Final answer:
a. The cost of equity using the DDM is 5.23%.
b. The cost of equity using the CAPM is 11.93%.
c. These estimates are different due to the different valuation models used and the assumptions underlying each model.
Step-by-step explanation:
a. To calculate the cost of equity using the Dividend Discount Model (DDM), we first need to calculate the expected dividend growth rate. Given that the dividend just paid is $0.85 and the dividends are expected to grow at 4%, the expected dividend next year would be $0.85 * (1 + 0.04) = $0.884. The cost of equity using DDM can be calculated as: Cost of equity = (Dividend / Stock price) + Dividend growth rate
Cost of equity = ($0.884 / $72) + 0.04 = 0.0123 + 0.04 = 0.0523 or 5.23%
b. To calculate the cost of equity using the Capital Asset Pricing Model (CAPM), we need the risk-free rate of return, the beta of the stock, and the market risk premium. The risk-free rate of return is 3.4%, the beta of the stock is 1.08, and the market risk premium is the difference between the expected return on the market (11.3%) and the risk-free rate of return (3.4%). The cost of equity using CAPM can be calculated as: Cost of equity = Risk-free rate + (Beta * Market risk premium)
Cost of equity = 3.4% + (1.08 * (11.3% - 3.4%)) = 3.4% + (1.08 * 7.9%) = 3.4% + 8.532% = 11.932% or 11.93%
c. The estimates in (a) and (b) are different because they are based on different valuation models. DDM focuses on the present value of expected future dividends, while CAPM considers the risk and return relationship of the stock in relation to the overall market. Additionally, DDM relies on the assumption that the stock's value lies in its ability to generate dividends, while CAPM considers the stock's sensitivity to market movements.