Question

The current risk-free rate is 2 percent and the market risk premium is 3 percent. You are trying to value ABC company and it has an equity beta of 0.7. The company earned $3.50 per share in the year that just ended. You expect the company's earnings to grow 2 percent per year. The company has an ROE of 12 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

Given that,

Risk free rate Rf = 2%

Market risk premium MRP = 3%

For ABC company,

equity beta = 0.7

So, cost of equity of the company is calculated using CAPM Model,

Cost of equity Ke = Rf + Beta*MRP = 2 + 0.7*3 = 4.1%

Last years earning E0 = $3.5

Growth rate g = 2%

ROE = 12%

So, payout ratio b = 1 - g/ROE = 1 - 2/12 = 83.33%

So, Dividend in year 1, D1 = b*E0*(1+g) = 0.8333*3.5*1.02 = $2.98

a). So value of stock P0 = D1/(Ke - g) = 2.98/(0.041-0.02) = $141.67

b). Present value of growth opportunity = P0 - E1/Ke = 141.67 - 3.5*1.02/0.041 = $54.59