Question

Sierra Corporation has just paid a dividend of $2 per share, and its dividends are expected to grow at a steady rate of 6% for the foreseeable future. The firm’s shares are currently selling for $30 per share, with an equity beta of 1.2. The risk-free rate is 5% and expected market return is 12%. What is the firm’s estimated cost of equity if we were to calculate it as the average of the costs of equity from the dividend growth model and the security market line?

Select one:

a. 13.07%

b. 13.23%

c. 13.43%

d. 14.23%

e. 14.37%

Answer #1

**b. 13.23%**

Cost of equity using the security market line = Risk-free rate + Beta(Market return - Risk-free rate)

Cost of equity using the security market line = 0.05 + 1.2(0.12 - 0.05)

Cost of equity using the security market line = 0.134 or 13.4%

Cost of equity using the gordon dividend growth model = [D0(1 + g) / P0] + g

Cost of equity using the gordon dividend growth model = [$2(1.06) / $30] + 0.06

Cost of equity using the gordon dividend growth model = 0.130667 or 13.0667%

Now we have two diferent rates, so we can do an average to get the best estimate cost of equity:

= (0.134 + 0.130667) / 2

= 0.1323 or 13.23%

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