Keidis Industries will pay a dividend of $$ \$ 4.45, \$ 5.55 $$, and $$ \$ 6.75 $$ per share for each of the next three years, respectively, In four years, you believe that the company will be acquired for $$ \$ 62.00 $$ per share. The return on similar stocks is 9.6 percent. What is the current stock price? a. 354.89 b. $$ \$ 59.12 $$ o. $$ \$ 61.95 $$ d. $$ \$ 56.78 $$ e. $$ \$ 71.01 $$

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UpStudy AI · Accepted Answer

To find the current stock price, we can use the formula for the present value of a series of future cash flows.

Given:
- Dividend for the next three years: $4.45, $5.55, $6.75
- Acquisition price in four years: $62.00
- Return on similar stocks: 9.6%

Let's denote the current stock price as $$ P $$.

The present value of the dividends for the next three years can be calculated using the formula for the present value of a series of future cash flows:

$$ PV = \frac{D_1}{1 + r} + \frac{D_2}{(1 + r)^2} + \frac{D_3}{(1 + r)^3} $$

Where:
- $$ PV $$ is the present value
- $$ D_1, D_2, D_3 $$ are the dividends for the next three years
- $$ r $$ is the return on similar stocks

The present value of the acquisition price in four years can be calculated using the formula for the present value of a future cash flow:

$$ PV = \frac{A}{(1 + r)^4} $$

Where:
- $$ PV $$ is the present value
- $$ A $$ is the acquisition price
- $$ r $$ is the return on similar stocks

The current stock price $$ P $$ is the sum of the present value of the dividends and the present value of the acquisition price.

Let's calculate the present value of the dividends and the acquisition price, and then find the current stock price.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{4.45}{\left(1+0.096\right)}+\frac{5.55}{\left(1+0.096\right)^{2}}+\frac{6.75}{\left(1+0.096\right)^{3}}$$
- step1: Remove the parentheses:
  $$\frac{4.45}{1+0.096}+\frac{5.55}{\left(1+0.096\right)^{2}}+\frac{6.75}{\left(1+0.096\right)^{3}}$$
- step2: Add the numbers:
  $$\frac{4.45}{1+0.096}+\frac{5.55}{1.096^{2}}+\frac{6.75}{\left(1+0.096\right)^{3}}$$
- step3: Add the numbers:
  $$\frac{4.45}{1+0.096}+\frac{5.55}{1.096^{2}}+\frac{6.75}{1.096^{3}}$$
- step4: Add the numbers:
  $$\frac{4.45}{1.096}+\frac{5.55}{1.096^{2}}+\frac{6.75}{1.096^{3}}$$
- step5: Convert the expressions:
  $$\frac{4.45}{1.096}+\frac{5.55}{\left(\frac{137}{125}\right)^{2}}+\frac{6.75}{1.096^{3}}$$
- step6: Convert the expressions:
  $$\frac{4.45}{1.096}+\frac{5.55}{\left(\frac{137}{125}\right)^{2}}+\frac{6.75}{\left(\frac{137}{125}\right)^{3}}$$
- step7: Divide the terms:
  $$\frac{2225}{548}+\frac{5.55}{\left(\frac{137}{125}\right)^{2}}+\frac{6.75}{\left(\frac{137}{125}\right)^{3}}$$
- step8: Divide the terms:
  $$\frac{2225}{548}+\frac{346875}{75076}+\frac{6.75}{\left(\frac{137}{125}\right)^{3}}$$
- step9: Divide the terms:
  $$\frac{2225}{548}+\frac{346875}{75076}+\frac{27\times 125^{3}}{4\times 137^{3}}$$
- step10: Reduce fractions to a common denominator:
  $$\frac{2225\times 137\times 137}{548\times 137\times 137}+\frac{346875\times 137}{75076\times 137}+\frac{27\times 125^{3}}{4\times 137^{3}}$$
- step11: Multiply the terms:
  $$\frac{2225\times 137\times 137}{10285412}+\frac{346875\times 137}{75076\times 137}+\frac{27\times 125^{3}}{4\times 137^{3}}$$
- step12: Multiply the numbers:
  $$\frac{2225\times 137\times 137}{10285412}+\frac{346875\times 137}{10285412}+\frac{27\times 125^{3}}{4\times 137^{3}}$$
- step13: Rewrite the expression:
  $$\frac{2225\times 137\times 137}{4\times 137^{3}}+\frac{346875\times 137}{4\times 137^{3}}+\frac{27\times 125^{3}}{4\times 137^{3}}$$
- step14: Transform the expression:
  $$\frac{2225\times 137\times 137+346875\times 137+27\times 125^{3}}{4\times 137^{3}}$$
- step15: Multiply the terms:
  $$\frac{41761025+346875\times 137+27\times 125^{3}}{4\times 137^{3}}$$
- step16: Multiply the numbers:
  $$\frac{41761025+47521875+27\times 125^{3}}{4\times 137^{3}}$$
- step17: Add the numbers:
  $$\frac{89282900+27\times 125^{3}}{4\times 137^{3}}$$
Calculate or simplify the expression $$ 62/(1+0.096)^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{62}{\left(1+0.096\right)^{4}}$$
- step1: Add the numbers:
  $$\frac{62}{1.096^{4}}$$
- step2: Convert the expressions:
  $$\frac{62}{\left(\frac{137}{125}\right)^{4}}$$
- step3: Simplify the expression:
  $$\frac{62}{\frac{137^{4}}{125^{4}}}$$
- step4: Rewrite the expression:
  $$\frac{62\times 125^{4}}{137^{4}}$$
Calculate or simplify the expression $$ 13.807641 + 42.968429 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$13.807641+42.968429$$
- step1: Add the numbers:
  $$56.77607$$
The present value of the dividends is approximately $13.81 and the present value of the acquisition price is approximately $42.97.

Therefore, the current stock price is approximately $56.78.
The current stock price is approximately \$56.78.

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