Question: Problem 10-28 All techniques with NPV profile: Mutually exclusive projects. Projects A and B, of equal risk, are alternatives for expanding Rosa Companys capacity. The
| Problem 10-28 | |||||||||
| All techniques with NPV profile: Mutually exclusive projects. Projects A and B, of equal risk, are alternatives for expanding Rosa Companys capacity. The firms cost of capital is 13%. The cash flows for each project are shown in the following table. | |||||||||
| Project A | Project B | ||||||||
| Initial investment (CF0) | -$80,000 | -$50,000 | |||||||
| Year (t) | Cash inflows (CFt) | ||||||||
| 1 | $15,000 | $15,000 | |||||||
| 2 | 20,000 | $15,000 | |||||||
| 3 | 25,000 | $15,000 | |||||||
| 4 | 30,000 | $15,000 | |||||||
| 5 | 35,000 | $15,000 | |||||||
| a. | Calculate each projects payback period. | ||||||||
| b. | Calculate the net present value (NPV) for each project. | ||||||||
| c. | Calculate the internal rate of return (IRR) for each project. | ||||||||
| d. | Draw the NPV profiles for both projects on the same set of axes, and discuss any conflict in ranking that may exist between NPV and IRR. | ||||||||
| e. | Summarize the preferences dictated by each measure, and indicate which project you would recommend. Explain why. | ||||||||
| Solution | |||||||||
| a. | Calculate each projects payback period. | ||||||||
| Project A | Project B | ||||||||
| Period | Cash flows | Investment balance | Payback period | Cash flows | Investment balance | Payback period | |||
| 0 | |||||||||
| 1 | |||||||||
| 2 | |||||||||
| 3 | |||||||||
| 4 | |||||||||
| 5 | |||||||||
| b. | Calculate the net present value (NPV) for each project. | ||||||||
| Project A | Project B | ||||||||
| Cost of Capital | |||||||||
| CF0 | |||||||||
| CF1 | |||||||||
| CF2 | |||||||||
| CF3 | |||||||||
| CF4 | |||||||||
| CF5 | |||||||||
| NPV of project | |||||||||
| c. | Calculate the internal rate of return (IRR) for each project. | ||||||||
| Project A | Project B | ||||||||
| CF0 | |||||||||
| CF1 | |||||||||
| CF2 | |||||||||
| CF3 | |||||||||
| CF4 | |||||||||
| CF5 | |||||||||
| IRR | |||||||||
| d. | Draw the NPV profiles for both projects on the same set of axes, and discuss any conflict in ranking that may exist between NPV and IRR. | ||||||||
| Data for NPV Profiles | |||||||||
| NPV | |||||||||
| Cost of Capital | Project A | Project B | |||||||
| 0.00% | |||||||||
| 5.00% | |||||||||
| 13.00% | |||||||||
| 13.86765% | |||||||||
| 14.00% | |||||||||
| 0.00% | |||||||||
| 0.00% | |||||||||
| To find the NPV profiles for projects A and B, begin by generating a set of points representing combinations of discount rates and NPVs for each project. [NPV for a 0% discount rate, for example, is simply the sum of undiscounted cash outflows and inflows for the project. Part b provides NPVs for a 13% discount rate, and part c. provides IRRs (NPV = 0).] Then, sketch a line connecting combinations of discounts rates and NPVs for each project: | |||||||||
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