It is January 1, 2017. Company Y is expected to have earnings of $15 million for

Question

It is January 1, 2017. Company Y is expected to have earnings of $15 million for theyear which are realized exactly one year from today. The plowback ratio for the firm has historically been 40% and is not expected to change into the future. Earnings are expected to grow at 5% per year, forever. The risk-free return is 3% and the expected return of the market portfolio is 13%. Suppose Company Y is valued at $85 million and all equity-financed

A. What is the cost of equity of the company?

B. What is the beta of the company?

Explanation / Answer

(A)

Plowback ratio = 40%

So, dividend payout ratio = (100 - 40)% = 60%

Next period dividend (D1) = $15 million x 60% = $9 million

So, cost of equity (ke) = [D1 / V0] + g

= ($9 million / $85 million) + 0.05

= 0.1059 + 0.05 = 0.1559, or 15.59%

(B)

Using CAPM,

ke = Risk-fee rate + beta x (Expected market return - Risk free rate)

0.1559 = 0.03 + Beta x (0.13 - 0.03) = 0.03 + Beta x 0.1

Beta x 0.1 = 0.1559 - 0.03 = 0.1259

Beta = 0.1259 / 0.1 = 1.259 ~ 1.26

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