Chapter 6 Investment Decision Rules 6.1 NPV and Stand-Alone Projects 1) Which of the following statements is false? A) About 75% of firms surveyed used the NPV rule for making investment decisions. B) If you are unsure of your cost of capital estimate, it is important to determine how sensitive your analysis is to errors in this estimate. C) To decide whether to invest using the NPV rule, we need to know the cost of capital. D) NPV is positive only for discount rates greater than the internal rate of return. Answer: D Diff: 1 Skill: Conceptual 2) Which of the following statements is false? A) In general, the difference between the cost of capital and the IRR is the maximum amount of estimation error in the cost of capital estimate that can exist without altering the original decision. B) The IRR can provide information on how sensitive your analysis is to errors in the estimate of your cost of capital. C) If you are unsure of your cost of capital estimate, it is important to determine how sensitive your analysis is to errors in this estimate. D) If the cost of capital estimate is more than the IRR, the NPV will be positive. Answer: D Explanation: D) If the cost of capital estimate is more than the IRR, the NPV will be negative. Diff: 1 Skill: Conceptual Chapter 6 Investment Decision Rules 105 Use the table for the question(s) below. Consider a project with the following cash flows: Year Cash Flow 0 -10,000 1 4,000 2 4,000 3 4,000 4 4,000 3) If the appropriate discount rate for this project is 15%, then the NPV is closest to: A) $6,000 B) -$867 C) $1,420 D) $867 Answer: C Explanation: C) NPV = -10,000 + 4000 / (1.15)1 + 4000 / (1.15)2 + 4000 / (1.15)3 + 4000 / (1.15)4 = 1419.91 Diff: 1 Skill: Analytical Use the table for the question(s) below. Consider the following two projects: Project Year 0 Cash Flow Year 1 Cash Flow Year 2 Cash Flow Year 3 Cash Flow Year 4 Cash Flow Discount Rate A -100 40 50 60 N/A .15 B -73 30 30 30 30 .15 4) The NPV of project A is closest to: A) 12.0 B) 12.6 C) 15.0 D) 42.9 Answer: A Explanation: A) NPV = -100 + 40 / (1.15)1 + 50 / (1.15)2 + 60 / (1.15)3 = 12.04 Diff: 1 Skill: Analytical 106 Berk/DeMarzo · Corporate Finance 5) The NPV of project B is closest to: A) 12.6 B) 23.3 C) 12.0 D) 15.0 Answer: A Explanation: A) NPV = -73+ 30 / (1.15)1 + 30 / (1.15)2 + 30 / (1.15)3 + 30 / (1.15)4 = 12.6494 Diff: 1 Skill: Analytical Use the information for the question(s) below. The Sisyphean Company is planning on investing in a new project. This will involve the purchase of some new machinery costing $450,000. The Sisyphean Company expects cash inflows from this project as detailed below: Year One Year Two Year Three Year Four $200,000 $225,000 $275,000 $200,000 The appropriate discount rate for this project is 16%. 6) The NPV for this project is closest to: A) $176,270 B) $123,420 C) $450,000 D) $179,590 Answer: A Explanation: A) NPV = -450000+ 200,000 / (1.16)1 +225000 / (1.15)2 + 275000 / (1.15)3 +200,000 / (1.15)4 = 176,265 Diff: 1 Skill: Analytical Chapter 6 Investment Decision Rules 107 Use the table for the question(s) below. Consider the following two projects: Project Year 0 C/F Year 1 C/F Year 2 C/F Year 3 C/F Year 4 C/F Year 5 C/F Year 6 C/F Year 7 C/F Discount Rate Alpha -79 20 25 30 35 40 N/A N/A 15% Beta -80 25 25 25 25 25 25 25 16% 7) The NPV for project alpha is closest to: A) $20.96 B) $16.92 C) $24.01 D) $14.41 Answer: B Explanation: B) NPV = -79+ 20 / (1.15)1 + 25 / (1.15)2 + 30 / (1.15)3 + 35 / (1.15)4 + 40 / (1.15)5= 16.92 Diff: 2 Skill: Analytical 8) The NPV for project beta is closest to: A) $24.01 B) $16.92 C) $20.96 D) $14.41 Answer: C Explanation: C) NPV = -80+ 25 / (1.16)1 + 25 / (1.16)2 + 25 / (1.16)3 + 25 / (1.16)4 + 25 / (1.16)5 + 50 / (1.16)6 + 25 / (1.16)7= 20.96 Diff: 2 Skill: Analytical 108 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below. Larry the Cucumber has been offered $14 million to star in the lead role of the next three Larry Boy adventure movies. If Larry takes this offer, he will have to forgo acting in other Veggie movies that would pay him $5 million at the end of each of the next three years. Assume Larryʹs personal cost of capital is 10% per year. 9) The NPV of Larryʹs three movie Larry Boy offer is closest to: A) 3.5 million B) -1.6 million C) 1.6 million D) -1.0 million Answer: C Explanation: C) NPV = 14 + -5 / (1.10)1 + -5 / (1.10)2 + -5 / (1.10)3 = 1.57 Diff: 2 Skill: Analytical Chapter 6 Investment Decision Rules 109 Use the information for the question(s) below. Boulderado has come up with a new composite snowboard. Development will take Boulderado four years and cost $250,000 per year, with the first of the four equal investments payable today upon acceptance of the project. Once in production the snowboard is expected to produce annual cash flows of $200,000 each year for 10 years. Boulderadoʹs discount rate is 10%. 10) The NPV for Boulderadoʹs snowboard project is closest to: A) $228,900 B) $46,900 C) $51,600 D) $23,800 Answer: C Explanation: C) CF0 = -250,000 CF1 = -250,000 CF2 = -250,000 CF3 = -250,000 CF4 = +200,000 CF5 = +200,000 CF6 = +200,000 CF7 = +200,000 CF8 = +200,000 CF9 = +200,000 CF10 = +200,000 CF11 = +200,000 CF12 = +200,000 CF13 = +200,000 I = 10 Compute NPV = 51,588 Diff: 2 Skill: Analytical 6.2 Alternative Decision Rules 1) Which of the following statements is false? A) The IRR investment rule will identify the correct decision in many, but not all, situations. B) By setting the NPV equal to zero and solving for r, we find the IRR. C) If you are unsure of your cost of capital estimate, it is important to determine how sensitive your analysis is to errors in this estimate. D) The simplest investment rule is the NPV investment rule. Answer: D Diff: 1 Skill: Conceptual 110 Berk/DeMarzo · Corporate Finance 2) Which of the following statements is false? A) It is possible that an IRR does not exist for an investment opportunity. B) If the payback period is less than a pre-specified length of time you accept the project C) The internal rate of return (IRR) investment rule is based upon the notion that if the return on other alternatives is greater than the return on the investment opportunity you should undertake the investment opportunity. D) It is possible that there is no discount rate that will set the NPV equal to zero. Answer: C Diff: 2 Skill: Conceptual 3) Which of the following statements is false? A) The payback investment rule is based on the notion that an opportunity that pays back its initial investments quickly is a good idea. B) An IRR will always exist for an investment opportunity. C) A NPV will always exist for an investment opportunity. D) In general, there can be as many IRRs as the number of times the projectʹs cash flows change sign over time. Answer: B Diff: 2 Skill: Conceptual 4) Which of the following statements is false? A) The IRR investment rule states you should turn down any investment opportunity where the IRR is less than the opportunity cost of capital. B) The IRR investment rule states that you should take any investment opportunity where the IRR exceeds the opportunity cost of capital. C) Since the IRR rule is based upon the rate at which the NPV equals zero, like the NPV decision rule, the IRR decision rule will always identify the correct investment decisions. D) There are situations in which multiple IRRs exist. Answer: C Diff: 2 Skill: Conceptual Chapter 6 Investment Decision Rules 111 5) Which of the following statements is false? A) In general, the IRR rule works for a stand-alone project if all of the projectʹs positive cash flows precede its negative cash flows. B) There is no easy fix for the IRR rule when there are multiple IRRs. C) The payback rule is primarily used because of its simplicity. D) No investment rule that ignores the set of alternative investment alternatives can be optimal. Answer: A Diff: 2 Skill: Conceptual 6) Which of the following statements is false? A) The payback rule is useful in cases where the cost of making an incorrect decision might not be large enough to justify the time required for calculating the NPV. B) The payback rule is reliable because it considers the time value of money and depends on the cost of capital. C) For most investment opportunities expenses occur initially and cash is received later. D) Fifty percent of firms surveyed reported using the payback rule for making decisions. Answer: B Diff: 2 Skill: Conceptual 7) Which of the following statements is false? A) The distinction between simply making money and creating value is the essence of the NPV calculation. B) The concept of economic profit has been popularized recently under the name Economic Value Added (EVA). C) EVA is a measure of value created over the life of a project. D) The EVA investment rule can be stated as accept any investment opportunity in which the present value of all future EVAs is positive. Answer: C Diff: 2 Skill: Conceptual 112 Berk/DeMarzo · Corporate Finance Use the table for the question(s) below. Consider a project with the following cash flows: Year Cash Flow 0 -10,000 1 4,000 2 4,000 3 4,000 4 4,000 8) Assume the appropriate discount rate for this project is 15%. The payback period for this project is closest to: A) 3 B) 2.5 C) 2 D) 4 Answer: B Explanation: B) Payback = 10000 / 4000 = 2.5 Diff: 1 Skill: Analytical 9) Assume the appropriate discount rate for this project is 15%. The IRR for this project is closest to: A) 21% B) 22% C) 15% D) 60% Answer: B Explanation: B) CF0 = -10000 CF1 = 4000 CF2 = 4000 CF3 = 4000 CF4 = 4000 Compute IRR = 21.86% Diff: 1 Skill: Analytical Chapter 6 Investment Decision Rules 113 Use the table for the question(s) below. Consider the following two projects: Project Year 0 Cash Flow Year 1 Cash Flow Year 2 Cash Flow Year 3 Cash Flow Year 4 Cash Flow Discount Rate A -100 40 50 60 N/A .15 B -73 30 30 30 30 .15 10) The payback period for project A is closest to: A) 2.0 years B) 2.4 years C) 2.5 years D) 2.2 years Answer: D Explanation: D) Payback period. It is clear that the project is not paid off after two years since we have only received 90 toward the 100 investment. To calculate the fraction of the third year, we take the $10 yet to be repaid ($100 investment - $40 (year 1) - $50 (year 2)) / $60 (cashflow in year 3) = .166667 so the payback is 2.166667 years. Diff: 2 Skill: Analytical 11) The payback period for project B is closest to: A) 2.5 years B) 2.0 years C) 2.2 years D) 2.4 years Answer: D Explanation: D) Payback = 73 / 30 = 2.43 years Diff: 1 Skill: Analytical 114 Berk/DeMarzo · Corporate Finance 12) The internal rate of return (IRR) for project A is closest to: A) 7.7% B) 21.6% C) 23.3% D) 42.9% Answer: B Explanation: B) CF0 = -100 CF1 = 40 CF2 = 50 CF3 = 60 Compute IRR = 21.64% Diff: 2 Skill: Analytical 13) The internal rate of return (IRR) for project B is closest to: A) 21.6% B) 23.3% C) 42.9% D) 7.7% Answer: B Explanation: B) CF0 = -73 CF1 = 30 CF2 = 30 CF3 = 30 CF4 = 30 Compute IRR = 23.34% Diff: 2 Skill: Analytical Chapter 6 Investment Decision Rules 115 14) Which of the following statements is correct? A) You should accept project A since its IRR 15% B) You should reject project B since its NPV 0 C) Your should accept project A since its NPV 0 D) You should accept project B since its IRR 15% Answer: A Explanation: A) NPVA = -100 + 40/(1.15)1 + 50/(1.15)2 + 60/(1.15)3 = 12.04 NPVB = -73+ 30/(1.15)1 + 30/(1.15)2 + 30/(1.15)3 + 30/(1.15)4 = 12.65 IRR A CF0 = -100 CF1 = 40 CF2 = 50 CF3 = 60 Compute IRR = 21.64% IRR B CF0 = -73 CF1 = 30 CF2 = 30 CF3 = 30 CF4 = 30 Compute IRR = 23.34% Diff: 3 Skill: Analytical 15) The maximum number of IRRs that could exist for project B is: A) 3 B) 1 C) 2 D) 0 Answer: B Diff: 1 Skill: Conceptual 116 Berk/DeMarzo · Corporate Finance Use the table for the question(s) below. Consider the following two projects: Project Year 0 C/F Year 1 C/F Year 2 C/F Year 3 C/F Year 4 C/F Year 5 C/F Year 6 C/F Year 7 C/F Discount Rate Alpha -79 20 25 30 35 40 N/A N/A 15% Beta -80 25 25 25 25 25 25 25 16% 16) The payback period for project Alpha is closest to: A) 3.2 years B) 2.9 years C) 3.1 years D) 2.6 years Answer: C Explanation: C) It is clear that the project will not be paid off until sometime after year 3. After the cashflow in year three there will still be $4 remaining to be paid back in year four (79 - 20 - 25 - 30) = 4 To find the fractional year take 4 / 35 = .1143 so payback is 3.11 years Diff: 2 Skill: Analytical 17) The payback period for project beta is closest to: A) 2.9 years B) 3.1 years C) 2.6 years D) 3.2 years Answer: D Explanation: D) Payback = 80 / 25 = 3.2 Diff: 1 Skill: Analytical Chapter 6 Investment Decision Rules 117 18) The internal rate of return (IRR) for project Alpha is closest to: A) 25.0% B) 22.2% C) 24.5% D) 22.7% Answer: D Explanation: D) CF0 = -79 CF1 = 20 CF2 = 25 CF3 = 30 CF4 = 35 CF5 = 40 Compute IRR = 22.68 Diff: 2 Skill: Analytical 19) The internal rate of return (IRR) for project Beta is closest to: A) 25.0% B) 22.7% C) 24.5% D) 22.2% Answer: C Explanation: C) PV = -80 PMT = 25 FV = 0 N = 7 Compute I = 24.52 Diff: 2 Skill: Analytical 118 Berk/DeMarzo · Corporate Finance 20) Which of the following statements is correct? A) You should invest in project Beta since NPVBeta 0 B) You should invest in project Alpha since IRRAlpha IRRBeta C) Your should invest i project Alpha since NPVAlpha 0 D) You should invest in project Beta since IRRBeta 0 Answer: A Explanation: A) NPV Alpha NPV = -79 + 20 / (1.15)1 + 25 / (1.15)2 + 30 / (1.15)3 + 35 / (1.15)4 + 40 / (1.15)5= 16.92 NPV Beta NPV = -80 + 25 / (1.16)1 + 25 / (1.16)2 + 25 / (1.16)3 + 25 / (1.16)4 + 25 / (1.16)5 + 25 / (1.16)6 + 25 / (1.16)7= 20.96 IRR Alpha CF0 = -79 CF1 = 20 CF2 = 25 CF3 = 30 CF4 = 35 CF5 = 40 Compute IRR = 22.68 IRR Beta PV = -80 PMT = 25 FV = 0 N = 7 Compute I = 24.52 Diff: 2 Skill: Analytical Chapter 6 Investment Decision Rules 119 Use the information for the question(s) below. The Sisyphean Company is planning on investing in a new project. This will involve the purchase of some new machinery costing $450,000. The Sisyphean Company expects cash inflows from this project as detailed below: Year One Year Two Year Three Year Four $200,000 $225,000 $275,000 $200,000 The appropriate discount rate for this project is 16%. 21) The payback period for this project is closest to: A) 2.1 years B) 3.0 years C) 2 years D) 2.2 years Answer: A Explanation: A) It is clear that the project will not be paid off after 2 years. The balance due after the second year is equal to 450000 - 200000 - 225000 = $25,000, so to find the fractional year we take 25000/275000 = .0909 so the payback period = 2.09 years Diff: 1 Skill: Analytical 22) The IRR for this project is closest to: A) 18.9% B) 22.7% C) 34.1% D) 39.1% Answer: C Explanation: C) CF0 = -450000 CF1 = 200000 CF2 = 225000 CF3 = 275000 CF4 = 200000 Compute IRR = 34.12% Diff: 1 Skill: Analytical 120 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below. Larry the Cucumber has been offered $14 million to star in the lead role of the next three Larry Boy adventure movies. If Larry takes this offer, he will have to forgo acting in other Veggie movies that would pay him $5 million at the end of each of the next three years. Assume Larryʹs personal cost of capital is 10% per year. 23) The IRR for Larryʹs three movie deal offer is closest to: A) 3.5% B) 1.6% C) -3.5% D) -1.6% Answer: A Explanation: A) CF0 = +14 CF1 = -5 CF2 = -5 CF3 = -5 Compute IRR = 3.53% Diff: 2 Skill: Analytical 24) Larry should: A) Reject the offer because the NPV 0 B) Accept the offer even though the IRR 10%, because the NPV 0 C) Reject the offer because the IRR 10% D) Accept the offer because the IRR 0% Answer: B Explanation: B) NPV = 14 + -5 / (1.10)1 + -5 / (1.10)2 + -5 / (1.10)3 = 1.57 CF0 = +14 CF1 = -5 CF2 = -5 CF3 = -5 Compute IRR = 3.53% Diff: 3 Skill: Analytical Chapter 6 Investment Decision Rules 121 Use the information for the question(s) below. Boulderado has come up with a new composite snowboard. Development will take Boulderado four years and cost $250,000 per year, with the first of the four equal investments payable today upon acceptance of the project. Once in production the snowboard is expected to produce annual cash flows of $200,000 each year for 10 years. Boulderadoʹs discount rate is 10%. 25) The IRR for Boulderadoʹs snowboard project is closest to: A) 10.4% B) 10.0% C) 11.0% D) 15.1% Answer: C Explanation: C) CF0 = -250,000 CF1 = -250,000 CF2 = -250,000 CF3 = -250,000 CF4 = +200,000 CF5 = +200,000 CF6 = +200,000 CF7 = +200,000 CF8 = +200,000 CF9 = +200,000 CF10 = +200,000 CF11 = +200,000 CF12 = +200,000 CF13 = +200,000 Compute IRR = 11.01% Diff: 2 Skill: Analytical 122 Berk/DeMarzo · Corporate Finance 26) Calculate the IRR for the snow board project and use it to determine he maximum deviation allowable in the cost of capital estimate that leaves the investment decision unchanged. The maximum deviation allowable is closest to: A) 11.0% B) 0.0% C) 2.5% D) 1.0% Answer: D Explanation: D) CF0 = -250,000 CF1 = -250,000 CF2 = -250,000 CF3 = -250,000 CF4 = +200,000 CF5 = +200,000 CF6 = +200,000 CF7 = +200,000 CF8 = +200,000 CF9 = +200,000 CF10 = +200,000 CF11 = +200,000 CF12 = +200,000 CF13 = +200,000 Compute IRR = 11.01% Maximum deviation = IRR - Cost of Capital = 11.0% - 10.0% = 1.0% Diff: 3 Skill: Analytical Use the information for the question(s) below. Larry the Cucumber has been offered $14 million to star in the lead role of the next three Larry Boy adventure movies. If Larry takes this offer, he will have to forgo acting in other Veggie movies that would pay him $5 million at the end of each of the next three years. Assume Larryʹs personal cost of capital is 10% per year. 27) Explain why the NPV decision rule might provide Larry with a different decision outcome than the IRR rule when evaluating Larryʹs three movie deal offer. Answer: The NPV rule will always give the right decision. In this problem, Larry starts with the cash up front, a positive cash flow, then followed by three negative cash flows. This is the exact opposite as what we want with the IRR. The IRR assumes that we start with a negative outflow followed by Inflow(s). Since we start with a positive cash inflow, the IRR rule cannot be trusted to give the correct answer. Diff: 3 Skill: Conceptual Chapter 6 Investment Decision Rules 123 28) You are considering an investment in an everlasting gobstopper machine. This machine will cost $10 million and will produce cash flows of $1 million and the end of every year forever. The appropriate cost of capital is 8%. Compute the economic value added (EVA) for this project. Calculate the PV of the EVAs for this project. Answer: The EVA in every year is: Cn - 10r = 1 - 10r Using the perpetuity formula, the present value of these EVAs is PV(EVA) = 1 - 10r (1 + Σ .08)n = 1 - 10(.08) .08 = 1 .08 - 10 = $2.5 million Diff: 2 Skill: Analytical 29) You are considering purchasing a new automated forklift system for your firmʹs warehouse. The automated forklift will cost $500,000 and generate cash flows of $125,000 per year. The forklift will depreciate evenly over the five years, at which point it must be replaced. The cost of capital is 8% per year. Based upon the EVA investment rule, should you invest in the automated forklift? Answer: The EVA is calculated as follows (all values in thousands): Year 0 1 2 3 4 5 Capital 500 400 300 200 100 0 Cash Flow 125 125 125 125 125 Capital Charge -40 -32 -24 -16 -8 Depreciation -100 -100 -100 -100 -100 EVA -15 -7 1 9 17 PV of EVA -13.89 -6.00 0.79 6.62 11.57 Sum of PV(EVA) -0.91 For example, EVA1 = $125 - 8%($500) - $100 = -15 Since the PV(EVA) = -91,000 0 you should not invest. Diff: 3 Skill: Analytical 6.3 Mutually Exclusive Investment Opportunities 1) Which of the following statements is false? A) Problems can arise using the IRR method when the mutually exclusive investments have different cash flow patterns. B) The IRR is affected by the scale of the investment opportunity. C) Multiple incremental IRRs might exist. D) The incremental IRR rule assumes that the riskiness of the two projects is the same. Answer: B Diff: 2 Skill: Conceptual 124 Berk/DeMarzo · Corporate Finance 2) Which of the following statements is false? A) The incremental IRR investment rule applies the IRR rule to the difference between the cash flows of the two mutually exclusive alternatives. B) When a manager must choose among mutually exclusive investments, the NPV rule provides a straightforward answer. C) The likelihood of multiple IRRs is greater with the regular IRR rule than with the incremental IRR rule. D) Problems can arise using the IRR method when the mutually exclusive investments have differences in scale. Answer: C Diff: 2 Skill: Conceptual 3) Which of the following statements is false? A) When using the incremental IRR rule, you must keep track of which project is the incremental project and ensure that the incremental cash flows are initially positive and then become negative. B) Picking one project over another simply because it has a larger IRR can lead to mistakes. C) Problems arise using the IRR method when the mutually exclusive investments have differences in scale. D) When the risks of two projects are different, only the NPV rule will give a reliable answer. Answer: A Diff: 2 Skill: Conceptual 4) Which of the following statements is false? A) The incremental IRR need not exist. B) If a change in the timing of the cash flows does not affect the NPV, then the change in timing will not impact the IRR. C) Although the incremental IRR rule can provide a reliable method for choosing among projects, it can be difficult to apply correctly. D) When projects are mutually exclusive, it is not enough to determine which projects have positive NPVs. Answer: B Diff: 2 Skill: Conceptual Chapter 6 Investment Decision Rules 125 5) Consider two mutually exclusive projects A B. If you subtract the cash flows of opportunity B from the cash flows of opportunity A, then you should A) take opportunity A if the regular IRR exceeds the cost of capital. B) take opportunity A if the incremental IRR exceeds the cost of capital. C) take opportunity B if the regular IRR exceeds the cost of capital. D) take opportunity B if the incremental IRR exceeds the cost of capital. Answer: B Diff: 1 Skill: Conceptual 6) You are trying to decide between three mutually exclusive investment opportunities. The most appropriate tool for identifying the correct decision is: A) NPV B) Profitability index C) IRR D) Incremental IRR Answer: A Diff: 1 Skill: Conceptual 126 Berk/DeMarzo · Corporate Finance Use the table for the question(s) below. Consider the following two projects: Project Year 0 Cash Flow Year 1 Cash Flow Year 2 Cash Flow Year 3 Cash Flow Year 4 Cash Flow Discount Rate A -100 40 50 60 N/A .15 B -73 30 30 30 30 .15 7) Assume that projects A and B are mutually exclusive. The correct investment decision and the best rational for that decision is to? A) Invest in project A since NPVB NPVA B) Invest in project B since IRRB IRRA C) Invest in project B since NPVB NPVA D) Invest in project A since NPVA 0 Answer: C Explanation: C) NPVA = -100 + 40 / (1.15)1 + 50 / (1.15)2 + 60 / (1.15)3 = 12.04 NPVB = -73+ 30 / (1.15)1 + 30 / (1.15)2 + 30 / (1.15)3 + 30 / (1.15)4 = 12.64 IRR A CF0 = -100 CF1 = 40 CF2 = 50 CF3 = 60 Compute IRR = 21.65% IRR B CF0 = -73 CF1 = 30 CF2 = 30 CF3 = 30 CF4 = 30 Compute IRR = 23.34% Diff: 3 Skill: Analytical Chapter 6 Investment Decision Rules 127 8) The incremental IRR of Project B over Project A is closest to: A) 12.6% B) 23.3% C) 1.7% D) 17.3% Answer: A Explanation: A) First we need to find the incremental cash flows by taking cashflows of A - cashflows of B. IRR A - B CF0 = (-100 - -73) = -27 CF1 = (40 - 30) = 10 CF2 = (50 - 30) = 20 CF3 = (60 - 30) = 30 CF4 = (0 - 30) = -30 Compute IRR = 12.63% Diff: 3 Skill: Analytical 9) The maximum number of incremental IRRs that could exist for project B over project A is? A) 1 B) 2 C) 0 D) 3 Answer: B Diff: 3 Skill: Conceptual 128 Berk/DeMarzo · Corporate Finance Use the table for the question(s) below. Consider the following two projects: Project Year 0 C/F Year 1 C/F Year 2 C/F Year 3 C/F Year 4 C/F Year 5 C/F Year 6 C/F Year 7 C/F Discount Rate Alpha -79 20 25 30 35 40 N/A N/A 15% Beta -80 25 25 25 25 25 25 25 16% 10) Assume that projects Alpha and Beta are mutually exclusive. The correct investment decision and the best rational for that decision is to? A) Invest in project Beta since NPVBeta 0 B) Invest in project Alpha since NPVBeta NPVAlpha C) Invest in project Beta since IRRB IRRA D) Invest in project Beta since NPVBeta NPVAlpha 0 Answer: D Explanation: D) NPV Alpha NPV = -79 + 20 / (1.15)1 + 25 / (1.15)2 + 30 / (1.15)3 + 35 / (1.15)4 + 40 / (1.15)5= 16.92 NPV Beta NPV = -80 + 25 / (1.16)1 + 25 / (1.16)2 + 25 / (1.16)3 + 25 / (1.16)4 + 25 / (1.16)5 + 50 / (1.16)6 + 25 / (1.16)7= 20.96 IRR Alpha CF0 = -79 CF1 = 20 CF2 = 25 CF3 = 30 CF4 = 35 CF5 = 40 Compute IRR = 22.68 IRR Beta PV = -80 PMT = 25 FV = 0 N = 7 Compute I = 24.52 Diff: 3 Skill: Analytical Chapter 6 Investment Decision Rules 129 11) Assume that projects Alpha and Beta are mutually exclusive. Which of the following statements is true regarding the investment decision toolsʹ suitability for deciding between projects Alpha Beta. A) The incremental IRR should not be used since the projects have different lives. B) The incremental IRR should not be used since the projects have different discount rates C) The incremental IRR should not be used since the projects have different cash flow patterns. D) Both the NPV and incremental IRR approaches are appropriate to solve this problem. Answer: B Diff: 2 Skill: Conceptual Use the table for the question(s) below. Consider two mutually exclusive projects with the following cash flows: Project C/F0 C/F1 C/F2 C/F3 C/F4 C/F5 C/F6 A $(41,215) $12,500 $14,000 $16,500 $18,000 20,000 N/A B $(46,775) $15,000 $15,000 $15,000 $15,000 $15,000 $15,000 12) You are considering using the incremental IRR approach to decide between the two mutually exclusive projects A B. How many potential incremental IRRs could there be? A) 3 B) 0 C) 2 D) 1 Answer: A Explanation: A) Project C/F0 C/F1 C/F2 C/F3 C/F4 C/F5 C/F6 A ($41,215) $12,500 $14,000 $16,500 $18,000 20,000 0 B ($46,775) $15,000 $15,000 $15,000 $15,000 $15,000 $15,000 B - A ($5,560) $2,500 $1,000 ($1,500) ($3,000) ($5,000) $15,000 Note that there are three sign changes hence there potential IRRs. Diff: 2 Skill: Analytical 130 Berk/DeMarzo · Corporate Finance 13) If the discount rate for project A is 16%, then what is the NPV for project A? Answer: NPV A CF0 = -41,215 CF1 = 12,500 CF2 = 14,000 CF3 = 16,500 CF4 = 18,000 CF5 = 20,000 I = 16 Compute NPV = $9,999.50 Diff: 2 Skill: Analytical 14) If the discount rate for project B is 15%, then what is the NPV for project B? Answer: NPV B CF0 = -46,775 CF1 = 15,000 CF2 = 15,000 CF3 = 15,000 CF4 = 15,000 CF5 = 15,000 CF6 = 15,000 Compute NPV = $9,9992.24 Diff: 2 Skill: Analytical 15) What is the incremental IRR for project B over project A? Would you feel comfortable basing your decision on the incremental IRR? Answer: Project C/F0 C/F1 C/F2 C/F3 C/F4 C/F5 C/F6 A ($41,215) $12,500 $14,000 $16,500 $18,000 20,000 0 B ($46,775) $15,000 $15,000 $15,000 $15,000 $15,000 $15,000 B - A ($5,560) $2,500 $1,000 ($1,500) ($3,000) ($5,000) $15,000 Compute IRR = 8.95%, no since there are multiple sign changes in the incremental cash flows. Diff: 2 Skill: Analytical Chapter 6 Investment Decision Rules 131 16) Assuming that the discount rate for project A is 16% and the discount rate for B is 15%, then given that these are mutually exclusive projects, which project would you take and why? Answer: NPV A CF0 = -41,215 CF1 = 12,500 CF2 = 14,000 CF3 = 16,500 CF4 = 18,000 CF5 = 20,000 I = 16 Compute NPV = $9,999.50 NPV B CF0 = -46,775 CF1 = 15,000 CF2 = 15,000 CF3 = 15,000 CF4 = 15,000 CF5 = 15,000 CF6 = 15,000 Compute NPV = $9,9992.24 Take A, since NPV of A NPV of B and both are positive. Diff: 3 Skill: Analytical 6.4 Project Selection with Resource Restraints 1) Which of the following statements is false? A) If there is a fixed supply of resource available, you should rank projects by the profitability index, selecting the project with the lowest profitability index first and working your way down the list until the resource is consumed. B) Practitioners often use the profitability index to identify the optimal combination of projects when there is a fixed supply of resources. C) If there is a fixed supply of resources available, so that you cannot undertake all possible opportunities, then simply picking the highest NPV opportunity might not lead to the best decision. D) The profitability index is calculated as the NPV divided by the resources consumed by the project. Answer: A Diff: 2 Skill: Conceptual 132 Berk/DeMarzo · Corporate Finance 2) Which of the following statements is false? A) The profitability index measures the value created in terms of NPV per unit of resource consumed. B) The profitability index is the ratio of value created to resources consumed. C) The profitability index can can be easily adapted for determining the correct investment decisions when multiple resource constraints exist. D) The profitability index measures the ʺbang for your buck.ʺ Answer: C Diff: 2 Skill: Conceptual 3) You are opening up a brand new retail strip mall. You presently have more potential retail outlets wanting to locate in your mall than you have space available. What is the most appropriate tool to use if you are trying to determine the optimal allocation of your retail space? A) IRR B) Payback period C) NPV D) Profitability index Answer: D Diff: 1 Skill: Conceptual Chapter 6 Investment Decision Rules 133 Use the table for the question(s) below. Consider a project with the following cash flows: Year Cash Flow 0 -10,000 1 4,000 2 4,000 3 4,000 4 4,000 4) Assume the appropriate discount rate for this project is 15%. The profitability index for this project is closest to: A) .14 B) .22 C) .60 D) .15 Answer: A Explanation: A) NPV = -10,000 + 4,000 (1.15)1 + 4,000 (1.15)2 + 4,000 (1.15)3 + 4,000 (1.15)4 = $1420 PI = NPV / investment = 1420 / 10000 = .1420 Diff: 1 Skill: Analytical 134 Berk/DeMarzo · Corporate Finance Use the table for the question(s) below. Consider the following two projects: Project Year 0 Cash Flow Year 1 Cash Flow Year 2 Cash Flow Year 3 Cash Flow Year 4 Cash Flow Discount Rate A -100 40 50 60 N/A .15 B -73 30 30 30 30 .15 5) The profitability index for project A is closest to: A) 0.12 B) 21.65 C) 0.17 D) 12.04 Answer: A Explanation: A) PI = NPV / Investment (or resources consumed) NPV = -100 + 40 / (1.15)1 + 50 / (1.15)2 + 60 / (1.15)3 = 12.04 So, PI = 12.04 / 100 = .1204 Diff: 2 Skill: Analytical 6) The profitability index for project B is closest to: A) 23.34 B) 12.64 C) 0.17 D) 0.12 Answer: C Explanation: C) PI = NPV / Investment (or resources consumed) NPV = -73 + 30 / (1.15)1 + 30 / (1.15)2 + 30 / (1.15)3 + 30 / (1.15)4 = 12.64 So, PI = 12.64 / 73 = .1732 Diff: 2 Skill: Analytical Chapter 6 Investment Decision Rules 135 Use the table for the question(s) below. Consider the following list of projects: Project Investment NPV A 135,000 6,000 B 200,000 30,000 C 125,000 20,000 D 150,000 2,000 E 175,000 10,000 F 75,000 10,000 G 80,000 9,000 H 200,000 20,000 I 50,000 4,000 7) Assuming that your capital is constrained, which investment tool should you use to determine the correct investment decisions? A) Profitability Index B) Incremental IRR C) NPV D) IRR Answer: A Diff: 1 Skill: Conceptual 8) Assuming that your capital is constrained, which project should you invest in first? A) Project C B) Project G C) Project B D) Project F Answer: A Explanation: A) Project Investment NPV Profitability Index Rank A 135,000 6,000 0.0444 8 B 200,000 30,000 0.1500 2 C 125,000 20,000 0.1600 1 D 150,000 2,000 0.0133 9 E 175,000 10,000 0.0571 7 F 75,000 10,000 0.1333 3 G 80,000 9,000 0.1125 4 H 200,000 20,000 0.1000 5 I 50,000 4,000 0.8000 6 Diff: 2 Skill: Analytical 136 Berk/DeMarzo · Corporate Finance 9) Assuming that your capital is constrained, what is the fifth project that you should invest in? A) Project H B) Project I C) Project B D) Project A Answer: A Explanation: A) Project Investment NPV Profitability Index Rank A 135,000 6,000 0.0444 8 B 200,000 30,000 0.1500 2 C 125,000 20,000 0.1600 1 D 150,000 2,000 0.0133 9 E 175,000 10,000 0.0571 7 F 75,000 10,000 0.1333 3 G 80,000 9,000 0.1125 4 H 200,000 20,000 0.1000 5 I 50,000 4,000 0.8000 6 Diff: 2 Skill: Analytical 10) Assuming that your capital is constrained, which project should you invest in last? A) Project A B) Project I C) Project D D) Project C Answer: C Explanation: C) Project Investment NPV Profitability Index Rank A 135,000 6,000 0.0444 8 B 200,000 30,000 0.1500 2 C 125,000 20,000 0.1600 1 D 150,000 2,000 0.0133 9 E 175,000 10,000 0.0571 7 F 75,000 10,000 0.1333 3 G 80,000 9,000 0.1125 4 H 200,000 20,000 0.1000 5 I 50,000 4,000 0.8000 6 Diff: 2 Skill: Analytical Chapter 6 Investment Decision Rules 137 11) Assuming that your capital is constrained, so that you only have $600,000 available to invest in projects, which project should you invest in and in what order? A) CBFH B) CBGF C) BCFG D) CBFG Answer: A Explanation: A) Project Investment NPV Profitability Index Rank A 135,000 6,000 0.0444 8 B 200,000 30,000 0.1500 2 C 125,000 20,000 0.1600 1 D 150,000 2,000 0.0133 9 E 175,000 10,000 0.0571 7 F 75,000 10,000 0.1333 3 G 80,000 9,000 0.1125 4 H 200,000 20,000 0.1000 5 I 50,000 4,000 0.8000 6 This is a tricky problem in that by the rankings CBFG seem optimal, but this combination leaves $120,000 on the table uninvested. By replacing G with H the full $600,000 is invested and the NPV of the combination of projects is increased by $11,000. Therefore you should invest in projects CBFH. Diff: 3 Skill: Analytical 138 Berk/DeMarzo · Corporate Finance 12) Assume that your capital is constrained, so that you only have $600,000 available to invest in projects. If you invest in the optimal combination of projects given your capital constraint, then the total NPV for all the projects you invest in will be closest to: A) $65,000 B) $80,000 C) $69,000 D) $111,000 Answer: B Explanation: B) Project Investment NPV Profitability Index Rank A 135,000 6,000 0.0444 8 B 200,000 30,000 0.1500 2 C 125,000 20,000 0.1600 1 D 150,000 2,000 0.0133 9 E 175,000 10,000 0.0571 7 F 75,000 10,000 0.1333 3 G 80,000 9,000 0.1125 4 H 200,000 20,000 0.1000 5 I 50,000 4,000 0.8000 6 This is a tricky problem in that by the rankings CBFG seem optimal, but this combination leaves $120,000 on the table uninvested. By replacing G with H the full $600,000 is invested and the NPV of the combination of projects is increased by $11,000. Therefore you should invest in projects CBFH. The NPV = NPVC + NPVB + NPVF + NPVH = 20000 + 30000 + 10000 + 20000 = $80,000. Diff: 3 Skill: Analytical Chapter 6 Investment Decision Rules 139 13) Assume that your capital is constrained, so that you only have $500,000 available to invest in projects. If you invest in the optimal combination of projects given your capital constraint, then the total NPV for all the projects you invest in will be closest to: A) $111,000 B) $69,000 C) $80,000 D) $58.000 Answer: B Explanation: B) Project Investment NPV Profitability Index Rank A 135,000 6,000 0.0444 8 B 200,000 30,000 0.1500 2 C 125,000 20,000 0.1600 1 D 150,000 2,000 0.0133 9 E 175,000 10,000 0.0571 7 F 75,000 10,000 0.1333 3 G 80,000 9,000 0.1125 4 H 200,000 20,000 0.1000 5 I 50,000 4,000 0.8000 6 The optimal combination based upon PI rankings is CBFG, so the total NPV = 20000 + 30000 + 10000 + 9000 = $69,000 Diff: 3 Skill: Analytical 140 Berk/DeMarzo · Corporate Finance Use the information for the question(s) below. The Sisyphean Company is planning on investing in a new project. This will involve the purchase of some new machinery costing $450,000. The Sisyphean Company expects cash inflows from this project as detailed below: Year One Year Two Year Three Year Four $200,000 $225,000 $275,000 $200,000 The appropriate discount rate for this project is 16%. 14) The profitability index for this project is closest to: A) .44 B) .26 C) 0.39 D) .34 Answer: C Explanation: C) PI = NPV / Investment NPV = -450000 + 200000/(1.16)1 + 225000/(1.16)2 + 275000/(1.16)3 + 2000000/(1.16)4 = 176,265 So, PI = 176265 / 450000 = 0.39 Diff: 1 Skill: Analytical Chapter 6 Investment Decision Rules 141 Use the information for the question(s) below. Your firm is preparing to open a new retail strip mall and you have multiple businesses that would like lease space in it. Each business will pay a fixed amount of rent each month plus a percentage of the gross sales generated each month. The cash flows from each of the businesses has approximately the same amount of risk. The business names, square footage requirements, and monthly expected cash flows for each of the businesses that would like to lease space in your strip mall are provided below: Business Name Square Feet Required Expected Monthly Cash Flow Videos Now 4,000 70,000 Gords Gym 3,500 52,500 Pizza Warehouse 2,500 52,500 Super Clips 1,500 25,500 30 1/2 Flavors 1,500 28,500 S-Mart 12,000 180,000 WalVerde Drugs 6,000 147,000 Multigular Wireless 1,000 22,250 15) If your new strip mall will have 15,000 square feet of retail space available to be leased, to which businesses should you lease and why? Answer: Business Name Square Feet Required Expected Monthly Cash Flow C/F per S.F. Project Rank Videos Now 4,000 70,000 17.5 5 Gords Gym 3,500 52,500 15 7 Pizza Warehouse 2,500 52,500 21 3 Super Clips 1,500 25,500 17 6 30 1/2 Flavors 1,500 28,500 19 4 S-Mart 12,000 180,000 15 8 WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 So we select projects based upon their ranking until we run out of space. The optimal combination is shown below: WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 Pizza Warehouse 2,500 52,500 21 3 30 1/2 Flavors 1,500 28,500 19 4 Videos Now 4,000 70,000 17.5 5 Total 15,000 $320,250 Diff: 3 Skill: Analytical 142 Berk/DeMarzo · Corporate Finance 16) If your new strip mall will have 16,000 square feet of retail space available to be leased, to which businesses should you lease and why? Answer: Business Name Square Feet Required Expected Monthly Cash Flow C/F per S.F. Project Rank Videos Now 4,000 70,000 17.5 5 Gords Gym 3,500 52,500 15 7 Pizza Warehouse 2,500 52,500 21 3 Super Clips 1,500 25,500 17 6 30 1/2 Flavors 1,500 28,500 19 4 S-Mart 12,000 180,000 15 8 WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 So we select projects based upon their ranking until we run out of space. This combination is shown below: WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 Pizza Warehouse 2,500 52,500 21 3 30 1/2 Flavors 1,500 28,500 19 4 Videos Now 4,000 70,000 17.5 5 Total 15,000 $320,250 But notice that this combination leaves 1,000 square feet unleased. We therefore should look to see if there is a combination that leases more space and offers a higher monthly cash flow. If we forgo renting to Videos Now and instead rent to both Super Clips and Gords Gym we will obtain a higher monthly cash flow. The optimal combination is shown below: WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 Pizza Warehouse 2,500 52,500 21 3 30 1/2 Flavors 1,500 28,500 19 4 Super Clips 1,500 25,500 17 6 Gords Gym 3,500 52,500 15 7 Total 16,000 $328,250 Diff: 3 Skill: Analytical Chapter 6 Investment Decision Rules 143 17) Consider the following list of projects: Project Investment NPV A 405,000 18,000 B 600,000 90,000 C 375,000 60,000 D 450,000 6,000 E 525,000 30,000 F 225,000 30,000 G 240,000 27,000 H 600,000 60,000 I 150,000 12,000 J 270,000 30,000 You are given a budget of only $1,800,000 to invest in projects. Which projects will you select, in what order will you select them, and why? Answer: Project Investment NPV PI Rank A 405,000 18,000 0.0444 9 B 600,000 90,000 0.1500 2 C 375,000 60,000 0.1600 1 D 450,000 6,000 0.0133 10 E 525,000 30,000 0.0571 8 F 225,000 30,000 0.1333 3 G 240,000 27,000 0.1125 4 H 600,000 60,000 0.1000 6 I 150,000 12,000 0.0800 7 J 270,000 30,000 0.1111 5 Beginning Project Cost Ending 1,800,000 C 375,000 1,425,000 1,425,000 B 600,000 825,000 825,000 F 525,000 300,000 300,000 J 270,000 30,000 Normally we would want to take projects CBFG. However, we can do better by dumping G and taking J instead. Allow it has a lower profitability index, it has a higher NPV and allows more capital to be invested. Diff: 3 Skill: Analytical
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