Question

The current risk-free rate is 2 percent and the market risk premium is 4 percent. You are trying to value ABC company and it has an equity beta of 0.8. The company earned $3.50 per share in the year that just ended. You expect the company's earnings to grow 4 percent per year. The company has an ROE of 13 percent.

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

Answer 1

As Per Dividend Approach , Value of Stock = Present value of all Future Dividends.

And it is given by the formulae

Iv = D1/Re-g

Iv= Stock Price

D1 = Next Dividend = D0+ Growth ( Refer : Working Note 2)

Re = Expected Return calculated as per CAPM Model , Re = Rf+ Beta (Rm-Rf) (Refer Working Note 3)

g = Growth , As given in the Question = 4%

Iv =2.52/(.052-.04) =$ 210

Value of Stock = $210

Working Note 1 : Calulation of Payout Ratio inorder to determine Current Dividend (D0) and There by calculating Next Dividend

g = b* r

g = growth =4%

b= retention ratio we have to calculate

r = ROE = 13%

b =g/r =4/13 = 30.77%

Retention Ratio = 30.77%

Divdend payout Ratio = 1- Retention Ratio

= 1-30.77% = 69.23%

Working Note 2 : Calcuation of Current Dividend and Next Dividend

D0 = Earnings * Payout Ratio =3.5 * 69.23% = 2.42

D1 = D0+ Growth = 2.42 *1.04 = 2.52

Working Note 3 : Calculation of Re

Re = Rf + Beta (Rm-Rf) , as per CAPM Model, (Rm -Rf) = Market Risk Premium =4%

Re = 2+.8(4) =5.2%