Question

1. A company recently paid a $3 per share dividend, which is expected to grow at a constant rate forever. The company’s stock, has a beta coefficient equal to 1.1, is selling for $40.50 per share. Currently, the risk-free rate of return is 3 percent and the return on an average stock is 10 percent. If the stock is selling at its equilibrium price, what is its growth rate?

Answer 1

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 3 + 1.1 * (10 - 3) = 3+1.1*7=3+7.7 = 10.7

Expected return% = 10.7

As per DDM

Price = recent dividend* (1 + growth rate )/(cost of equity - growth rate)

40.5 = 3 * (1+Growth rate) / (0.107 - Growth rate)

40.5*(0.107 - Growth rate)=3 * (1+Growth rate)

40.5*0.107-40.5*growth rate = 3*1+3*growth rate

4.3335-40.5*growth rate=3+3*growth rate

4.3335-3=40.5*growth rate+3*growth rate

1.3335=43.5*growth rate

growth rate=1.3335/43.5=0.03065 = 3.07%

In DDM , for growing perpetual dividends

the price = present value of this perpetual growing dividends.

Formula to calculate this present value of future cash flows is

Dividend recently paid*(1+annual growth rate of dividends)/(cost of equity-annual growth rate of dividends)

Which is what I have used