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Cost of Equity

I have the answer for a problem below. I understand how to calculate CAPM and Risk Premium, but not how to calculate the Discounted Cash Flow (DCF) method.

Problem:
Acme Corporation's next expected dividend (D1) is $2.50. The firm has maintained a constant payment ratio of 50 percent during the past 7 years. Seven years ago its EPS was $1.50. The firm's beta coefficient is 1.2. The required rate of return on an average stock in the market is 13 percent, and the risk-free rate is 7 percent. Acme's A-rated bonds are yielding 10 percent, and its current stock price is $30. Which of the following values is the most reasonable estimate of Acme's cost of common equity, rs?

Answer 14%

CAPM: Cost of common equity (rs) = Risk-free rate + (Market risk - Risk-free rate)Beta 7% + (13% - 7%)1.2 = 14.2%

Risk Premium: rs = Bond yield + Risk premium = 10% + 4% = 14%

DCF: Cost of common equity (rs)= expected dividend (D1) / stock price is $30 = growth (g), where g can be estimated as follows:
$0.75 = $2.50 (PVIF r,7)
PVIF r,7 = $0.75 / $2.5 = 0.3000

The books states, "Thus r, which is the compound growth rate, g is about 19%, or using a calculator, 18.8%. Therefore, rs = 0.083 + 0.1888 = 27.1%."

My question: How do you calculate 19%, or using a calculator, 18.8%?

Thank you.

Solution Preview

My question: How do you calculate 19%, or using a calculator, 18.8%?

What the value of 19% or 18.8% is the compound rate of growth. The initial value of EPS is 1.50 and dividend is 50% of EPS. So the dividend seven years ago was 0.75. The dividend ...

Solution Summary

The solution explains how to calculate the cost of equity

$2.19