Question

Suppose that your firm is considering the following two mutually exclusive projects. Both projects have the same initial cost of $312,500 and the resulting annual cash flows for the first five years are as shown in the table below: Year Alpha Beta 0 $ (312,500) $ (312,500) 1 375,000 28,935 2 46,875 80,376 3 15,625 99,229 4 15,625 160,788 5 3,125 191,414 It is your job to analyze the feasibility of these two projects and to make recommendations as to which project should be undertaken. You must present a written report of your findings and your recommendations to middle managers, many of whom may be unfamiliar with some of your computations. You may choose to present the results of your calculations in table form. In your report, you must address each of the following: Analyses: a. Calculate the IRR of each project. Which project should be selected using IRR as the criterion? b. In its analyses of projects of this type, your firm uses a 14.0 percent discount rate. Compute the NPV for each project using the 14.0 percent discount rate. Which project should be chosen based on this result? c. In some cases, your firm uses the payback period to assess projects, with a cut-off point of 3 years. Calculate the payback period for each project and explain which project should be chosen using this criterion. d. Based on all of your analyses, which project do you recommend? Explain why you recommend this project. e. Suppose that the firm previously spent 15,000 dollars to conduct an environmental study for project Alpha. Explain how this affects your analyses and your recommendations.

Answer 1

To calculate my answers, I used a TI-84 calculator Finance functions.

a. Alpha: irr(-312500,{375000,46875,15625,15625,3125}) = 36.012%

Beta: irr(-312500,{28935,80376,99229,160788,191414}) = 17.64%

Using IRR, you would want to select Alpha because it has a higher internal rate of return.

b. Alpha: npv(14,-312500,{375000,46875,15625,15625,3125}) = $73936.87

Beta: npv(14,-312500,{28935,80376,99229,160788,191414}) = $36318.89

Using NPV, you would still want to choose Alpha because it has a higher net present value

c. Alpha: 312500 - 375000 - 46875 - 15625 = -125000 (Actual payback period is .83 years (312500/375000)

Beta: 312500 - 28935 - 80376 - 99229 = 103960 (Actual payback period is 3.65 years (103960/160788)

Using payback, you would still want to pick Alpha because the project is paid back in less than a year, whereas for Beta it takes over 3 years to pay back.

d. After all the analysis, I would pick Alpha because it has a better IRR and NPV and has a shorter payback period.

e. This extra cost would not affect my decision because even when added to the initial cost, the IRR and NPV are still higher than Beta and the payback period is still less than Beta.

Answer 2

a. Enter cash flow into calculator and then compute IRR. Cash flow zero is negative because it is what we are initially investing. (I have a TI-BA II Plus, which has a CF button) Alpha = 36% Beta =17.64% So alpha is better. b. Same cash flow button, but compute NPV. First remove the initial cash flow and make it zero. Then when it asks for an interest rate, put 14 (as stated in the problem) Alpha = 386,436.87 Beta = 348,818.89 So alpha is better. c. This is how long it takes to get our cash back. Alpha is in the first year since year one's inflow is greater than the investment. We take 312500/375000 = 5/6 or 10 months. Beta is 312500-28935(year 1)-80376(year 2)-99299(year 3)=103,890. The payback period ends here and we still don't have our money, so alpha is better.