You have been asked to evaluate the following investment opportunity. A small firm is available for purchase at an initial cost of $150,000, to be paid to the current owner in equal installments over the next five years. The firm has been generating annual revenues of $100,000. Operating costs are 65 percent of revenues. For tax purposes, the firm's earnings would appear on your personal income tax return, and the applicable tax rate would be about 36 percent. Your investment would be deductible when calculating taxes. Under these assumptions, the NPV (at a discount rate of 10 percent) for this project is $12,131.
In light of the fact that most of your information about this firm comes from the current owner, you are concerned that some of your assumptions may be inaccurate. After some research, you have determined the following about the key inputs to this problem:
• Actual revenues could be as low as $60,000 or as high as $125,000. The most likely amount is $100,000. Revenues in successive years are independent.
• Operating costs could be as low as 55 percent of revenues or as high as 75 percent, with any value in between being equally likely. Costs in successive years are independent.
• The tax rate in any year will be 36 percent with probability 0.4 and 40 percent with probability 0.6, depending on factors outside your control and independent from year to year.
• In the case of negative taxable income, you will have other income, so the tax effects represented in the model will still hold.
a. What probability distributions are appropriate for the three uncertain quantities in this analysis?
b. What is the mean NPV under the assumptions given above?
c. What is the probability that the NPV will be negative?
d. What is the probability that the cash flow will be positive in all five years?