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Com 2FA3 Tutorial 7 Week of March 4, 2002 Question 1: MGD Inc. is considering a capital budgeting proposal that would cost $200,000 to start. The project is forecast to generate annual cash flows of $25,000 per year for 12 years and have a salvage value of $125,000 at that time. MGD has a cost of capital of 9.75%. Evaluate this project using NPV, IRR, PB, DPB, and PI. k= 9.75% The easiest method to calculate T CF PV net PV all of the required decision 0 -200 -200.00 -200.00 1 25 22.78 -177.22 criteria is to construct a table 2 25 20.76 -156.47 of the present value of each 3 25 18.91 -137.55 cash flow, since the discounted 4 25 17.23 -120.32 payback period is most readily 5 25 15.70 -104.62 6 25 14.31 -90.32 calculated in that manner. 7 25 13.03 -77.28 8 25 11.88 -65.40 The NPV, IRR and PI all accept 9 25 10.82 -54.58 the project. It is unclear if the 10 25 9.86 -44.72 PB or DPB criteria would accept 11 25 8.98 -35.74 12 150 49.12 13.38 the project since the cutoff NPV = 13.38 > 0 accept rate is arbitrary and not given. IRR = 10.83% > cost of capital, accept However, the payback period of PI = 1.0669 > 1 accept 8 years is quite long, so it is PB = 8 What cutoff value? DPB = 11.7 What cutoff value? likely that the payback criteria would reject the project. The discounted payback being almost the same as the life of the project would also be likely to reject the project. If multiple decision criteria are in use, the project will require further study to assess its acceptability. Com 2FA3 Tutorial 7 Week of March 4, 2002 Question 2: MFM Inc. is considering two mutually exclusive projects. Project A has a startup cost of $100,000 and is expected to generate cashflows of $20,000 per year for ten years with no salvage value. Project B costs $25,000 to start and should generate $6,000 per year with no salvage value. The cost of capital for both projects is 11%. Find the NPV and IRR for each project. What decision should MFM's managers make? Why? Copying the spreadsheet used in k= 11.00% A B question 1; you can calculate the T CF PV CF PV 0 -100 -100.00 -25 NPV and IRR quite quickly. -25.00 1 20 18.02 6 5.41 2 20 16.23 6 4.87 MFM should proceed with project 3 20 14.62 6 4.39 4 20 13.17 6 3.95 A because it will increase the 5 20 11.87 6 3.56 6 20 10.69 6 value of the company more than 3.21 7 20 9.63 6 2.89 if the company does project B 8 20 8.68 6 2.60 9 20 7.82 6 2.35 since the NPV is higher. 10 20 7.04 6 2.11 NPV = 17.78 10.34 IRR = 15.1% 20.2% This is an example of the scale problem caused by the IRR when mutually exclusive projects are considered. In this case although Project B's IRR is higher than the IRR of project A, project A is on a larger scale than project B and therefore has a better dollar value return. Com 2FA3 Tutorial 7 Week of March 4, 2002 Com 2FA3 Tutorial 7 Week of March 4, 2002 Question 3: Quick Buck Inc. has a project that will cost $450 to start. The project will generate $1,000 next year, but will cost $555 to shut down during the second year. Find the internal rates of return for this project. What decision should Quick Buck's management make if their cost of capital is 7%? Describe the NPV profile. This is an example of a project with non-conventional cash flows. There are two sign changes over the life of the project. Therefore, there can be more than two solutions that set the NPV equal to zero. With only three total cash flows the NPV = 0 equation can be converted into a quadratic equation by setting x = (1 + IRR) and multiplying both sides by x2. $1,000 555 0 $450 1 IRR 1 IRR2 0 450 x 2 1,000 x 555 b b 2 4ac x 2a 1,000 1,0002 4 450 555 2 450 x 1.0760 or x 1.1462 IRR 7.6% or IRR 14.62% Com 2FA3 Tutorial 7 Week of March 4, 2002 To figure out what decision should be made we should look at the NPV profile. With a discount rate of 0% the NPV of the project is -$5. At an infinite discount rate, the NPV is -$450. Since the NPV profile crosses the x-axis twice, the NPV is positive if the company's discount rate is between 7.60% and 14.62%. Given that Quick Buck's cost of capital is 7%; the NPV will be negative and the project should be rejected. The NPV profile of the project is -$5 at a discount rate of 0%. The profile increases until it crosses the x-axis at 7.6%. It reaches a maximum and starts to decline, crossing the x-axis a second time at 14.62%. It continues to decline at a decreasing rate, approaching a value of -$450 as the discount rate approaches infinity. NPV Profile 2 0 0% 5% 10% 15% 20% 25% 30% -2 -4 -6 -8 -10 NPV