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

The facts of the question are -

Total cost of coffee shop, C = $65,000

Debt amount, D = $50,000

Expected cash flow at the end of year -

1. if demand is weak = $65,000
2. If demand is as expected = $81,250
3. if demand is strong = $89,375

Risk free interest rate, r_d = 5%

Risk premium = r_u - r_d = 9%

A) Value of equity, E

= C - D

= $65,000 - $50,000

= $15,000

B) Expected return will be equal to expected cost of levered equity (company financed with debt & equity combined) . According to Modigliani Miller Proposition II, cost of levered equity,

r_e = r_d + D/E (r_u - r_d)

   = 5% + ($50,000/$15,000) * 9%

   = 5% + 30%

r_e = 35%

C) Expected debt obligations in one year = $50,000 * (1+0.05) [as 5% is cost of debt] = $52,500

So expected payoff in one year when demand is strong = $89,375 - $52,500 = $36,875

Hence, return on equity in this scenario = Expected payoff net of debt obligations / Total Equity - 1

   = $36,875/$15,000 - 1

   = 145.83%

D) Expected debt obligations in one year remains same i.e. $52,500

Expected payoff in one year when demand is weak = $65,000 - $52,500 = $12,500

Hence return on equity in this scenario = $12,500/$15,000 - 1

= -16.67%