Question

The current risk-free rate is 3 percent and the market risk premium is 5 percent. You are trying to value ABC company and it has an equity beta of 0.7. The company earned $2.00 per share in the year that just ended. You expect the company's earnings to grow 3 percent per year. The company has an ROE of 13 percent.

1. What is the value of the stock? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. What is the present value of the growth opportunity? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

Answer 1

Let us first calculate te required return on equity:

Re = rf + beta* ( Rm - Rf)

= 3 + 0.7*5

= 6.5%

The sustainable growth rate can be calculated as :

G = ROE * b

b is the retention ratio

0.03 = 0.13* b

b = 23.0769

Dividend payout ratio = 0.7692 ( 1 - retention ratio)

Po = D1/ Re - g

D1 = E1* dividend payout ratio

= 2*1.03

= 2.06 * 0.7692

= 1.5846

a. P0 = D1 / Re - g

= $1.5846 / 0.065 - 0.03

= $45.2743

= $45.27 ( rounded off to two decimal places)

b. Now present value of growth opportunities

= Current value of stock - E1 / cost of capital

= $45.2743 - 2.06/ 0.065

= $13.582

= $13.58 ( rounded off to two decimal places)