Question

A stock just paid a dividend of $1.31. The dividend is expected to grow at 27.42% for two years and then grow at 3.40% thereafter. The required return on the stock is 13.10%. What is the value of the stock?

Answer 1

Using the two-stage dividend discount model, we project dividends for the first two years considering the special growth rate and then the terminal value at the lower perpetual growth rate. By discounting these values back to the present using the required rate of return, we calculate the stock value to be $20.63.

Step-by-step explanation:

To calculate the value of the stock with variable growth dividends, we can use the dividend discount model (DDM). Given a dividend of $1.31 that grows at 27.42% for the first two years and 3.40% thereafter and a required return of 13.10%, we project the dividends for the first two years:

• D1 = $1.31 * (1 + 27.42%) = $1.669282
• D2 = $1.669282 * (1 + 27.42%) = $2.12600364

Next, we determine the terminal value (TV) at the end of year two when the dividend growth rate drops to 3.40%:

TV = D2 * (1 + 3.40%) / (13.10% - 3.40%)

TV = $2.12600364 * (1 + 0.034) / (0.131 - 0.034) = $22.3288155

Finally, we discount the projected dividends and the terminal value back to present value:

• PV of D1 = $1.669282 / (1 + 13.10%)
• PV of D2 = $2.12600364 / (1 + 13.10%)^2
• PV of TV = $22.3288155 / (1 + 13.10%)^2

Adding these up gives us the current stock price:

Price = PV of D1 + PV of D2 + PV of TV = $1.47669196 + $1.67011488 + $17.4853212 = $20.63

Therefore, the final answer is the stock is valued at $20.63 using the two-stage dividend discount model.