Question

Suppose you borrow $50,000 when financing a coffee shop with a cost of $65,000. You expect to generate a cash flow of $65,000 at the end of the year if demand is weak, $81,250 if demand is as expected and $89,375 if demand is strong. Each scenario is equally likely. The current risk-free interest rate is 5% (risk of debt) and there's an 9% risk premium for the risk of the assets:

A) What should the value of the equity be?

B) What is the expected return?

C) What would be the return of equity if the demand is strong?

D) What would be the return of equity if the demand is weak?

E) What would be the expected return if you borrowed $30,000 instead?

Answer 1

Amount Borrowed - 50,000

Total Cost = 65,000

The total cash flows in the company are 65,000

a. If I borrow 50,000$ , the firm's value of equity will be 65,000-50,000 = 15,000

b. Expected return to be calculated from

Cash flows of the firm net of debt payment(repayment of principal and interest)

Amount to be paid to the debt holders = 50,000 *1.05 = 52,500 by the end of the year

Returns expected by the end of the year = 81,250

the payoff to equity holders = Returns - Debt Payment = 81,250 - 52,500 = 28,750

Return = Payoff/Cash paid = 28750/15000 - 1 = 91.6%

c. If the demand is strong = Returns - Debt payment

Returns = 89375

payoff = 89375 - 52,500 = 36,875

Return = 36875/15000 = 145.83%

d. If the demand is weak

Return = 75000

Payoff = 75000-52500 = 22500

Return = 22500/15000 - 1 = 50%

e.

Cash flows of the firm net of debt payment(repayment of principal and interest)

Amount to be paid to the debt holders = 30,000 *1.05 = 31,500 by the end of the year

Returns expected by the end of the year = 81,250

the payoff to equity holders = Returns - Debt Payment = 81,250 - 31,500 = 49,750

Return = Payoff/Cash paid = 49750/35000 - 1 = 42%