##### Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

**Week 3 Problem Set**

**Answer the following questions and solve the following problems in the space provided. When you are done, save the file in the format flastname_Week_3_Problem_Set.docx, where flastname is your first initial and you last name, and submit it to the appropriate dropbox.**

**Chapter 7 (pages 225–228):**

1.

Your brother wants to borrow $10,000 from you. He has offered to pay you back $12,000 in a year. If the cost of capital of this investment opportunity is 10%, what is its NPV? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

**8.**

You are considering an investment in a clothes distributor. The company needs $100,000 today and expects to repay you $120,000 in a year from now. What is the IRR of this investment opportunity? Given the riskiness of the investment opportunity, your cost of capital is 20%. What does the IRR rule say about whether you should invest?

**19.**

You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $5,000 and will be posted for one year. You expect that it will generate additional revenue of $500 per month. What is the payback period?

**21.**

You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $10 million. Investment A will generate $2 million per year (starting at the end of the first year) in perpetuity. Investment B will generate $1.5 million at the end of the first year and its revenues will grow at 2% per year for every year after that.

- a. Which investment has the higher IRR?
- b. Which investment has the higher NPV when the cost of capital is 7%?
- c. In this case, for what values of the cost of capital does picking the higher IRR give the correct answer as to which investment is the best opportunity?

**Chapter 8 (260–262)**

**1.**

Pisa Pizza, a seller of frozen pizza, is considering introducing a healthier version of its pizza that will be low in cholesterol and contain no trans fats. The firm expects that sales of the new pizza will be $20 million per year. While many of these sales will be to new customers, Pisa Pizza estimates that 40% will come from customers who switch to the new, healthier pizza instead of buying the original version.

a. Assume customers will spend the same amount on either version. What level of incremental sales is associated with introducing the new pizza?

b. Suppose that 50% of the customers who will switch from Pisa Pizza’s original pizza to its healthier pizza will switch to another brand if Pisa Pizza does not introduce a healthier pizza. What level of incremental sales is associated with introducing the new pizza in this case?

**6.**

Cellular Access, Inc. is a cellular telephone service provider that reported net income of $250 million for the most recent fiscal year. The firm had depreciation expenses of $100 million, capital expenditures of $200 million, and no interest expenses. Working capital increased by $10 million. Calculate the free cash flow for Cellular Access for the most recent fiscal year.

**12.**

A bicycle manufacturer currently produces 300,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $2 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $250,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $50,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored because it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $20,000.

If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?