CFA 35: Capital Budgeting

Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent. Year 0 1 2 3 4 5 Cash flow −50,000 15,000 15,000 20,000 10,000 5,000 NPV IRR A $1,905 10.9% B $1,905 26.0% C $3,379 10.9% Correct answer- C is correct. NPV=−50,000+15,0001.08+15,0001.082+20,0001.083+10,0001.084+5,0001.085NPV= −50,000+13,888.89+12,860.08+15,876.64+7,350.30+ 3,402.92NPV=−50,000+53,378.83=3,378.83 The IRR, found with a financial calculator, is 10.88 percent. Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent. Year 0 1 2 3 4 5 Cash flow −50,000 15,000 15,000 20,000 10,000 5,000 The discounted payback period is: 0.16 years longer than the payback period. 0.51 years longer than the payback period. 1.01 years longer than the payback period. Correct answer- C is correct. Year 0 1 2 3 4 5 Cash flow −50,000 15,000 15,000 20,000 10,000 5,000 Cumulative cash flow −50,000 −35,000 −20,000 0 10,000 15,000 Discounted cash flow −50,000 13,888.89 12,860.08 15,876.64 7,350.30 3,402.92 Cumulative DCF −50,000 −36,111.11 −23,251.03 −7,374.38 −24.09 3,378.83 As the table shows, the cumulative cash flow offsets the initial investment in exactly three years. The payback period is 3.00 years. The discounted payback period is between four and five years. The discounted payback period is 4 years plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The discounted payback period is 4.01 − 3.00 = 1.01 years longer than the payback period. An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net present value is closest to: $42.22. $58.33. $68.52. Correct answer- B is correct. NPV=∑t=03CFt(1+r)t=−100+401.20+801.202+1201.203=$58.33 An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in one year and another $120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return? 28.39 percent. 28.59 percent. 28.79 percent. Correct answer- C is correct. The IRR can be found using a financial calculator or with trial and error. Using trial and error, the total PV is equal to zero if the discount rate is 28.79 percent. Present Value Year Cash Flow 28.19% 28.39% 28.59% 28.79% 0 −150,000 −150,000 −150,000 −150,000 −150,000 1 100,000 78,009 77,888 77,767 77,646 2 120,000 73,025 72,798 72,572 72,346 Total 1, −8 A more precise IRR of 28.7854 percent has a total PV closer to zero. Kim Corporation is considering an investment of 750 million won with expected after-tax cash inflows of 175 million won per year for seven years. The required rate of return is 10 percent. What is the project's: NPV? IRR? A 102 million won 14.0% B 157 million won 23.3% C 193 million won 10.0% Correct answer- A is correct. TheNPV=−750+∑t=.10t=−750+851.97=101.97millionwon. The IRR, found with a financial calculator, is 14.02 percent. (The PV is −750, N = 7, and PMT = 175.) Kim Corporation is considering an investment of 750 million won with expected after-tax cash inflows of 175 million won per year for seven years. The required rate of return is 10 percent. Expressed in years, the project's payback period and discounted payback period, respectively, are closest to: 4.3 years and 5.4 years. 4.3 years and 5.9 years. 4.8 years and 6.3 years. Correct answer- B is correct. Year 0 1 2 3 4 5 6 7 Cash flow − Cumulative cash flow −750 −575 −400 −225 − The payback period is between four and five years. The payback period is four years plus 50/175 = 0.29 of the fifth year cash flow, or 4.29 years. Year 0 1 2 3 4 5 6 7 Cash flow − Discounted cash flow −750 159.09 144.63 131.48 119.53 108.66 98.78 89.80 Cumulative DCF −750 −590.91 −446.28 −314.80 −195.27 −86.61 12.17 101.97 The discounted payback period is between five and six years. The discounted payback period is five years plus 86.61/98.78 = 0.88 of the sixth year cash flow, or 5.88 years. An investment of $20,000 will create a perpetual after-tax cash flow of $2,000. The required rate of return is 8 percent. What is the investment's profitability index? 1.08. 1.16. 1.25. Correct answer- C is correct. ThepresentvalueoffuturecashflowsisPV=2,0000.08=25,000TheprofitabilityindexisPI=PVI nvestment=25,00020,000=1.25 Hermann Corporation is considering an investment of €375 million with expected after- tax cash inflows of €115 million per year for seven years and an additional after-tax salvage value of €50 million in Year 7. The required rate of return is 10 percent. What is the investment's PI? 1.19. 1.33. 1.56. Correct answer- C is correct. PV=∑t=.10t+501.107=585.53millioneurosPI=585.53375=1.56 Erin Chou is reviewing a profitable investment project that has a conventional cash flow pattern. If the cash flows for the project, initial outlay, and future after-tax cash flows all double, Chou would predict that the IRR would: increase and the NPV would increase. stay the same and the NPV would increase. stay the same and the NPV would stay the same. Correct answer- B is correct. The IRR would stay the same because both the initial outlay and the after-tax cash flows double, so that the return on each dollar invested remains the same. All of the cash flows and their present values double. The difference between total present value of the future cash flows and the initial outlay (the NPV) also doubles. Shirley Shea has evaluated an investment proposal and found that its payback period is one year, it has a negative NPV, and it has a positive IRR. Is this combination of results possible? Yes. No, because a project with a positive IRR has a positive NPV. No, because a project with such a rapid payback period has a positive NPV. Correct answer- A is correct. If the cumulative cash flow in one year equals the outlay and additional cash flows are not very large, this scenario is possible. For example, assume the outlay is 100, the cash flow in Year 1 is 100 and the cash flow in Year 2 is 5. The required return is 10 percent. This project would have a payback of 1.0 years, an NPV of −4.96, and an IRR of 4.77 percent. An investment has an outlay of 100 and after-tax cash flows of 40 annually for four years. A project enhancement increases the outlay by 15 and the annual after-tax cash flows by 5. As a result, the vertical intercept of the NPV profile of the enhanced project shifts: up and the horizontal intercept shifts left. up and the horizontal intercept shifts right. down and the horizontal intercept shifts left. Correct answer- A is correct. The vertical intercept changes from 60 to 65 (NPV when cost of capital is 0%), and the horizontal intercept (IRR, when NPV equals zero) changes from 21.86 percent to 20.68 percent. Projects 1 and 2 have similar outlays, although the patterns of future cash flows are different. The cash flows as well as the NPV and IRR for the two projects are shown below. For both projects, the required rate of return is 10 percent. Cash Flows Year 0 1 2 3 4 NPV IRR (%) Project 1 − 13.40 21.86 Project 2 − 18.30 18.92 The two projects are mutually exclusive. What is the appropriate investment decision? Invest in both projects. Invest in Project 1 because it has the higher IRR. Invest in Project 2 because it has the higher NPV. Correct answer- C is correct. When valuing mutually exclusive projects, the decision should be made with the NPV method because this method uses the most realistic discount rate, namely the opportunity cost of funds. In this example, the reinvestment rate for the NPV method (here 10 percent) is more realistic than the reinvestment rate for the IRR method (here 21.86 percent or 18.92 percent). Consider the two projects below. The cash flows as well as the NPV and IRR for the two projects are given. For both projects, the required rate of return is 10 percent. Cash Flows Year 0 1 2 3 4 NPV IRR (%) Project 1 − 14.12 16.37 Project 2 − 19.53 15.02 What discount rate would result in the same NPV for both projects? A rate between 0.00 percent and 10.00 percent. A rate between 10.00 percent and 15.02 percent. A rate between 15.02 percent and 16.37 percent. Correct answer- B is correct. For these projects, a discount rate of 13.16 percent would yield the same NPV for both (an NPV of 6.73). Wilson Flannery is concerned that this project has multiple IRRs. Year 0 1 2 3 Cash flows −50 100 0 −50 How many discount rates produce a zero NPV for this project? One, a discount rate of 0 percent. Two, discount rates of 0 percent and 32 percent. Two, discount rates of 0 percent and 62 percent. Correct answer- C is correct. Discount rates of 0 percent and approximately 61.8 percent both give a zero NPV. Rate 0% 20% 40% 60% 61.8% 80% 100% NPV 0.00 4.40 3.21 0.29 0.00 −3.02 −6.25 With regard to the net present value (NPV) profiles of two projects, the crossover rate is best described as the discount rate at which: two projects have the same NPV. two projects have the same internal rate of return. a project's NPV changes from positive to negative. Correct answer- A is correct. The crossover rate is the discount rate at which the NPV profiles for two projects cross; it is the only point where the NPVs of the projects are the same. With regard to net present value (NPV) profiles, the point at which a profile crosses the vertical axis is best described as: the point at which two projects have the same NPV. the sum of the undiscounted cash flows from a project. a project's internal rate of return when the project's NPV is equal to zero. Correct answer- B is correct. The vertical axis represents a discount rate of zero. The point where the profile crosses the vertical axis is simply the sum of the cash flows. With regard to net present value (NPV) profiles, the point at which a profile crosses the horizontal axis is best described as: the point at which two projects have the same NPV. the sum of the undiscounted cash flows from a project. a project's internal rate of return when the project's NPV is equal to zero. Correct answer- C is correct. The horizontal axis represents an NPV of zero. By definition, the project's IRR equals an NPV of zero. With regard to capital budgeting, an appropriate estimate of the incremental cash flows from a project is least likely to include: externalities. interest costs. opportunity costs. Correct answer- B is correct. Costs to finance the project are taken into account when the cash flows are discounted at the appropriate cost of capital; including interest costs in the cash flows would result in double-counting the cost of debt.