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 of 10.8 percent on the company's stock, what is the stock price? a. \( \$ 33.80 \) b. \( \$ 38.37 \) c. \( \$ 36.40 \) d. \( \$ 44.69 \) e. \( \$ 31.98 \)

To find the stock price, we need to calculate the present value of the dividends paid over the next four years. Given: - Dividends for each year: $5.70, $9.80, $12.65, $14.40 - Required return on investment: 10.8% We will use the formula for present value of a series of cash flows: \[ PV = \frac{PMT}{1 + r} + \frac{PMT}{(1 + r)^2} + \frac{PMT}{(1 + r)^3} + \frac{PMT}{(1 + r)^4} \] Where: - PV = Present Value - PMT = Annual dividend - r = Required return on investment (10.8% in this case) Let's calculate the present value of the dividends and then find the stock price. Calculate the value by following steps: - step0: Calculate: \(\frac{5.7}{\left(1+0.108\right)}+\frac{9.8}{\left(1+0.108\right)^{2}}+\frac{12.65}{\left(1+0.108\right)^{3}}+\frac{14.4}{\left(1+0.108\right)^{4}}\) - step1: Remove the parentheses: \(\frac{5.7}{1+0.108}+\frac{9.8}{\left(1+0.108\right)^{2}}+\frac{12.65}{\left(1+0.108\right)^{3}}+\frac{14.4}{\left(1+0.108\right)^{4}}\) - step2: Add the numbers: \(\frac{5.7}{1+0.108}+\frac{9.8}{1.108^{2}}+\frac{12.65}{\left(1+0.108\right)^{3}}+\frac{14.4}{\left(1+0.108\right)^{4}}\) - step3: Add the numbers: \(\frac{5.7}{1+0.108}+\frac{9.8}{1.108^{2}}+\frac{12.65}{1.108^{3}}+\frac{14.4}{\left(1+0.108\right)^{4}}\) - step4: Add the numbers: \(\frac{5.7}{1+0.108}+\frac{9.8}{1.108^{2}}+\frac{12.65}{1.108^{3}}+\frac{14.4}{1.108^{4}}\) - step5: Add the numbers: \(\frac{5.7}{1.108}+\frac{9.8}{1.108^{2}}+\frac{12.65}{1.108^{3}}+\frac{14.4}{1.108^{4}}\) - step6: Convert the expressions: \(\frac{5.7}{1.108}+\frac{9.8}{\left(\frac{277}{250}\right)^{2}}+\frac{12.65}{1.108^{3}}+\frac{14.4}{1.108^{4}}\) - step7: Convert the expressions: \(\frac{5.7}{1.108}+\frac{9.8}{\left(\frac{277}{250}\right)^{2}}+\frac{12.65}{\left(\frac{277}{250}\right)^{3}}+\frac{14.4}{1.108^{4}}\) - step8: Convert the expressions: \(\frac{5.7}{1.108}+\frac{9.8}{\left(\frac{277}{250}\right)^{2}}+\frac{12.65}{\left(\frac{277}{250}\right)^{3}}+\frac{14.4}{\left(\frac{277}{250}\right)^{4}}\) - step9: Divide the terms: \(\frac{1425}{277}+\frac{9.8}{\left(\frac{277}{250}\right)^{2}}+\frac{12.65}{\left(\frac{277}{250}\right)^{3}}+\frac{14.4}{\left(\frac{277}{250}\right)^{4}}\) - step10: Divide the terms: \(\frac{1425}{277}+\frac{612500}{277^{2}}+\frac{12.65}{\left(\frac{277}{250}\right)^{3}}+\frac{14.4}{\left(\frac{277}{250}\right)^{4}}\) - step11: Divide the terms: \(\frac{1425}{277}+\frac{612500}{277^{2}}+\frac{197656250}{277^{3}}+\frac{14.4}{\left(\frac{277}{250}\right)^{4}}\) - step12: Divide the terms: \(\frac{1425}{277}+\frac{612500}{277^{2}}+\frac{197656250}{277^{3}}+\frac{1152\times 5^{11}}{277^{4}}\) - step13: Reduce fractions to a common denominator: \(\frac{1425\times 277\times 277\times 277}{277\times 277\times 277\times 277}+\frac{612500\times 277\times 277}{277^{2}\times 277\times 277}+\frac{197656250\times 277}{277^{3}\times 277}+\frac{1152\times 5^{11}}{277^{4}}\) - step14: Multiply the terms: \(\frac{1425\times 277\times 277\times 277}{5887339441}+\frac{612500\times 277\times 277}{277^{2}\times 277\times 277}+\frac{197656250\times 277}{277^{3}\times 277}+\frac{1152\times 5^{11}}{277^{4}}\) - step15: Multiply the terms: \(\frac{1425\times 277\times 277\times 277}{5887339441}+\frac{612500\times 277\times 277}{277^{4}}+\frac{197656250\times 277}{277^{3}\times 277}+\frac{1152\times 5^{11}}{277^{4}}\) - step16: Calculate: \(\frac{1425\times 277\times 277\times 277}{5887339441}+\frac{612500\times 277\times 277}{277^{4}}+\frac{197656250\times 277}{277^{4}}+\frac{1152\times 5^{11}}{277^{4}}\) - step17: Rewrite the expression: \(\frac{1425\times 277\times 277\times 277}{277^{4}}+\frac{612500\times 277\times 277}{277^{4}}+\frac{197656250\times 277}{277^{4}}+\frac{1152\times 5^{11}}{277^{4}}\) - step18: Transform the expression: \(\frac{1425\times 277\times 277\times 277+612500\times 277\times 277+197656250\times 277+1152\times 5^{11}}{277^{4}}\) - step19: Multiply the terms: \(\frac{30286854525+612500\times 277\times 277+197656250\times 277+1152\times 5^{11}}{277^{4}}\) - step20: Multiply the terms: \(\frac{30286854525+46996512500+197656250\times 277+1152\times 5^{11}}{277^{4}}\) - step21: Multiply the numbers: \(\frac{30286854525+46996512500+54750781250+1152\times 5^{11}}{277^{4}}\) - step22: Add the numbers: \(\frac{132034148275+1152\times 5^{11}}{277^{4}}\) The present value of the dividends is approximately $31.98. Therefore, the stock price is $31.98.