Question

You are considering opening a drive-in movie theater and running it for ten years. You have spent after-tax $10,000 researching the land that will be used for theater, but if you take the project you expect to incur another immediate after-tax expense of $20,000 as you work with a consulting firm to decide how to most efficiently run the business.

The project entails an immediate $100,000 capital expenditure, which can be depreciated over 10 years. You expect to sell this capital investment for $25,000 at the end of the ten year project. Working capital expenses for the project are $50,000 immediately, $40,000 incurred two years from today, both of which are fully recovered in ten years (at the end of the project).

The project’s operating costs are expected to be $100,000 for each of the first five years and then (starting between t=5 and t=6) grow at -5% per year through the end of the project (i.e., through t=10). You expect the project’s revenues to start at $100,000 starting one year from today and remain constant for the life of the project.

1. (1 points) To determine the discount rate for the project, you have found an all-equity firm with a risk level similar to the company you’re starting. That firm’s equity has a standard deviation of returns of 35% and a correlation with the stock market of 0.8. The risk free rate is 4%, the expected market returns are 9.5% and the standard deviation of market returns is 28%. What is your estimated cost of capital?
2. (7 Points) You decide to use 10% as the project’s opportunity cost of capital (ignore your answer from part a). Your expected tax rate is 25%. What is the project’s NPV?
3. (2 points) You find out that the government is interested in buying the capital investment from you at the end of the project. Instead of selling it for $25,000 at the end of the project, the government will commit today to buying the capital from you for $75,000 post-tax ten years from today. You trust the government and think that this sale is risk free should you take the project. To what extent (if any) should the above information factor in to your decision regarding whether or not to open the theater? Does it change the NPV in any way, if so how? (hint: think of the capital investment as its own project – how will this affect the cash flows and/or the discount rate)

Answer 1

a) Cost of capital

SD (firm) = 35%, correlation of firm with Mkt = 0.8, Rf= 4%, Rm = 9.5%, SD (mkt) = 28%

Beta (firm) = (correlation between firm and mkt) * (SD of firm) / (SD of mkt) = 0.8 * 0.35 / 0.28 = 1

Cost of Equity = Rf + Beta(firm) * ( Rm - Rf) = 0.4 + 1 * (0.095 - 0.04) = 0.455 = 45.5%

b) Net present value

NPV =

NPV = 100000/(1+10%)^1+100000/(1+10%)^2 +100000/(1+10%)^3 +100000/(1+10%)^4 +100000/(1+10%)^5 +100000/(1+10%)^1 +100000/(1+10%)^6 +100000/(1+10%)^7 +100000/(1+10%)^8 +100000/(1+10%)^9 +215000/(1+10%)^10

= $ 658,794

For Yr 10, Rt = 215000 = 100,000 (each yr revenue) + 25,000 (sell of initial investment) + 90,000 (Recovery of working Capex of 50,000 and 40,000)

c) Govt Purchase of CAPEX at $75,000 today

For this we need to compare today's value of CAPEX of both options

NPV of 25,000 = 25,000

NPV of 75,000 = 75,000/ (1.1)10 = 28,915

Since, the NPV of Govt Buy is higher it should be preffered.