Question

. You are considering buying equity in a firm. If you purchase the equity, in one year you will receive $1.5 million with 40% probability and $1.2 million with 60% probability. Currently the yield on one year T-bills is 4%. Suppose that you require a risk premium of 10% to invest in the equity of this firm. In other words, your minimum required return on this investment is 14%.

(a) What is the most you would be willing to pay for the equity?

(b) If you pay this, what is the expected rate of return on your investment?

(c) What is the standard deviation of the return to your investment in the firm?

Answer 1

Option	Probability	Return
Scenario 1	40%	$1.5 million
Scenario 2	60%	$1.2 million

Expected return = Prob_1 x Ret_1 + Prob_2 x Ret_2

= 40% x $ 1.5 million + 60% x $ 1.2 million

= $1.32 million

A) Minimum required return = 14%, Rf = 4% (1-year T-bill), Risk premium = 10%,

Using CAPM model, cost of equity = Rf + Beta x risk premium = 4% + 1 * 10% = 14%

Expected cash flow after one year = $1.32 million

Present value of this cash flow =

So investor can pay maximum of $1.157 million

B) If investor pays $1.157 million then he will get a return of 14% because this amount is present value of future cash flow discounted by 14% cost of capital

C) Standard deviation of the return: Using modern portfolio theory

Option	Probability	Return	Deviation From expected return	Square of deviation
Scenario 1	40%	$1.5 million	(1.5 -1.32) = .18	0.0324
Scenario 2	60%	$1.2 million	(1.2-1.32) = - .12	0.0144

Variance = prob_1 * Square of Dev_1 + Prob_2 * Square of Dev_2

= 40% * 0.0324 + 60% * 0.0144

= 0.0216

Standard Deviation = Square root of variance = ( 0.0216)^0.5 = .1469 million