Question

The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $10 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 20% per year on all reinvested earnings forever.

Answer 1

Answer:

Risk-free rate (Rf) = 8%

Return on market portfolio (Rm) = 15%

Beta (β) = 1.2

Ke = Rf + β(Rm - Rf)

Ke = 8 + 1.2(15 - 8)

Ke = 8 + 1.2(7)

Ke = 8 + 8.4

Ke = 16.40%

Earnings per share (EPS) = $10

Current dividend paid (Do) = 40% x $10 = $4

Retention rate (b) = &6/$10 x 100 = 60% = 0.6

ROE (r) = 20% = 0.2

Growth rate (g) = b x r

                         = 0.6 x 0.2

                         = 0.12 = 12%

Current market price (Po)

= Do(1 + g)  

        Ke - g

= $4(1 + 0.12)

     0.1640 - 0.12

= $4(1.12)

      0.044

= $101.82

             

Explanation:

First and foremost, we need to calculate the cost of equity based on capital asset pricing model. Then, we will determine the growth rate, which is a function of retention rate (b) and return on equity(r).

Finally, we will calculate the current market price, which is dividend paid, subject to growth, divided by the excess of cost of equity over growth rate.