You are an entrepreneur with an investment opportunity. This is a project that lasts 1 year. The initial investment is 12,000. This investment generates the following final cash flows:

• If the economy is strong: 20,000

• If the economy is weak: 10,000

  The probability that the economy is strong is 50%. The risk-free rate is 5%, and the risk premium associated with such cash flows is 10% (note: this is exclusively systematic risk). Financial markets are competitive.

  Questions

1. What is the NPV of this investment opportunity? What is its expected rate of

   return? What is its required rate of return?

2. Assume you finance this investment with 70% debt, and 30% with outside equity.

   2.1. What is the required return on equity?

   2.2. How does the required return you found compare to the required return if the firm was unlevered?

   2.3. What is the optimal capital structure from the entrepreneurs point of view?

3. What is the price, at the beginning of the year, of the Arrow security that promises

   to pay 1 when the economy is weak (and 0 if the economy is strong)?

4. Imagine that, instead of debt, you finance your investment with a financial innovation that you call SoM coins, and the rest with outside equity. Each coin can be re-exchanged at the end of the year for 6 if the economy is strong and 10 if the economy is weak. After that, they expire and are worth nothing. You issue 1,000 of these coins. What is the market price of a coin at the beginning of the year (i.e. at which price are you able to sell them)? How much outside equity

do you need to raise?