Pregunta
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Asonia Co. will pay a dividend of \( \$ 5.70, \$ 9.80, \$ 12.65 \), and \( \$ 14.40 \) per share for each of the next four years, respectively. The company will then close its doors. If investors require a return of10.8 percent on the company's stock, what is the stock price?

Ask by Lindsey Chambers. in the United States
Mar 12,2025

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The stock price is approximately \$33.00.

Solución

We are given the following dividends: \[ D_1 = \$5.70,\quad D_2 = \$9.80,\quad D_3 = \$12.65,\quad D_4 = \$14.40 \] and a required return of \( r = 10.8\% = 0.108 \). Since the company pays these dividends over the next 4 years and then closes, the stock price is the sum of the present values of these dividends. The present value of each dividend is given by: \[ PV_t = \frac{D_t}{(1+r)^t} \] Thus, the stock price \( P \) is: \[ P = \frac{5.70}{(1.108)^1} + \frac{9.80}{(1.108)^2} + \frac{12.65}{(1.108)^3} + \frac{14.40}{(1.108)^4} \] Now, we compute each term step by step: 1. For \( t = 1 \): \[ PV_1 = \frac{5.70}{1.108} \approx 5.145 \] 2. For \( t = 2 \): \[ (1.108)^2 \approx 1.227664,\quad PV_2 = \frac{9.80}{1.227664} \approx 7.978 \] 3. For \( t = 3 \): \[ (1.108)^3 \approx 1.359279,\quad PV_3 = \frac{12.65}{1.359279} \approx 9.305 \] 4. For \( t = 4 \): \[ (1.108)^4 \approx 1.505,\quad PV_4 = \frac{14.40}{1.505} \approx 9.569 \] Finally, summing these present values gives: \[ P \approx 5.145 + 7.978 + 9.305 + 9.569 \approx 32.997 \] Therefore, the stock price is approximately: \[ \boxed{\$33.00} \]

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To find the stock price, we must calculate the present value of future dividends expected from Asonia Co. over the next four years and then discount these dividends back to today. 1. Calculate the present value of each dividend: - Year 1 Dividend: \( \frac{5.70}{(1 + 0.108)^1} \) - Year 2 Dividend: \( \frac{9.80}{(1 + 0.108)^2} \) - Year 3 Dividend: \( \frac{12.65}{(1 + 0.108)^3} \) - Year 4 Dividend: \( \frac{14.40}{(1 + 0.108)^4} \) 2. Compute the values: - Year 1: \( \frac{5.70}{1.108} = 5.15 \) - Year 2: \( \frac{9.80}{1.228864} = 7.99 \) - Year 3: \( \frac{12.65}{1.364029} = 9.28 \) - Year 4: \( \frac{14.40}{1.513614} = 9.53 \) 3. Sum these present values to find the stock price: - Stock Price = \( 5.15 + 7.99 + 9.28 + 9.53 = 31.95 \) Thus, the stock price of Asonia Co. is approximately \( \$ 31.95 \).

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