value back to t = 0 at the WACC. Problems (11-2) NPV C I Answer: a EASY . Anderson Systems is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected. WACC: 9.00% Year 0 1 2 3 Cash flows -$1,000 $500 $500 $500 a. $265.65 b. $278.93 c. $292.88 d. $307.52 e. $322.90 (11-2) NPV C I Answer: c EASY . Tuttle Enterprises is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected. WACC: 11.00% Year 0 1 2 3 4 Cash flows -$1,000 $350 $350 $350 $350 a. $77.49 b. $81.56 c. $85.86 d. $90.15 e. $94.66 (11-2) NPV C I Answer: e EASY . Harry's Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected. WACC: 10.25% Year 0 1 2 3 4 5 Cash flows -$1,000 $300 $300 $300 $300 $300 a. $105.89 b. $111.47 c. $117.33 d. $123.51 e. $130.01 (11-3) IRR C I Answer: b EASY . Simms Corp. is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC or negative, in both cases it will be rejected. Year 0 1 2 3 Cash flows -$1,000 $425 $425 $425 a. 12.55% b. 13.21% c. 13.87% d. 14.56% e. 15.29% (11-3) IRR C I Answer: d EASY . Warr Company is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC or negative, in both cases it will be rejected. Year 0 1 2 3 4 Cash flows -$1,050 $400 $400 $400 $400 a. 14.05% b. 15.61% c. 17.34% d. 19.27% e. 21.20% (11-3) IRR C I Answer: a EASY . Thorley Inc. is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC or negative, in both cases it will be rejected. Year 0 1 2 3 4 5 Cash flows -$1,250 $325 $325 $325 $325 $325 a. 9.43% b. 9.91% c. 10.40% d. 10.92% e. 11.47% (11-8) Payback C I Answer: c EASY . Taggart Inc. is considering a project that has the following cash flow data. What is the project's payback? Year 0 1 2 3 Cash flows -$1,150 $500 $500 $500 a. 1.86 years b. 2.07 years c. 2.30 years d. 2.53 years e. 2.78 years (11-8) Payback C I Answer: c EASY . Resnick Inc. is considering a project that has the following cash flow data. What is the project's payback? Year 0 1 2 3 Cash flows -$350 $200 $200 $200 a. 1.42 years b. 1.58 years c. 1.75 years d. 1.93 years e. 2.12 years (11-8) Payback C I Answer: c EASY . Susmel Inc. is considering a project that has the following cash flow data. What is the project's payback? Year 0 1 2 3 Cash flows -$500 $150 $200 $300 a. 2.03 years b. 2.25 years c. 2.50 years d. 2.75 years e. 3.03 years (11-8) Payback C I Answer: c EASY . Mansi Inc. is considering a project that has the following cash flow data. What is the project's payback? Year 0 1 2 3 Cash flows -$750 $300 $325 $350 a. 1.91 years b. 2.12 years c. 2.36 years d. 2.59 years e. 2.85 years (11-2) NPV C I Answer: a EASY/MEDIUM . Cornell Enterprises is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected. WACC: 10.00% Year 0 1 2 3 Cash flows -$1,050 $450 $460 $470 a. $92.37 b. $96.99 c. $101.84 d. $106.93 e. $112.28 (11-2) NPV C I Answer: c EASY/MEDIUM . Warnock Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected. WACC: 10.00% Year 0 1 2 3 Cash flows -$950 $500 $400 $300 a. $54.62 b. $57.49 c. $60.52 d. $63.54 e. $66.72 (11-2) NPV C I Answer: e EASY/MEDIUM . Jazz World Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected. WACC: 14.00% Year 0 1 2 3 4 Cash flows -$1,200 $400 $425 $450 $475 a. $41.25 b. $45.84 c. $50.93 d. $56.59 e. $62.88 (11-2) NPV C I Answer: b EASY/MEDIUM . Barry Company is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected. WACC: 12.00% Year 0 1 2 3 4 5 Cash flows -$1,100 $400 $390 $380 $370 $360 a. $250.15 b. $277.94 c. $305.73 d. $336.31 e. $369.94 (11-3) IRR C I Answer: d EASY/MEDIUM . Datta Computer Systems is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC (and even negative), in which case it will be rejected. Year 0 1 2 3 Cash flows -$1,100 $450 $470 $490 a. 9.70% b. 10.78% c. 11.98% d. 13.31% e. 14.64% (11-3) IRR C I Answer: a EASY/MEDIUM . Simkins Renovations Inc. is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC (and even negative), in which case it will be rejected. Year 0 1 2 3 4 Cash flows -$850 $300 $290 $280 $270 a. 13.13% b. 14.44% c. 15.89% d. 17.48% e. 19.22% (11-3) IRR C I Answer: c EASY/MEDIUM . Maxwell Feed & Seed is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC (and even negative), in which case it will be rejected. Year 0 1 2 3 4 5 Cash flows -$9,500 $2,000 $2,025 $2,050 $2,075 $2,100 a. 2.08% b. 2.31% c. 2.57% d. 2.82% e. 3.10% (11-2) NPV sensitivity to WACC C I Answer: d MEDIUM . Last month, Lloyd's Systems analyzed the project whose cash flows are shown below. However, before the decision to accept or reject the project, the Federal Reserve took actions that changed interest rates and therefore the firm's WACC. The Fed's action did not affect the forecasted cash flows. By how much did the change in the WACC affect the project's forecasted NPV? Note that a project's projected NPV can be negative, in which case it should be rejected. Old WACC: 10.00% New WACC: 11.25% Year 0 1 2 3 Cash flows -$1,000 $410 $410 $410 a. -$18.89 b. -$19.88 c. -$20.93 d. -$22.03 e. -$23.13 (11-2) NPV sensitivity to WACC C I Answer: a MEDIUM . Lasik Vision Inc. recently analyzed the project whose cash flows are shown below. However, before Lasik decided to accept or reject the project, the Federal Reserve took actions that changed interest rates and therefore the firm's WACC. The Fed's action did not affect the forecasted cash flows. By how much did the change in the WACC affect the project's forecasted NPV? Note that a project's projected NPV can be negative, in which case it should be rejected. Old WACC: 8.00% New WACC: 11.25% Year 0 1 2 3 Cash flows -$1,000 $410 $410 $410 a. -$59.03 b. -$56.08 c. -$53.27 d. -$50.61 e. -$48.08 (11-6) MIRR C I Answer: e MEDIUM . Ehrmann Data Systems is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's projected MIRR can be less than the WACC (and even negative), in which case it will be rejected. WACC: 10.00% Year 0 1 2 3 Cash flows -$1,000 $450 $450 $450 a. 9.32% b. 10.35% c. 11.50% d. 12.78% e. 14.20% (11-6) MIRR C I Answer: e MEDIUM . Ingram Electric Products is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's projected MIRR can be less than the WACC (and even negative), in which case it will be rejected. WACC: 11.00% Year 0 1 2 3 Cash flows -$800 $350 $350 $350 a. 8.86% b. 9.84% c. 10.94% d. 12.15% e. 13.50% (11-6) MIRR C I Answer: b MEDIUM . Malholtra Inc. is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's projected MIRR can be less than the WACC (and even negative), in which case it will be rejected. WACC: 10.00% Year 0 1 2 3 4 Cash flows -$850 $300 $320 $340 $360 a. 14.08% b. 15.65% c. 17.21% d. 18.94% e. 20.83% (11-6) MIRR C I Answer: c MEDIUM . Hindelang Inc. is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's projected MIRR can be less than the WACC (and even negative), in which case it will be rejected. WACC: 12.25% Year 0 1 2 3 4 Cash flows -$850 $300 $320 $340 $360 a. 13.42% b. 14.91% c. 16.56% d. 18.22% e. 20.04% (11-8) Payback C I Answer: e MEDIUM . Stern Associates is considering a project that has the following cash flow data. What is the project's payback? Year 0 1 2 3 4 5 Cash flows -$1,100 $300 $310 $320 $330 $340 a. 2.31 years b. 2.56 years c. 2.85 years d. 3.16 years e. 3.52 years (11-8) Discounted payback C I Answer: b MEDIUM . Fernando Designs is considering a project that has the following cash flow and WACC data. What is the project's discounted payback? WACC: 10.00% Year 0 1 2 3 Cash flows -$900 $500 $500 $500 a. 1.88 years b. 2.09 years c. 2.29 years d. 2.52 years e. 2.78 years (11-8) Discounted payback C I Answer: d MEDIUM . Masulis Inc. is considering a project that has the following cash flow and WACC data. What is the project's discounted payback? WACC: 10.00% Year 0 1 2 3 4 Cash flows -$950 $525 $485 $445 $405 a. 1.61 years b. 1.79 years c. 1.99 years d. 2.22 years e. 2.44 years (Comp.) NPV vs. IRR C I Answer: a MEDIUM . Tesar Chemicals is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone, i.e., what's the chosen NPV versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. NPV will have no effect on the value gained or lost. WACC: 7.50% Year 0 1 2 3 4 CFS -$1,100 $550 $600 $100 $100 CFL -$2,700 $650 $725 $800 $1,400 a. $138.10 b. $149.21 c. $160.31 d. $171.42 e. $182.52 (11-5) NPV vs. IRR C I Answer: c MEDIUM/HARD . A firm is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO wants to use the IRR criterion, while the CFO favors the NPV method. You were hired to advise the firm on the best procedure. If the wrong decision criterion is used, how much potential value would the firm lose? WACC: 6.00% Year 0 1 2 3 4 CFS -$1,025 $380 $380 $380 $380 CFL -$2,150 $765 $765 $765 $765 a. $188.68 b. $198.61 c. $209.07 d. $219.52 e. $230.49 (11-5) NPV vs. IRR C I Answer: c MEDIUM/HARD . Sexton Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the one with the higher IRR will also have the higher NPV, so no value will be lost if the IRR method is used. WACC: 10.25% Year 0 1 2 3 4 CFS -$2,050 $750 $760 $770 $780 CFL -$4,300 $1,500 $1,518 $1,536 $1,554 a. $134.79 b. $141.89 c. $149.36 d. $164.29 e. $205.36 (11-5) NPV vs. IRR C I Answer: e MEDIUM/HARD . Moerdyk & Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the one with the higher IRR will also have the higher NPV, i.e., no conflict will exist. WACC: 10.00% Year 0 1 2 3 4 CFS -$1,025 $650 $450 $250 $50 CFL -$1,025 $100 $300 $500 $700 a. $5.47 b. $6.02 c. $6.62 d. $7.29 e. $7.82 (11-5) NPV vs. IRR C I Answer: b MEDIUM/HARD . Kosovski Company is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost. WACC: 7.75% Year 0 1 2 3 4 CFS -$1,050 $675 $650 CFL -$1,050 $360 $360 $360 $360 a. $11.45 b. $12.72 c. $14.63 d. $16.82 e. $19.35 (Comp.) NPV vs. MIRR C I Answer: d MEDIUM/HARD . Nast Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher MIRR rather than the one with the higher NPV, how much value will be forgone? Note that under some conditions choosing projects on the basis of the MIRR will cause $0.00 value to be lost. WACC: 8.75% Year 0 1 2 3 4 CFS -$1,100 $375 $375 $375 $375 CFL -$2,200 $725 $725 $725 $725 a. $32.12 b. $35.33 c. $38.87 d. $40.15 e. $42.16 (Comp.) NPV vs. payback C I Answer: d MEDIUM/HARD . Yonan Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost. WACC: 10.25% Year 0 1 2 3 4 CFS -$950 $500 $800 $0 $0 CFL -$2,100 $400 $800 $800 $1,000 a. $24.14 b. $26.82 c. $29.80 d. $33.11 e. $36.42 (Comp.) IRR vs. MIRR C I Answer: a HARD . Noe Drilling Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the MIRR. If the decision is made by choosing the project with the higher IRR rather than the one with the higher MIRR, how much, if any, value will be forgone, i.e., what's the NPV of the chosen project versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. MIRR will have no effect on the value lost. WACC: 7.00% Year 0 1 2 3 4 CFS -$1,100 $550 $600 $100 $100 CFL -$2,750 $725 $725 $800 $1,400 a. $185.90 b. $197.01 c. $208.11 d. $219.22 e. $230.32 CHAPTER 11 ANSWERS AND SOLUTIONS . (11-1) Capital budget F I Answer: b EASY . (11-2) PV of cash flows F I Answer: b EASY . (11-2) NPV F I Answer: b EASY . (11-2) NPV and IRR F I Answer: b EASY . (11-2) Mutually exclusive projects F I Answer: a EASY . (11-2) Mutually exclusive projects F I Answer: b EASY . (11-3) IRR F I Answer: a EASY . (11-3) IRR F I Answer: b EASY . (11-4) Multiple IRRs F I Answer: a EASY . (11-4) Multiple IRRs F I Answer: b EASY . (11-5) Reinvestment rate assumption F I Answer: a EASY . (11-5) Reinvestment rate assumption F I Answer: b EASY . (11-5) Reinvestment rate assumption F I Answer: a EASY . (11-6) Modified IRR F I Answer: a EASY . (11-6) Modified IRR F I Answer: b EASY . (11-6) Modified IRR F I Answer: b EASY . (11-8) Payback period F I Answer: a EASY . (11-2) Mutually exclusive projects F I Answer: b MEDIUM Think about the following equally risky projects. The cost of capital is WACC = 10% 0 1 2 3 4 5 6 S -1000.00 1400.00 L -1000.00 378.34 378.34 378.34 378.34 378.34 378.34 IRRS = 40.0% NPVS = $272.73 IRRL = 30.0% NPVL = $647.77 S has the higher IRR, but L has a much higher NPV and is therefore preferable. If the project could be repeated, though, S would turn out to be better—it would have both a higher NPV and IRR. . (11-5) NPV vs. IRR F I Answer: b MEDIUM . (11-5) NPV vs. IRR F I Answer: b MEDIUM . (11-5) NPV vs. IRR F I Answer: b MEDIUM . (11-5) NPV vs. IRR F I Answer: a MEDIUM . (11-7) NPV profiles F I Answer: a MEDIUM . (11-8) Discounted payback F I Answer: b MEDIUM The discounted payback corrects the fault of not considering the timing of cash flows, but it does not correct for the nonconsideration of after-payback cash flows. . (11-9) Ranking methods F I Answer: a MEDIUM . (11-9) Ranking methods F I Answer: b MEDIUM One project might have cash flows that extend well past the payback year, leading to different rankings. . (11-10) Small business practices F I Answer: a MEDIUM . (Comp.) NPV and IRR F I Answer: b MEDIUM . (11-7) NPV profiles F I Answer: b HARD Project X may have a negative NPV if r > IRR. The NPV profile line crosses the horizontal axis, and the NPV at the cost of capital is in the lower right quadrant. EMBED Word.Document.12 . (11-7) NPV profiles F I Answer: b HARD We can see from the graph that S has the higher NPV if r > 0. . (11-7) NPV profiles F I Answer: b HARD We do not know if the cost of capital is to the right or left of the crossover point. Therefore, NPVX may be either higher or lower than NPVY. . (11-2) NPV C I Answer: c EASY . (11-3) IRR C I Answer: e EASY The IRR assumes reinvestment at the IRR, and that is generally not as valid as assuming reinvestment at the WACC, as with the NPV. . (11-3) IRR C I Answer: e EASY The IRR would rank a project that cost $100 and had a 100% IRR ahead of a project that cost $1,000,000 and had an IRR of 90%. The larger project would increase the firm's value more, as the NPV would demonstrate. . (11-3) IRR C I Answer: d EASY . (11-3) IRR C I Answer: d EASY . (11-4) Normal vs. nonnormal CFs C I Answer: e EASY . (11-4) Normal vs. nonnormal CFs C I Answer: a EASY . (11-8) Payback C I Answer: d EASY Statement d is true. The payback does indicate how long it should take to recover the investment; hence, it is a measure of liquidity. . (11-8) Payback C I Answer: b EASY . (11-8) Payback C I Answer: b EASY . (Comp.) Ranking methods C I Answer: b EASY . (Comp.) Ranking methods C I Answer: d EASY . (11-4) Normal vs. nonnormal CFs C I Answer: d EASY/MEDIUM . (11-2) NPV C I Answer: e MEDIUM Statement e is correct. The others are all false. If you draw an NPV profile for one project, you will see that if the WACC is less than the IRR, the NPV will be positive. . (11-2) NPV C I Answer: b MEDIUM . (11-4) Multiple IRRs C I Answer: d MEDIUM . (11-5) NPV and IRR C I Answer: a MEDIUM . (11-5) NPV and IRR C I Answer: e MEDIUM . (11-5) NPV vs. IRR C I Answer: d MEDIUM . (11-5) NPV vs. IRR C I Answer: c MEDIUM . (11-5) NPV vs. IRR C I Answer: e MEDIUM Statement e is correct. In a weak economy, the interest rates and the WACC are likely to be low, and these conditions favor long-term projects. But the constant 4-year payback would not recognize this situation. . (11-7) NPV profiles C I Answer: a MEDIUM Statement a is true and the other statements are false. Distant cash flows are more severely penalized by high discount rates, so if the NPV profile line has a steep slope, this indicates that cash flows occur relatively late. . (11-7) NPV profiles C I Answer: b MEDIUM Statement b is true, while the other statements are false. Since Project L's undiscounted CFs are larger, they must occur in the more distant future, and since distant cash flows are impacted more by changes in the discount rate, L's NPV profile must be steeper. One can also see this in an NPV profile graph like the one in Question 52. The higher Y-axis intercept indicates more undiscounted CFs, and for the profiles to cross, the one with the higher intercept must be steeper. . (11-7) NPV profiles C I Answer: a MEDIUM The NPV profiles cross at 12%. To the left, or at lower discount rates, C has the higher NPV, so its slope is steeper, causing its profile to hit the X axis sooner. This means that C has the lower IRR , hence D has the higher IRR. . (11-8) Payback C I Answer: d MEDIUM . (Comp.) NPV, IRR, and MIRR C I Answer: a MEDIUM . (Comp.) NPV, IRR, and MIRR C I Answer: c MEDIUM . (Comp.) NPV, IRR, and MIRR C I Answer: c MEDIUM . (Comp.) NPV, IRR, and MIRR C I Answer: e MEDIUM . (Comp.) Ranking methods: NPV C I Answer: b MEDIUM Statement b is correct, and the others are false. Cash flows from a project can be used to replace funds that would be raised in the market at the WACC, so the WACC is the opportunity cost for reinvested cash flows. Since the NPV assumes reinvestment at the WACC while the IRR assumes reinvestment at the IRR, NPV is generally the better method. . (Comp.) Miscellaneous concepts C I Answer: a MEDIUM . (11-7) NPV profiles C I Answer: a MEDIUM/HARD The easiest way to think about this question is to begin by drawing an NPV profile as shown below, then using it to decide which statement is correct. Statement a is true, because both projects have an IRR greater than the WACC and thus will have a positive NPV. Statement b is false, because at 6%, the WACC is less than the crossover rate and Project L has a higher NPV than S. Statement c is false, because at 13% the WACC is greater than the crossover rate and S would have a higher NPV than L. Statement d is false, because of reasons mentioned for statement a. Statement e is false, because Project L’s NPV profile is steeper, which means Project L’s NPV is more sensitive to changes in WACC. . (11-7) NPV profiles C I Answer: e MEDIUM/HARD Statement e is true, while the others are false. . (11-7) NPV profiles C I Answer: b MEDIUM/HARD Again, it is useful to draw NPV profiles that fit the description given in the question. Any numbers that meet the criteria will do. Statement a is false, because if the profiles do not cross, then one will dominate the other, with both a higher IRR and a higher NPV at every discount rate. Statement b is true. Statement c is false. Statement d is false because a conflict can result from differences in the timing of the cash flows. Statement e is false because scale differences can result in profile crossovers and thus conflicts. . (11-7) NPV profiles C I Answer: b MEDIUM/HARD Again, it is useful to draw NPV profiles that fit the description given in the question. Any number that meets the criteria will do. As we can see from the graph, statement b is true, but the other statements are false. . (11-4) Multiple IRRs C I Answer: c HARD Statement c is true, while the other statements are false. It is not necessary to calculate the two IRRs and the MIRR as the data in the problem are correct, but we show the Excel calculations below. WACC 10% Years 0 1 2 CF -$15,000 $110,000 -$100,000 NPV $2,355.37 IRR1 6.33% IRR2 527.01% MIRR 11.32% . (11-6) MIRR C I Answer: e HARD Answer e is essentially the definition of the MIRR, hence it is correct. . (11-7) NPV profiles C I Answer: e HARD Refer to the NPV profile below. Statement a is false, because you do not know which project has the higher NPV unless you know the WACC. Statement b is false, because if the WACC is greater than IRRL but less than IRRS then Project S will have a positive NPV and Project L’s NPV will be negative. Statements c and d are false, because IRR is independent of WACC. Statement e is true, because Project S has the higher IRR, so Project L’s NPV profile is above Project S’s when the WACC is less than the crossover rate. . (11-7) NPV profiles C I Answer: c HARD Recall that the very definition of the IRR is the discount rate at which the NPV is zero. Therefore, statement c is true. All the other statements are false. . (11-7) NPV profiles C I Answer: d HARD Statement d is true; the other statements are false. . (11-7) NPV profiles C I Answer: c HARD Statement c is true, while the other statements are false. If we draw an NPV profile graph, we would see that A must have the steeper slope. If the crossover is 8% and the WACC is 10%, then B will have the higher NPV. . (11-7) NPV profiles C I Answer: c HARD Consider the following NPV profile graph: We can see that statements a, d, and e are all incorrect. Statement be is also incorrect, because if the projects have the same timing pattern, then A must have the higher cost. That leaves statement c as being correct, and that conclusion is confirmed by noting that since A have the steeper slope, its cash flows must come in slower, hence B has the faster cash flows and thus the faster payback. . (11-6) MIRR C I Answer: c VERY HARD One could prove that (1) if the IRR is equal to the WACC, then the MIRR and the IRR will be equal, (2) if the IRR is greater than the WACC, the MIRR will be less than the IRR, and (3) the MIRR will be greater than the IRR if the IRR is less than the WACC. This situation exists because the MIRR assumes reinvestment at the WACC and therefore compounds at that rate, while the IRR assumes reinvestment at the IRR itself and therefore compounds at the IRR. Therefore, if the IRR exceeds the WACC, the TV found under the IRR method will be larger, and vice versa. The IRR and the MIRR are found as the rate that causes the PV of the TV to equal the cost. Therefore, if the IRR exceeds the WACC, causing the IRR's TV to be larger, then the IRR will exceed the MIRR, and vice versa. As a result, statement c is correct—if the IRR exceeds the WACC, the IRR will exceed the MIRR. The other statements are false. Note too that this answer could also be confirmed with a numerical example. . (11-2) NPV C I Answer: a EASY WACC: 9.00% Year 0 1 2 3 Cash flows -$1,000 $500 $500 $500 NPV = $265.65 . (11-2) NPV C I Answer: c EASY WACC: 11.00% Year 0 1 2 3 4 Cash flows -$1,000 $350 $350 $350 $350 NPV = $85.86 . (11-2) NPV C I Answer: e EASY WACC: 10.25% Year 0 1 2 3 4 5 Cash flows -$1,000 $300 $300 $300 $300 $300 NPV = $130.01 . (11-3) IRR C I Answer: b EASY Year 0 1 2 3 Cash flows -$1,000 $425 $425 $425 IRR = 13.21% . (11-3) IRR C I Answer: d EASY Year 0 1 2 3 4 Cash flows -$1,050 $400 $400 $400 $400 IRR = 19.27% . (11-3) IRR C I Answer: a EASY Year 0 1 2 3 4 5 Cash flows -$1,250 $325 $325 $325 $325 $325 IRR = 9.43% . (11-8) Payback C I Answer: c EASY Year 0 1 2 3 Cash flows -$1,150 $500 $500 $500 Cumulative CF -$1,150 -$650 -$150 $350 Payback = 2.30 - - - 2.30 Payback = last year before cum CF turns positive + abs. val. last neg. cum CF/CF in payback year. . (11-8) Payback C I Answer: c EASY Year 0 1 2 3 Cash flows -$350 $200 $200 $200 Cumulative CF -$350 -$150 $50 $250 Payback = 1.75 - - 1.75 - Payback = last year before cum CF turns positive + abs. val. last neg. cum CF/CF in payback year. . (11-8) Payback C I Answer: c EASY Year 0 1 2 3 Cash flows -$500 $150 $200 $300 Cumulative CF -$500 -$350 -$150 $150 Payback = 2.50 - - - 2.50 Payback = last year before cum CF turns positive + abs. val. last neg. cum CF/CF in payback year. . (11-8) Payback C I Answer: c EASY Year 0 1 2 3 Cash flows -$750 $300 $325 $350 Cumulative CF -$750 -$450 -$125 $225 Payback = 2.36 - - - 2.36 Payback = last year before cum CF turns positive + abs. val. last neg. cum CF/CF in payback year. . (11-2) NPV C I Answer: a EASY/MEDIUM WACC: 10.00% Year 0 1 2 3 Cash flows -$1,050 $450 $460 $470 NPV =$92.37 . (11-2) NPV C I Answer: c EASY/MEDIUM WACC: 10.00% Year 0 1 2 3 Cash flows -$950 $500 $400 $300 NPV = $60.52 . (11-2) NPV C I Answer: e EASY/MEDIUM WACC: 14.00% Year 0 1 2 3 4 Cash flows -$1,200 $400 $425 $450 $475 NPV = $62.88 . (11-2) NPV C I Answer: b EASY/MEDIUM WACC: 12.00% Year 0 1 2 3 4 5 Cash flows -$1,100 $400 $390 $380 $370 $360 NPV = $277.94 . (11-3) IRR C I Answer: d EASY/MEDIUM Year 0 1 2 3 Cash flows -$1,100 $450 $470 $490 IRR = 13.31% . (11-3) IRR C I Answer: a EASY/MEDIUM Year 0 1 2 3 4 Cash flows -$850 $300 $290 $280 $270 IRR = 13.13% . (11-3) IRR C I Answer: c EASY/MEDIUM Year 0 1 2 3 4 5 Cash flows -$9,500 $2,000 $2,025 $2,050 $2,075 $2,100 IRR = 2.57% . (11-2) NPV sensitivity to WACC C I Answer: d MEDIUM Old WACC: 10.00% New WACC: 11.25% Year 0 1 2 3 Cash flows -$1,000 $410 $410 $410 Old NPV = $19.61 New NPV = -$2.42 Change = -$22.03 . (11-2) NPV sensitivity to WACC C I Answer: a MEDIUM Old WACC: 8.00% New WACC: 11.25% Year 0 1 2 3 Cash flows -$1,000 $410 $410 $410 Old NPV = $56.61 New NPV = -$2.42 Change = -$59.03 . (11-6) MIRR C I Answer: e MEDIUM WACC: 10.00% Year 0 1 2 3 Cash flows -$1,000 $450 $450 $450 Compounded values, FVs $544.50 $495.00 $450.00 TV = Sum of compounded inflows: $1,489.50 MIRR = 14.20% Found as discount rate that equates PV of TV to cost, discounted back 3 years @ WACC MIRR = 14.20% Alternative calculation, using Excel's MIRR function . (11-6) MIRR C I Answer: e MEDIUM WACC: 11.00% Year 0 1 2 3 Cash flows -$800 $350 $350 $350 Compounded values, FVs $431.24 $388.50 $350.00 TV = Sum of compounded inflows: $1,169.74 MIRR = 13.50% Found as discount rate that equates PV of TV to cost, discounted back 3 years @ WACC MIRR = 13.50% Alternative calculation, using Excel's MIRR function . (11-6) MIRR C I Answer: b MEDIUM WACC: 10.00% Year 0 1 2 3 4 Cash flows -$850 $300 $320 $340 $360 Compounded values $399.30 $387.20 $374.00 $360.00 TV = Sum of comp'ed inflows: $1,520.50 MIRR = 15.65% Found as discount rate that equates PV of TV to cost, discounted back 4 years @ WACC MIRR = 15.65% Alternative calculation, using Excel's MIRR function . (11-6) MIRR C I Answer: c MEDIUM WACC: 12.25% Year 0 1 2 3 4 Cash flows -$850 $300 $320 $340 $360 Compounded values $424.31 $403.20 $381.65 $360.00 TV = Sum of comp'ed inflows: $1,569.16 MIRR = 16.56% Found as discount rate that equates PV of TV to cost, discounted back 4 years @ WACC MIRR = 16.56% Alternative calculation, using Excel's MIRR function . (11-8) Payback C I Answer: e MEDIUM Year 0 1 2 3 4 5 Cash flows -$1,100 $300 $310 $320 $330 $340 Cumulative CF -$1,100 -$800 -$490 -$170 $160 $500 Payback = 3.52 - - - - 3.52 - . (11-8) Discounted payback C I Answer: b MEDIUM WACC: 10.00% Year 0 1 2 3 Cash flows -$900 $500 $500 $500 PV of CFs -$900 $455 $413 $376 Cumulative CF -$900 -$445 -$32 $343 Payback = 2.09 - - - 2.09 . (11-8) Discounted payback C I Answer: d MEDIUM WACC: 10.00% Year 0 1 2 3 4 Cash flows -$950 $525 $485 $445 $405 PV of CFs -$950 $477 $401 $334 $277 Cumulative CF -$950 -$473 -$72 $262 $539 Payback = 2.22 - - - 2.22 - . (Comp.) NPV vs. IRR C I Answer: a MEDIUM First, recognize that NPV makes theoretically correct capital budgeting decisions, so the highest NPV tells us how much value could be added. We calculate the two projects' NPVs, IRRs, and MIRRs, but the MIRR information is not needed for this problem. We then see what NPV would result if the decision were based on the IRR (and the MIRR). The difference between the NPV is the loss incurred if the IRR criterion is used. Of course, it's possible that IRR could choose the correct project. WACC: 7.5000% Year 0 1 2 3 4 TV MIRR CFS -$1,100 $550 $600 $100 $100 Compounded CFs: 673.77 686.94 107.00 100.00 $1,567.71 9.5469% CFL -$2,700 $650 $725 $800 $1,400 Compounded CFs: 796.28 830.05 856.00 1400.00 $3,882.33 9.6663% MIRR, L = 9.67% IRR, L = 10.71181% NPV, L = $224.3065 MIRR, S = 9.55% IRR, S = 12.24157% NPV, S = $86.2036 MIRR Choice: L IRR Choice: S NPV Choice: L NPV using MIRR: $224.31 NPV using IRR: $86.20 NPV using NPV: $224.31 Lost value using IRR versus MIRR: $138.10 Loss below: 7.9850% Lost value using MIRR versus NPV: $0.00 Loss below: 10.1638% Lost value using IRR versus NPV: $138.10 Loss below: 10.1638% . (11-5) NPV vs. IRR C I Answer: c MEDIUM/HARD WACC: 6.000% Year 0 1 2 3 4 CFS -$1,025 $380 $380 $380 $380 CFL -$2,150 $765 $765 $765 $765 IRR, L 15.781% IRR, S 17.861% NPV, L $500.81 $209.07 NPV, S $291.74 $209.07 = Value lost if use the IRR criterion S L 291.7 500.8 0% 495.0 910.0 2% 421.9 762.9 4% 354.4 626.9 6% 291.7 500.8 8% 233.6 383.8 10% 179.5 274.9 12% 129.2 173.6 13.860% 85.4 85.4 14% 82.2 79.0 16% 38.3 -9.4 18% -2.8 -92.1 20% -41.3 -169.6 22% -77.4 -242.4 24% -111.4 -310.7 Note that the WACC is constrained to be less than the crossover point, so there is a conflict between NPV and IRR, hence following the IRR rule results in a loss of value. In the next problem the constraint is relaxed. Graphs such as this one could be created for the following problems, but we do not show them. . (11-5) NPV vs. IRR C I Answer: c MEDIUM/HARD WACC: 10.25% 13.275% = crossover Year 0 1 2 3 4 CFS -$2,050 $750 $760 $770 $780 CFL -$4,300 $1,500 $1,518 $1,536 $1,554 IRR, L 15.58% IRR, S 18.06% NPV, L $507.40 NPV, S $358.05 $149.36 = Value lost if use the IRR criterion Note that the WACC is not constrained to be less than the crossover point, so there may not be a conflict between NPV and IRR, hence following the IRR rule may not result in a loss of value. In that case, the correct answer is $0.00. . (11-5) NPV vs. IRR C I Answer: e MEDIUM/HARD WACC: 10.000% 10.549% = crossover Year 0 1 2 3 4 CFS -$1,025 $650 $450 $250 $50 CFL -$1,025 $100 $300 $500 $700 IRR, L 15.66% IRR, S 19.86% NPV, L $167.61 NPV, S $159.79 $7.82 = Value lost if use the IRR criterion Note that the WACC is not constrained to be less than the crossover point, so there may not be a conflict between NPV and IRR, hence following the IRR rule may not result in a loss of value. In that case, the correct answer is $0.00. . (11-5) NPV vs. IRR C I Answer: b MEDIUM/HARD WACC: 7.75% 8.994% = crossover Year 0 1 2 3 4 CFS -$1,050 $675 $650 CFL -$1,050 $360 $360 $360 $360 IRR, L 13.95% IRR, S 17.13% NPV, L $149.03 NPV, S $136.31 $12.72 = Value lost if use the IRR criterion Note that the WACC is not constrained to be less than the crossover point, so there may not be a conflict between NPV and IRR, hence following the IRR rule may not result in a loss of value. In that case, the correct answer is $0.00. . (Comp.) NPV vs. MIRR C I Answer: d MEDIUM/HARD WACC: 8.750% Crossover = 10.396% Year 0 1 2 3 4 TV MIRR CFS -$1,100 $375 $375 $375 $375 482.30 443.50 407.81 375.00 $1,708.61 11.64% CFL -$2,200 $725 $725 $725 $725 932.45 857.43 788.44 725.00 $3,303.31 10.70% MIRR, L 10.70% MIRR, S 11.64% NPV, L $161.74 NPV, S $121.59 $40.15 = Value lost if use the MIRR criterion Note that the WACC is not constrained to be less than the crossover point, so there may not be a conflict between NPV and IRR, hence following the MIRR rule may not result in a loss of value. In that case, the correct answer is $0.00. . (Comp.) NPV vs. payback C I Answer: d MEDIUM/HARD WACC: 10.250% Crossover = 11.093% Year 0 1 2 3 4 CFS -$950 $500 $800 $0 $0 CFL -$2,100 $400 $800 $800 $1,000 Cumulative CF, S -$950 -$450 $350 $350 $350 Cumulative CF, L -$2,100 -$1,700 -$900 -$100 $900 Payback S = 1.56 - - 1.56 - - Payback L = 3.10 - - - - 3.10 NPV, L = $194.79 NPV, S = $161.68 Value lost $33.11 Note that the WACC is not constrained to be less than the crossover point, so there may not be a conflict between NPV and payback, hence following the IRR rule may not result in a loss of value, so the correct answer may be $0.00. . (Comp.) IRR vs. MIRR C I Answer: a HARD First, recognize that NPV makes theoretically correct capital budgeting decisions, so the higher NPV tells us how much value could be added. We calculate the two projects' NPVs, IRRs, and MIRRs. We then see what NPV would result if the decision were based on the IRR and the MIRR. Under some conditions, MIRR will choose the project with the higher NPV while the IRR chooses the lower NPV project. Then, the difference between the NPVs is the loss incurred if the IRR criterion is used. Of course, it's possible that both the MIRR and the IRR could choose the wrong project; with this set of cash flows, that happens at WACC > 8.62133%. WACC: 7.00% Year 0 1 2 3 4 TV IRR/MIRR CFS -$1,100 $550 $600 $100 $100 12.2416% Compounded CFs: 673.77 686.94 107.00 100.00 $1,567.71 9.2618% CFL -$2,750 $725 $725 $800 $1,400 10.9810% Compounded CFs: 888.16 830.05 856.00 1400.00 $3,974.21 9.6426% -0.3808% MIRR, S = 9.2618% IRR, S = 12.2416% NPV, S = $96.00 MIRR, L = 9.6426% IRR, L = 10.9810% NPV, L = $281.90 MIRR Choice: L IRR Choice: S NPV Choice: L NPV based on MIRR: $281.90 NPV based on IRR: $96.00 NPV using NPV: $281.90 Lost value using IRR versus MIRR: NPVl – NPVs = $185.90 Loss below: 8.6213% Page PAGE 438 True/False Chapter 11: Capital Budgeting Chapter 11: Capital Budgeting True/False Page PAGE 437