Finance Chapter 11
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 crossover rate.
False
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 costs of capital.
False
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: 11.00% Year 0 1 2 3 Cash flows -$1,000 $500 $500 $500 a. 0221.86 b. 0257.35 c. 0259.57 d. 0195.23 e. 0241.82
a. 0221.86
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.
True
The NPV method is based on the assumption that projects' cash flows are reinvested at the project's risk-adjusted cost of capital.
True
IRR
A project's internal rate of return (IRR) is the discount rate that forces the PV of its inflows to equal its cost. The IRR is an estimate of the project's rate of return, and it is comparable to the YTM on a bond. CFt is the expected cash flow in Period t and cash outflows are treated as negative cash flows. There must be a change in cash flow signs to calculate the IRR. The IRR equation is simply the NPV equation solved for the particular discount rate that causes NPV to equal zero. The IRR calculation assumes that cash flows are reinvested at the IRR. If the IRR is greater than the project's risk-adjusted cost of capital, then the project should be accepted; however, if the IRR is less than the project's risk-adjusted cost of capital, then the project should be rejected. Because of the IRR reinvestment rate assumption, when mutually exclusive projects are evaluated the IRR approach can lead to conflicting results from the NPV method. Two basic conditions can lead to conflicts between NPV and IRR: timing differences (earlier cash flows in one project vs. later cash flows in the other project) and project size (the cost of one project is larger than the other). When mutually exclusive projects are considered, then the NPV method should be used to evaluate projects.
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.
False
Payback Period
Payback period was the earliest capital budgeting selection criterion. The payback is a "break-even" calculation in the sense that if a project's cash flows come in at the expected rate, the project will break even. The shorter a project's payback, the better the project is. However, payback has 3 main disadvantages: (1) All dollars received in different years are given equal weight. (2) Cash flows beyond the payback year are ignored. (3) The payback merely indicates when a project's investment will be recovered. There is no necessary relationship between a given payback and investor wealth maximization. A variant of the regular payback is the discounted payback. Unlike regular payback, the discounted payback considers capital costs. However, the discounted payback still disregards cash flows beyond the payback year. In addition, there is no specific payback rule to justify project acceptance. Both methods provide information about liquidity and risk.
NPV
The net present value (NPV) method estimates how much a potential project will contribute to shareholders weath , and it is the best selection criterion. The larger the NPV, the more value the project adds; and added value means a higher stock price. CFt is the expected cash flow at Time t, r is the project's risk-adjusted cost of capital, and N is its life, and cash outflows are treated as negative cash flows. The NPV calculation assumes that cash inflows can be reinvested at the project's risk-adjusted WACC. When the firm is considering independent projects, if the project's NPV exceeds zero the firm should accept the project. When the firm is considering mutually exclusive projects, the firm should accept the project with the higher positive NPV.
A 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 is less than the rate at which the projects' NPV profiles cross.
True
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.
True
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.
True
Quantitative Problem: Bellinger Industries is considering two projects for inclusion in its capital budget, and you have been asked to do the analysis. Both projects' after-tax cash flows are shown on the time line below. Depreciation, salvage values, net operating working capital requirements, and tax effects are all included in these cash flows. Both projects have 4-year lives, and they have risk characteristics similar to the firm's average project. Bellinger's WACC is 10%. Project A -950 0 550 1 370 2 220 3 360 4 Project B -950 0 150 1 305 2 370 3 810 4
What is Project A's IRR? Do not round intermediate calculations. Round your answer to two decimal places. Review the IRR equation. The solution for IRR is a percentage rate not a dollar value. The IRR calculation is not dependent on the firm's WACC. Don't forget the minus sign for the Year 0 cash flow. Don't forget to include the Year 0 cash flow in your calculation. Equation solution: In order to solve by the equation, you would have to use a trial and error approach. Because this is so time consuming, the calculator and spreadsheet solutions are preferred. Calculator solution: Enter the data into your financial calculator as follows: CF0 = -950; CF1 = 550; CF2 = 370; CF3 = 220; CF4 = 360; and I/YR = 10. Solve for IRR = 24.12%. What is Project B's IRR? Do not round intermediate calculations. Round your answer to two decimal places. Equation solution: In order to solve by the equation, you would have to use a trial and error approach. Because this is so time consuming, the calculator and spreadsheet solutions are preferred. Calculator solution: Enter the data into your financial calculator as follows: CF0 = -950; CF1 = 150; CF2 = 305; CF3 = 370; CF4 = 810; and I/YR = 10. Solve for IRR = 19.63%. If the projects were independent, which project(s) would be accepted according to the IRR method? Both projects A and B If the projects were mutually exclusive, which project(s) would be accepted according to the IRR method? Project A Could there be a conflict with project acceptance between the NPV and IRR approaches when projects are mutually exclusive? Yes The reason is the NPV and IRR approaches use different reinvestment rate assumptions so there can be a conflict in the project acceptance when mutually exclusive projects are considered. Reinvestment at the WACC is the superior assumption, so when mutually exclusive projects are evaluated the NPV approach should be used for the capital budgeting decision.
Quantitative Problem: Bellinger Industries is considering two projects for inclusion in its capital budget, and you have been asked to do the analysis. Both projects' after-tax cash flows are shown on the time line below. Depreciation, salvage values, net operating working capital requirements, and tax effects are all included in these cash flows. Both projects have 4-year lives, and they have risk characteristics similar to the firm's average project. Bellinger's WACC is 8%. Project A -1,300 0 700 1 435 2 260 3 310 4 Project B -1,300 0 300 1 370 2 410 3 760 4
What is Project A's payback? Round your answer to four decimal places. Do not round your intermediate calculations. 2.635 years What is Project A's discounted payback? Round your answer to four decimal places. Do not round your intermediate calculations. 3.318 years What is Project B's payback? Round your answer to four decimal places. Do not round your intermediate calculations. 3.289 years What is Project B's discounted payback? Round your answer to four decimal places. Do not round your intermediate calculations. 3.679 years
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 -$1,025 $425 $425 $425 a. 11.29% b. 9.64% c. 11.76% d. 10.82% e. 12.58%
c. 11.76%
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: 9.50% Year 0 1 2 3 4 5 Cash flows -$1,000 $300 $300 $300 $300 $300 a. 0133.68 b. 0179.26 c. 0135.20 d. 0151.91 e. 0120.01
d. 0151.91
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. If the WACC falls, each project's IRR will increase. b. If Project S has a positive NPV, Project L must also have a positive NPV. c. If the WACC increases, each project's IRR will decrease. d. 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. e. Project S must have a higher NPV than Project L.
d. 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. Refer to the NPV profile below. "Project S must have a higher NPV than Project L" is false, because you do not know which project has the higher NPV unless you know the WACC. "If Project S has a positive NPV, Project L must also have a positive NPV" 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. "If the WACC falls, each project's IRR will increase" and "If the WACC increases, each project's IRR will decrease" are false, because IRR is independent of WACC. "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" 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.
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 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. 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%. d. The crossover rate for the two projects must be less than 12%. e. Assuming the two projects have the same scale, Project B probably has a faster payback than Project A.
e. Assuming the two projects have the same scale, Project B probably has a faster payback than Project A. We can see that "The crossover rate for the two projects must be less than 12%", "The crossover rate for the two projects must be 12%", and "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%" are all incorrect. "Assuming the timing pattern of the two projects' cash flows is the same, Project B probably has a higher cost (and larger scale)" is also incorrect, because if the projects have the same timing pattern, then A must have the higher cost. That leaves "Assuming the two projects have the same scale, Project B probably has a faster payback than Project A" as being correct, and that conclusion is confirmed by noting that since A has the steeper slope, its cash flows must come in slower, hence B has the faster cash flows and thus the faster payback.
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 $51,600, annual cash flows of $16,000 for 5 years, and an IRR of 16.65%. The projects are equally risky. Which of the following statements is CORRECT? a. 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. b. 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. c. 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. d. 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. e. 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 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. "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" is true; the other statements are false.
Quantitative Problem: Bellinger Industries is considering two projects for inclusion in its capital budget, and you have been asked to do the analysis. Both projects' after-tax cash flows are shown on the time line below. Depreciation, salvage values, net operating working capital requirements, and tax effects are all included in these cash flows. Both projects have 4-year lives, and they have risk characteristics similar to the firm's average project. Bellinger's WACC is 10%. Project A -1,080 0 660 1 345 2 190 3 240 4 Project B -1,080 0 260 1 280 2 340 3 690 4
What is Project A's NPV? Round your answer to the nearest cent. Do not round your intermediate calculations. Use the NPV equation to calculate Project A's NPV: NPV = -$1,080 + $660/1.10 + $345/(1.10)2 + $190/(1.10)3 + $240/(1.10)4 NPV = -$1,080 + $600.0000 + $285.1240 + $142.7498 + $163.9232 NPV = $111.80 Calculator solution: Enter the data into your financial calculator as follows: CF0 = -1,080; CF1 = 660; CF2 = 345; CF3 = 190; CF4 = 240; and I/YR = 10. Solve for NPV = $111.80 What is Project B's NPV? Round your answer to the nearest cent. Do not round your intermediate calculations. Equation solution: Use the NPV equation to calculate Project B's NPV: NPV = -$1,080 + $260/1.10 + $280/(1.10)2 + $340/(1.10)3 + $690/(1.10)4 NPV = -$1,080 + $236.3636 + $231.4050 + $255.4470 + $471.2793 NPV = $114.49 Calculator solution: Enter the data into your financial calculator as follows: CF0 = -1,080; CF1 = 260; CF2 = 280; CF3 = 340; CF4 = 690; and I/YR = 10. Solve for NPV = $114.49 If the projects were independent, which project(s) would be accepted? Both project A and B If the projects were mutually exclusive, which project(s) would be accepted? Project B When the projects are independent, the decision rule is to accept all positive NPV projects. When the projects are mutually exclusive, the decision rule is to accept the project with the highest positive NPV.
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: 11.50% Year 0 1 2 3 4 Cash flows -$1,000 $350 $350 $350 $350 a. 082.54 b. 064.70 c. 059.49 d. 084.03 e. 074.36
e. 074.36
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. If the WACC is 8%, Project X will have the higher NPV. b. Project X is larger in the sense that it has the higher initial cost. c. The crossover rate must be greater than 10%. d. If the WACC is 18%, Project Y will have the higher NPV. e. The crossover rate must be less than 10%.
c. The crossover rate must be greater than 10%.
A basic rule in capital budgeting is that if a project's NPV exceeds its IRR, then the project should be accepted.
False
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.
False
Other things held constant, an increase in the cost of capital will result in a decrease in a project's IRR.
False
The IRR method is based on the assumption that projects' cash flows are reinvested at the project's risk-adjusted cost of capital.
False
The phenomenon called "multiple internal rates of return" arises when two or more mutually exclusive projects that have different lives are being compared.
False
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.
False
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.
False S -1000.00 0 1400.00 1 L -1000.00 0 378.34 1 378.34 2 378.34 3 378.34 4 378.34 5 378.34 6 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.
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. The NPV profile graph is inconsistent with the statement made in the problem. b. More of Project A's cash flows occur in the later years. c. More of Project B's cash flows occur in the later years. d. The crossover rate, i.e., the rate at which Projects A and B have the same NPV, is greater than either project's IRR. e. We must have information on the cost of capital in order to determine which project has the larger early cash flows.
b. More of Project A's cash flows occur in the later years. "More of Project A's cash flows occur in the later years" 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.
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. Does not directly account for the time value of money. c. Does not provide any indication regarding a project's liquidity or risk. d. Ignores cash flows beyond the payback period. e. Does not take account of differences in size among projects.
c. Does not provide any indication regarding a project's liquidity or risk.
