# Capital Budgeting Exercise

April 2, 2018 General Studies

Corporate Finance Capital Budgeting Exercises Problem 1 ABC Industries is considering a proposed project whose estimated NPV is \$12 million. This estimate assume that economic conditions will be “average. ” However, the CFO realizes that conditions could be better or worse, so he performed a scenario analysis and obtained these results: Economic Probability of Scenario Outcome NPV Recession 0. 05 (\$70 million) Below Average 0. 20 (\$25 million) Average 0. 50 \$12 million Above Average 0. 20 \$20 million Boom 0. 05 \$30 million Calculate the project’s expected NPV, standard deviation, and 2 coefficient of variation.

Problem 1 E(NPV) = 0. 05 (-\$70) + 0. 20 (-\$25) + 0. 50 (\$12) + 0. 20 (\$20) + 0. 05 (\$30) = -\$3. 5 + -\$5. 0 + \$6. 0 + \$4. 0 + \$1. 5 = \$3. 0 million. ?NPV = [0. 05(-\$70 – \$3)2 + 0. 20(-\$25 – \$3)2 + 0. 50(\$12 – \$3)2 + 0. 20(\$20 – \$3)2 + 0. 05(\$30 – \$3)2 ]? = \$23. 622 million. 3 Problem 2 You must evaluate a proposed spectrometer for the R&D department. The base price \$140000, and it would cost another \$30000 to modify the equipment for special use by the firm. The equipment falls into the MACRS 3-year class and would be sold after 3 years for \$60000.

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The applicable depreciation rates are 33, 45, 15, and 7 percent. The equipment would require an \$8000 increase in working capital (spare parts inventory). The project would have no effect on revenues, but it should save the firm \$50000 per year before-tax labor costs. The firm’s marginal tax is 40%. 4 Problem 2-A A. What is the net cost of the spectrometer, that is what is the year 0 project cash flow? Cost of investment at t0: Base price Modification Increase in NOWC Cash outlay for new machine (\$140000) (\$30000) (\$8000) (\$178000) 5 Problem 2-B B. What are the net operating cash flows in years 1, 2, and 3?

Year 1 After-tax savings \$30000 Depreciation tax savings 22440 Net operating cash flow \$52440 Year 2 \$30000 30600 \$60600 Year 3 \$30000 10200 \$40200 Notes: 1. The after-tax cost savings is \$50000 (1 – t) = \$50000 (0. 6) = \$30000. 2. The depreciation expense in each year is the depreciable basis, \$170000, times the MACRS allowance percentages of 0. 33, 0. 45, and 0. 15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is \$56100, \$76500, and \$25500. The depreciation tax savings is calculated as the tax rate (40%) times the depreciation expense in each year. 6 Problem 2-C C. What is the terminal cash flow?

Salvage value \$60000 Tax on SV* (\$19240) Return of NOWC \$8000 Terminal Value \$48760 *Tax on SV = (\$60000 – \$11900)(0. 4) = \$19240. Remaining BV in Year 4 = \$170000 (0. 07) = \$11900. 7 Problem 2-D D. If the WACC is 12 percent, should the spectrometer be purchased? Year Net Cash Flow PV @ 12% 0 (\$178000) (\$178000) 1 52440 46821 2 60600 48310 3 88960 63320 NPV = (\$19549) The project has an NPV of (\$19549). Thus, it should not be accepted. 8 Problem 2-D Alternatively, place the cash flows on a time line: 0 1 12% | | -178000 52440 3 | 40200 48760 88960 With a financial calculator, input the cash flows into he cash flow register, I/YR = 12, and then solve for NPV = -\$19548. 65 ? -\$19549. IRR = 6. 03%. 2 | 60600 9 Problem 3 You must evaluate a proposal to buy a new milling machine. The base price is \$108000, and shipping and installation costs would add another \$12500. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for \$65000. The applicable depreciation rates are 33, 45, 15, and 7 percent. The machine would require a \$5500 increase in working capital (increased inventory less increased account payable). There would be no effect on revenues, but pre-tax labor costs would decline by \$44000 per year.

The marginal tax rate is 35%, and WACC is 12 percent. Also, the firm spent \$5000 last year investigating the feasibility of using the machine. 10 Problem 3-A A. How should the \$5000 spent last year be handled? The \$5000 spent last year on exploring the feasibility of the project is a sunk cost and should not be included in the analysis. 11 Problem 3-B B. What is the net cost of the machine for capital budgeting purposes, that is, the year 0 project cash flow? Price Modification Increase in NOWC Cash outlay for new machine (\$108000) (\$12500) (\$5500) (\$126000) 12 Problem 3-C

C. What are the net operating cash flows during the years 1, 2, and 3? The operating cash flows follow: Year 1 Year 2 After-tax savings \$28600 \$28600 Depreciation tax savings \$13918 \$18979 Net cash flow \$42518 \$47579 Year 3 \$28,600 \$6326 \$34926 Notes: 1. The after-tax cost savings is: \$44000 (1 – t)= \$44000 (0. 65) = \$28600. 2. The depreciation expense in each year is the depreciable basis, \$120500, times the MACRS allowance percentages of 0. 33, 0. 45, and 0. 15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is \$39765, \$54225, and \$18075.

The depreciation tax savings is calculated as the tax rate (35%) times 13 the depreciation expense in each year. Problem 3-D D. What is the terminal year cash flow? Salvage value Tax on SV* Return of NOWC Terminal Value * \$65000 (19798) 5500 \$50702 Tax on SV = (\$65000 – \$8435)(0. 35) = \$19798. BV in Year 4 = \$120500 (0. 07) = \$8435. 14 Problem 3-E E. Should the machine be purchased? Year 0 1 2 3 Net Cash Flow (\$126000) \$42518 \$47579 \$85628 NPV= PV @ 12% (\$126000) \$37963 \$37930 \$60948 \$10841 The project has an NPV of \$10841; thus, it should be accepted. 15 Problem 3-E Alternatively, place the cash flows on a time line: 2% 0 | -\$126000 3 | \$34926 \$50702 \$85628 With a financial calculator, input the appropriate cash flows into the cash flow register, input I/YR = 12, and then solve for NPV = \$10840. 51 ? \$10841. IRR = 16. 37% 16 1 | \$42518 2 | \$47579 Problem 4 The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs \$6750 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. \$6000 0. 2 \$0 0. 6 \$6750 0. 6 \$6750 0. 2 \$7500 0. 2 \$18000 BPC has decided to evaluate the riskier project at 12 percent and the less-risky project at 10 percent. 17 Problem 4-A A. What is each project’s expected annual cash flow? Project B’s standard deviation (? B) is \$5798 and coefficient of variation (CVB) is 0. 76. What are the values of ? A and CVA? Project A expected annual cash flows: Probable Probability ? Cash Flow = Cash Flow 0. 2 \$6000 \$1200 0. 6 \$6750 \$4050 0. 2 \$7500 \$1500 Expected annual cash flow = \$6750 18 Problem 4-A Project B expected annual cash flows:

Probability ? Cash Flow 0. 2 \$0 0. 6 \$6750 0. 2 \$18000 Expected annual cash flow = Probable Cash Flow \$0 \$4050 \$3600 \$7650 = 19 Problem 4-A Coefficient of variation: Standard deviation CV = Expected value Project A: ? NPV = Expected NPV ? A = (\$6000- \$6750)2 (0. 2)+ (\$6750- \$6750) 2 (0. 6)+ (\$7500- \$6750)2 (0. 2) = \$474. 34. Project B: 2 2 ? B = (\$0- \$7,650) (0. 2)+ (\$6750- \$7650)2 (0. 6)+ (\$18000- \$10,350) (0. 2) = \$5,797. 84 CVA = \$474. 34 / \$6750 = 0. 0703. CVB = \$5797. 84 / \$7650 = 0. 7579. 20 Problem 4-B B. Based on their risk-adjusted NPVs, which project should BPC choose?

Project B is the riskier project because it has the greater variability in its probable cash flows, whether measured by the standard deviation or the coefficient of variation. Hence, Project B is evaluated at the 12% cost of capital, while Project A requires only a 10% cost of capital. Using a financial calculator, input the appropriate expected annual cash flows for Project A into the cash flow register, input I/YR = 10, and solve for NPVA = \$10036. 25. 21 Problem 4-B Using a financial calculator, input the appropriate expected annual cash flows for Project B into the cash flow register, input I/YR = 12, and solve for NPVB = \$11624. 1. Project B has the higher NPV; therefore, the firm should accept Project B. 22 Problem 4-C C. If you knew that Project B’s cash flows were negatively correlated with the firm’s other cash flow, whereas Project A’s flows were positively correlated, how might this affect the decision? If Project B’s cash flows were negatively correlated with gross domestic product (GDP), while A’s flows were positively correlated, would that influence your risk assessment? 23 Problem 4-C The portfolio effects from Project B would tend to make it less risky than otherwise. This would tend to reinforce the decision to accept Project B.

Again, if Project B were negatively correlated with the GDP (Project B is profitable when the economy is down), then it is less risky and Project B’s acceptance is reinforced. 24 Problem 5 You are evaluating a capital budgeting project that should last for 4 years. The project requires \$800,000 of equipment. You are unsure what depreciation method to use in your analysis, straight-line or the 3-year MACRS accelerated method. Under the straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life (ignore the half-year convention for the straight-line method).

The applicable MACRS depreciation rates are 33, 45, 15, and 7 percent. Your company’s WACC is 10 percent, and its tax rate is 40 percent. 25 Problem 5-A A. What would be the depreciation expense be each year under each method? The applicable depreciation values are as follows for the two scenarios: Year 1 2 3 4 Scenario 1 (Straight-Line) \$200000 \$200000 \$200000 \$200000 Scenario 2 (MACRS) \$264000 \$360000 \$120000 \$56000 26 Problem 5-B B. Which depreciation method would produce the higher NPV, and how much higher would it be?

To find the difference in net present values under these two methods, we must determine the difference in incremental cash flows each method provides. The depreciation expenses cannot simply be subtracted from each other, as there are tax ramifications due to depreciation expense. The full depreciation expense is subtracted from Revenues to get operating income, and then taxes due are computed Then, depreciation is added to after-tax operating income to get the project’s operating cash flow. Therefore, if the tax rate is 40%, only 60% of the depreciation expense is actually subtracted out during the after-tax operating income calculation nd the full depreciation expense is added back to calculate operating income. So, there is a tax benefit associated with the depreciation expense that amounts to 40% of the depreciation expense. Therefore, the differences between depreciation expenses under each scenario should be computed and multiplied by 0. 4 to determine the benefit provided by the depreciation expense. 27 Problem 5-B Depreciation Expense Year 1 2 3 4 Difference (2 – 1) \$64000 \$160000 -\$80000 -\$144000 Depreciation Expense Diff. ? 0. (MACRS) \$25600 \$64000 -\$32000 -\$57600 Now to find the difference in NPV to be generated under these scenarios, just enter the cash flows that represent the benefit from depreciation expense and solve for net present value based upon a WACC of 10%. 28 Problem 5-B CF0 = 0; CF1 = \$25600; CF2 = \$64000; CF3 = -\$32000; CF4 = -\$57600; and I/YR = 10. Solve for NPV = \$12781. 64 So, all else equal the use of the accelerated depreciation method will result in a higher NPV (by \$12781. 64) than would the use of a straightline depreciation method. 29

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