Final answer:
To calculate the value of a stock with a growth-rate change, the dividend discount model (DDM) is used in conjunction with the CAPM to discount expected dividends and terminal value to present value. The calculated required rate of return is based on the given risk-free rate, beta, and market risk premium. The value of the stock is the present value of all expected future dividends and the discounted terminal value.
Step-by-step explanation:
The student has calculated the value of the stock by considering the risk-free rate, the market risk premium, and the stock's beta (β). To determine the stock's value, one must use the dividend discount model (DDM), which values a stock based on its dividend growth. Initially, dividends are expected to grow at 20.64% for three years and then at a constant rate of 4.52% thereafter. The required rate of return is determined using the Capital Asset Pricing Model (CAPM), which takes into account the risk-free rate, the stock's beta, and the market risk premium. The expected dividends are then discounted back to their present value using the required rate of return, and the terminal value of the stock (the value at the end of the high-growth period) is also calculated and discounted back to the present.
The formula for the CAPM is:
Required rate of return = Risk-free rate + (β * Market risk premium)
In this case, the required rate of return would be:
2.63% + (1.37 * 7.37%) = 12.7%
The value of the stock can then be calculated by discounting the expected dividends for the high-growth period and adding the discounted terminal value of the stock:
D1 / (1 + r) + D2 / (1 + r)^2 + D3 / (1 + r)^3 + Terminal value / (1 + r)^3
Where D1, D2, D3 are the dividends in years 1, 2, and 3 respectively, r is the required rate of return, and the Terminal value is the expected value of the stock at the end of the third year.