Final answer:
The stock's value is calculated using the two-stage dividend discount model, accounting for different growth rates for the first two years and a perpetual growth rate after that, with all future dividends discounted back to the present value using the required rate of return.
Step-by-step explanation:
The value of a stock that just paid a dividend of $2.92, with expected dividend growth rates of 21.65% for two years and then 4.49% thereafter, and a required return of 10.32%, can be determined using the dividend discount model. This model considers the present value of the expected future dividends. The calculation involves discounting the forecasted dividends at the given growth rates and then adding the present value of dividends that will grow at a perpetual rate beyond the initial high growth phase.
To calculate the stock's value, we must first find the expected dividends for the first two years, which will be growing at 21.65%, and then calculate the terminal value beginning in the third year when dividends grow at a perpetual rate of 4.49%. The formula incorporates the required return on the stock to discount these future dividends back to the present value.
Example Calculation:
- D1 = D0 × (1 + g1) = $2.92 × (1 + 0.2165)
- D2 = D1 × (1 + g1)
- D3 = D2 × (1 + g2)
- Terminal value (TV) = D3 / (r - g2)
- Stock value = Present value of D1 + Present value of D2 + Present value of TV
It is important to accurately calculate each term and sum them to find the current stock value, considering the two-stage growth model.