Question

Suppose you have an opportunity to open a company that will run for one year from now. You will need to make an up-front investment of $80,000 to start the business. After covering your operating costs, including paying yourself a nice wage, you expect to generate a cash flow of $115,000 at the end of the year. The current risk-free interest rate is 5%. You believe that your profits will be risky and sensitive to the overall economy, so a 10% risk premium is appropriate. Suppose that you are penniless, and decide to raise $50,000 by issuing debt. Under no circumstance will you default on your debt. For the rest of the money you need, you issue equity and promise to give equity investors all the residual cash flow after you repay your debt. What is the expected return to your equity investors? Assume all the assumptions of Modigliani-Miller theorem hold. Please choose the closest answer.

Answer 1

The expected return to equity investors is 81.16%, which is calculated based on the discounted cash flow of equity after repaying debt, taking into account a risk-free rate of 5% and a risk premium of 10%, totaling a cost of equity of 15%.

Step-by-step explanation:

To calculate the expected return to equity investors, we would use the formula for the expected return, which incorporates the risk-free rate and a risk premium. Given that the student needs to make an upfront investment of $80,000 and has decided to raise $50,000 through debt, the remainder of the funding, which is $30,000, will be financed through equity. The expected cash flow at the end of the year is $115,000, from which the debt must be repaid. The debt repayment includes the principal of $50,000 and the interest at the risk-free rate of 5%, which totals to $52,500. This leaves an equity cash flow of $62,500 ($115,000 - $52,500).

The cost of equity capital would be the risk-free rate plus the risk premium, which is 15% (5% + 10%). Therefore, the expected return to the equity investors would be the equity cash flow discounted back at the cost of equity capital, which is $62,500/(1+0.15), resulting in approximately $54,348. This represents the present value of the equity investors' cash flow. To find the expected return for the equity investors, we can compare this present value with the initial equity investment of $30,000. The return is (54,348 - 30,000) / 30,000 = 0.8116, or 81.16%. So, the expected return to equity investors is 81.16%.