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Capital Budgeting And Project Evaluation: NPV, IRR, MIRR, And Ethical Considerations

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    Capital Budgeting and Project Evaluation: NPV, IRR, MIRR, and Ethical Considerations 1.) IRR Project K costs $46,145.75, its expected cash inflows are $10,000 per year for 9 years, and its WACC is 9%. What is the project's IRR? Round your answer to two decimal places. % Using financial calculator CF = - 46,145.75, and CF1 – CF9 = 10,000; IRR = 15.9624 % ~ 16% 2.) Capital budgeting criteria A firm with a 13% WACC is evaluating two projects for this year's capital budget. After - tax cash flows, including depreciation, are as follows: 0 1 2 3 4 5 Project A - $30,000 $10,000 $10,000 $10,000 $10,000 $10,000 Project B - $90,000 $28,000 $28,000 $28,000 $28,000 $28,000 Calculate MIRR for each project. Round your answers to two decimal places. Project A _______ % Project B _______ % Terminal value of A = TV A = 10,000(1.13) 4 + 10,000(1.13) 3 + 10,000(1.13) 2 + 10,000(1.13) 1 + 10,000 = 16,304.74 + 14,428.97 + 12769 + 11,300 +10,000 = 64,802.71 Terminal value of B = TV B = 28,000(1.13) 4 + 28,000(1.13) 3 + 28,000(1.13) 2 + 28,000(1.13) 1 + 28,000 = 181,447.58 MIRR A = 30,000 (1 + MIRR) 5 = TV A = 30,000 (1 + MIRR) 5 = 64,802.71 = (1 + MIRR) 5 = 64,802.71/30,000 = (1 + MIRR) 5 = 2.16 = 1 + MIRR = 1.16651 = MIRR = 0.16651 or 16.65% MIRR B = 9 0,000(1 + MIRR) 5 = TV B = 9 0,000(1 + MIRR) 5 = 181,447.58 = (1 + MIRR) 5 = 181,447.58/90,000 = (1 + MIRR) 5 = 2. 0161 = 1 + MIRR = 1.1505 = MIRR = 0.1 505 or 15.05 % 3.) Capital budgeting criteria: ethical considerations A mining company is considering a new project. Because the mine has received a permit, the project would be legal; but it would cause significant harm to a nearby river. The firm could spend an additional $9.66 million at Year 0 to mitigate the environmental problem, but it would not be required to do so. Developing the mine (without mitigation) would cost $57 million, and the expected net cash inflows would be $19 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $20 million. The risk adjusted WACC is 10%. Calculate the NPV and IRR with mitigation. Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55. NPV $______ million CF 0 = - ($57 + $9.66) million = - $66.66 million [initial investment with mitigation]

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    CF 1 – CF 5 = $19 million WACC = 10% Using financial calculator we have NPV = 5.3649 million and IRR = 13.10% 4.) Capital budgeting criteria: ethical considerations An electric utility is considering a new power plant in northern Arizona. Power from the plant would be sold in the Phoenix area, where it is badly needed. Because the firm has received a permit, the plant would be legal; but it would cause some air pollution. The company could spend an additional $40 million at Year 0 to mitigate the environmental problem, but it would not be required to do so. The plant without mitigation would cost $270.46 million, and the expected cash inflows would be $90 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be $93.41 million. Unemployment in the area where the plant would be built is high, and the plant would provide about 350 good jobs. The risk adjusted WACC is 19%. Calculate the NPV and IRR with mitigation. (Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55.) IRR _______ % CF 0 = - ( $270.46 + $40 ) million = - $ 310.46 million [initial investment with mitigation] CF 1 – CF 5 = $93.41 million WACC = 19 % Using financial calculator we have NPV = - 24.84 million and IRR = 15.36 % Calculate the NPV and IRR without mitigation. Round your answers to two decimal places. Enter your answer for NPV in millions. For example, an answer of $10,550,000 should be entered as 10.55. IRR _______ % CF 0 = - $270.46 million CF 1 – CF 5 = $90 million WACC = 19% Using financial calculator we have NPV = 4.72 million and IRR = 19.78% 5.) IRR and NPV A company is analyzing two mutually exclusive projects, S and L, with the following cash flows: 0 1 2 3 4 Project S - $1,000 $875.10 $260 $10 $5 Project L - $1,000 $0 $260 $400 $771.81 The company's WACC is 8.0%. What is the IRR of the better project? ( Hint : The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places. ________% Project S WACC = 8% CF 0 = - $1,000 CF 1 = $875.10 CF 2 = $260 CF 3 = $10 CF 4 = $5 Using financial calculator we have NPV S = $44.8 and IRR S = 11.9 % TV S = 875.10(1.08) 3 + 260(1.08) 2 + 10(1.08) + 5 = 1102.374 + 303.264+ 10.8 + 5 = 1421.44

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    MIRR S = 9.19% Project L WACC = 8% CF 0 = - $1,000 CF 1 = $ 0 CF 2 = $260 CF 3 = $400 CF 4 = $771.81 Using financial calculator we have NPV L = $ 107.74 and IRR L = 11.4 % TV L = 0(1.08) 3 + 260(1.08) 2 + 400(1.08) + 771.81 = 0 + 303.264 + 432 + 771.81 = 1507.07 MIRR L = 10.8 % Since project L has higher MIRR and NPV, project L should be selected. IRR of better project (project L) is 11. 4% 6.) NPV A project has annual cash flows of $6,500 for the next 10 years and then $5,000 each year for the following 10 years. The IRR of this 20 - year project is 13.85%. If the firm's WACC is 10%, what is the project's NPV? (Round your answer to the nearest cent.) $_______ At IRR, the present value of cost is present value of revenue. The PV of revenue is, PV = 6 , 500{1/(1+0.1385) 1 + 1/(1+0.1385) 2 +….+ 1/(1+0.1385) 10 } + 5 , 000{1/(1+0.1385) 11 + 1/(1+0.1385) 12 +….+ 1/(1+0.1385) 20 } = 6 , 500 (5.24679) + 5 , 000 (1.434048) = 34 , 104.135 + 7 , 170.24 = 41 , 274.375 Assuming that the cost is incurred at the beginning. Thus NPV at 10% is NPV = - 41 , 274.375 + 6 , 500{1/(1+0.1) 1 + 1/(1+0.1) 2 +….+ 1/(1+0.1) 10 } + 5 , 000{1/(1+0.1) 11 + 1/(1+0.1) 12 +….+ 1/(1+0.1) 20 } = - 41 , 274.375 + 6 , 500 (6.144567) + 5 , 000 (2.368996) = - 41 , 274.375 + 39 , 939.686 + 11 , 844.98 = 10 , 510.29 NPV = %10,510.29 7.) Project cash flow Eisenhower Communications is trying to estimate the first - year net operating cash flow (at Year 1) for a proposed project. The financial staff has collected the following information on the project: Sales revenues $5 million Operating costs (excluding depreciation) 3.5 million Depreciation 1 million Interest expense 1 million

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    The company has a 40% tax rate, and its WACC is 11%. (Write out your answers completely. For example, 13 million should be entered as 13,000,000.) What is the project's operating cash flow for the first year (t = 1)? (Round yo ur answer to the nearest cent.) $______ Sales Revenue $5 million Operating cost $3.5 million Depreciation $1 million Operating income before taxes $0.5 million Taxes(40%) $0.2 million Operating income after taxes $0.3 million Add back depreciation $1 million Operating cash flow $1.3 million If this project would cannibalize other projects by $0.5 million of cash flow before taxes per year, how would this change your answer to part a? Round your answer to the nearest cent. The firm's OCF would now be $______ The cannibalization of existing sales needs to be considered in this analysis on an after - tax basis, because the cannibalized sales represent sales revenue the firm would realize without the new project but would lose if the new project is accepted. Thus, the after - tax effect would be to reduce the firm’s operating cash flow by $ 0.5 (1 – T) = $ 0.5 (0.6) = $ 0.3 million . Thus , the firm’s OCF would now be $1 million rather than $ 1.3 million. Ignore Part b. If the tax rate dropped to 35%, how would that change your answer to part a? Round your answer to the nearest cent. The firm's operating cash flow would ___________ increase _____________ by $______ If the tax rate fell to 35 %, the operating cash flow would change to: Operating income before taxes $ 0.5 million Taxes (35 %) 0.175 million Operating income after taxes $ 0.325 million Add back depreciation 1 million Operating cash flow $ 1.325 million Thus, the firm’s operating cash flow would increase by $ 0.025 million or $25,000 8.) Scenario analysis Huang Industries is considering a proposed project whose estimated NPV is $12 million. This estimate assumes that economic conditions will be "average." However the CFO realizes that conditions could be better or worse, so she performed a scenario analysis and obtained these results: Economic Scenario Probability of Outcome NPV Recession 0.05 - $54 million Below average 0.20 - $20 million Average 0.50 12 million Above average 0.20 14 million Boom 0.05 26 million Calculate the project's expected NPV, standard deviation, and coefficient of variation. Round your answers to two decimal places. Enter your answers for the project's expected NPV and standard deviation in millions. For example, an answer of $13,000,000 should be entered as 13.

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    E(NPV) = $______ million σ NPV = $______ million CV = ______ E(NPV) = 0.05( - 54) + 0.2( - 20) + 0.5*12 + 0.2*14 + 0.05*26 = - 2.7 - 4 + 6 + 2.8 + 1.3 = $3.4 million  NPV = [ 0.05( - 54 – 3.4 ) 2 + 0.2( - 20 – 3.4 ) 2 + 0.5* ( 12 – 3.4) 2 + 0.2* ( 14 – 3.4) 2 + 0.05* ( 26 - 3.4) 2 ] 1/2 = [164.738 + 4.68 + 36.98 + 22.472 + 25.538 ] 1/2 = (254.408) 1/2 = $15.95 million CV = $15.95/3.4 = 4.691 9.) Project risk analysis The Butler - Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $7,000 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions: Project A Project B Probability Cash Flows Probability Cash Flows 0.2 $6,500 0.2 $0 0.6 $7,000 0.6 $7,000 0.2 $7,500 0.2 $19,000 BPC has decided to evaluate the riskier project at 13% and the less - risky project at 8%. What is each project's expected annual cash flow? (Round your answers to two decimal places.) Project A. $______ Project B. $______ Expected annual cash flows: Project A: Probable Probability × Cash Flow = Cash Flow 0.2 $6,000 $1,200 0.6 $ 7,00 0 $ 4,20 0 0.2 $7,500 $1,500 Expected annual cash flow = $6,90 0 Project B: Probable Probability × Cash Flow = Cash Flow 0.2 $ 0 $0 0.6 $7 , 00 0 $ 4, 20 0 0.2 $ 19 ,000 $ 3,8 00 Expected annual cash flow = $8,0 0 0

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    Project A. $6,900 Project B. $8,000 Project B's standard deviation (σ B ) is $6,132 and its coefficient of variation (CV B ) is 0.77. What are the values of (σ A ) and (CV A )? Round your answer to two decimal places. σ A = $______ CV A =______ Project A: σ A = [( - 900) 2 *0.2 + (100) 2 *0.6 + (600) 2 *0.2] 1/2 = [162000 + 6000 + 72000] 1/2 = (240000) ½ = $ 489.9 Project B: σ B = [( - 8000) 2 *0.2 + ( - 1000) 2 *0.6 + (11000) 2 *0.2] 1/2 = [12800000 + 600000 + 24200000] 1/2 = (37600000) 1/2 = $6,131.88 CV A = $ 489.9 /$6,900 = 0.071 CV B = $6,131.88 /$8 , 00 0 = 0.7 665 . σ A = $489.9 CV A = 0.071 10.) Scenario analysis Your firm, Agrico Products, is considering a tractor that would have a cost of $37,000, would increase pretax operating cash flows before taking account of depreciation by $12,000 per year, and would be depreciated on a straight - line basis to zero over 5 years at the rate of $7,400 per year, beginning the first year. (Thus, annual cash flows would be $12,000 before taxes plus the tax savings that result from $7,400 of depreciation.) The managers are having a heated debate about whether the tractor would actually last 5 years. The controller insists that she knows of tractors that have lasted only 4 years. The treas urer agrees with the controller, but he argues that most tractors actually do give 5 years of service. The service manager then states that some last for as long as 8 years. Given this discussion, the CFO asks you to prepare a scenario analysis to determine the importance of the tractor's life on the NPV. Use a 40% marginal federal - plus - state tax rate, a zero salvage value, and a 8% WACC. Assuming each of the indicated lives has the same probability of occurring (probability = 1/3), what is the tractor's expected NPV? ( Hint: Use the 5 - year straight - line depreciation for all analyses and ignore the MACRS half - year convention for this problem.) Round your answers to two decimal places. Do not round intermediate calculations. Tractor's NPV if actual life is 4 years. $______ Tractor's NPV if actual life is 8 years. $______ Tractor's expected NPV.

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