Question

Solve the following problem (NO process, just the answers in an Excel document): Suppose you borrow $50000 when financing a coffe shop with a cost of $65000. You expect to generate a cash flow of $65000 at the end of the year if demand is weak, $81250 if demand is as expected and $89375 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: 1. What should the value of the equity be? (Answer the Question in Cell A1) 2. What is the expected return? (Answer the Question in Cell B1) 3. What would be the return of equity if the demand is strong? (Answer the Question in Cell C1) 4. What would be the return of equity if the demand is weak? (Answer the Question in Cell D1) s. What would be the expected return if you borrowed $30,000 instead? (Answer the Question in Cell E1)

Answer 1

(1) The value of equity is 65000 - 50000 = $15000

(2) Assuming we can borrow at risk-free rate the debt will grow to $50000 x 1.05 =$52500 over the year.

Therefore the net cash flow at the year end is

65000 - 52500 = $12500 if the demand is weak or

81250 - 52500 =$28750 if the demand is as expected or

89375 - 52500 =$36875 if the demand is strong

each with equal probability.

Therefore the expected return ={ (1/3) x (12500+28750+36875)/15000} - 1 = 73.61 %

(3) Return on equity if the demand is strong = (36875/15000) - 1 = 145.83 %

(4) Return on equity if the demand is weak = (12500/15000) - 1 = - 16.67 %

(5) Expected return if we borrow 30000 instead

=[(1/3) x {(65000-30000x1.05)+(81250-30000x1.05)+(89375-30000x1.05)} / (65000 - 30000)] - 1 = 34.40 %