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. $$ \$ 31.98 $$

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UpStudy AI · Accepted Answer

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.
The stock price is \$31.98.

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