Santa Klaus Toys just paid a dividend of \( \$ 2.80 \) per share. The required return is 11.1 percent and the perpetual dividend growth rate is 3.7 percent. What price should this stock sell for five years from today? a. \( \$ 47.05 \) b. \( \$ 37.84 \) c. \( \$ 45.38 \) d. \( \$ 48.80 \) e. \( \$ 43.76 \)

To find the expected stock price five years from today, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model calculates the price of a stock based on its expected future dividends growing at a constant rate. First, we need to determine the dividend expected in year 5. The formula for the dividend in year \( n \) is: \[ D_n = D_0 \times (1 + g)^n \] where \( D_n \) is the dividend at year \( n \), \( D_0 \) is the most recent dividend paid, \( g \) is the growth rate, and \( n \) is the number of years. Given: - \( D_0 = 2.80 \) - \( g = 0.037 \) - \( n = 5 \) Calculating \( D_5 \): \[ D_5 = 2.80 \times (1 + 0.037)^5 \approx 2.80 \times 1.194052 \approx 3.346 \] Now, we can find the price of the stock at year 5 using the Gordon Growth Model: \[ P_5 = \frac{D_6}{r - g} \] where \( D_6 \) is the dividend in year 6, \( r \) is the required return, and \( g \) is the growth rate. Calculating \( D_6 \): \[ D_6 = D_5 \times (1 + g) = 3.346 \times (1 + 0.037) \approx 3.346 \times 1.037 = 3.471 \] Now, substituting into the price formula: \[ P_5 = \frac{3.471}{0.111 - 0.037} = \frac{3.471}{0.074} \approx 46.92 \] None of the answer choices are exact, but the closest answer to our computed price is approximately \( \$ 47.05 \), which corresponds to choice (a). Thus, the answer is: **a. \( \$ 47.05 \)**.