Chapter 9, Problem 2MC

Summary Introduction

To determine: Estimated stock price.

Price Earnings Ratio:

Price earnings ratio is that ratio through which value of the company can be determined. It shows the relationship between the current price of share and earnings per share.

Value per Share:

Through the value per share, performance of the company can be measured, whether company is capable to rive retune of the investment or not. Value per share can be found by the total value of the stock divided by the total number of share.

Explanation of Solution

Solution:

Given,

Number of the share is 300,000.

Number of companies are 3.

Earnings per share are 4.52.

Industrial average of dividends per share is $0.44.

Formula to calculate the value per share,

$\text{Value}\text{per}\text{share}=\frac{\text{Present}\text{value}\text{of}\text{the}\text{stock}}{\text{Share}\text{outstanding}}$

Substitute, $11,655,749.48for the total equity value and 300,000 for the share outstanding,

$\begin{array}{c}\text{Value}\text{per}\text{share}=\frac{\$12,023,710.55}{300,000}\\ =\$40.08\end{array}$

Working notes:

Calculate the Industrial Earnings per share,

$\begin{array}{c}\text{Industry}\text{EPS}=\frac{\text{EPS}\text{of}\text{the}\text{three}\text{companies}}{\text{Number}\text{of}\text{companies}}\\ =\frac{\$1.19+\$1.26+\$2.07}{3}\\ =\frac{\$4.52}{3}\\ =\$1.51\end{array}$

Calculate the industry payout ratio,

$\begin{array}{c}\text{Industry}\text{payout}\text{ratio}=\frac{\text{Industry}\text{average}\text{of}\text{DPS}\left(\text{Dividends}\text{per}\text{share}\right)}{\text{Industry}\text{EPS}\left(\text{Earnings}\text{per}\text{share}\right)}\\ =\frac{\$0.44}{\$1.51}\\ =0.2913\end{array}$

Calculate the industry retention ratio,

$\begin{array}{c}\text{Industry}\text{retention}\text{ratio}=\text{1}-\text{Industry}\text{payout}\text{ratio}\\ =\text{1}-\text{0}\text{.2913}\\ =0.7087\end{array}$

Calculate the industry growth rate,

$\begin{array}{c}\text{Industry}\text{growth}\text{rate}=\text{Industry}\text{<x-custom-btb-me data-me-id="2172" class="microExplainerHighlight">ROE</x-custom-btb-me>}\times \text{Industry}\text{Retention}\text{Ratio}\\ =0.11\times 0.7087\\ =0.077957\end{array}$

Given,

Dividends of the year are $640,000.

Growth rate is 0.1263.

Calculate the dividend for the 1^st year,

$\begin{array}{c}{\text{D}}_{\text{n}+\text{1}}={\text{D}}_{\text{n}}\left(\text{1}+\text{G}\right)\\ =\$640,000\left(1+0.1263\right)\\ =\$720,832\end{array}$

Where,

• ${\text{D}}_{\text{n}+\text{1}}$ is the dividends of current year.
• ${\text{D}}_{\text{n}}$ is the dividends of the last year.
• G is the growth rate.

Calculate the dividend for the 2^nd year,

$\begin{array}{c}{\text{D}}_{\text{n}+\text{1}}={\text{D}}_{\text{n}}\left(\text{1}+\text{G}\right)\\ =\$720,832\left(1+0.1263\right)\\ =\$811,873.0816\end{array}$

Calculate the dividend for the 3^rd year,

$\begin{array}{c}{\text{D}}_{\text{n}+\text{1}}={\text{D}}_{\text{n}}\left(\text{1}+\text{G}\right)\\ =\$811,873\left(1+0.1263\right)\\ =\$914,412.65\end{array}$

Calculate the dividend for the 4^th year,

$\begin{array}{c}{\text{D}}_{\text{n}+\text{1}}={\text{D}}_{\text{n}}\left(\text{1}+\text{G}\right)\\ =\$914,412.65\left(1+0.1263\right)\\ =\$1,029,902.97\end{array}$

Calculate the dividend for the 5^th year,

$\begin{array}{c}{\text{D}}_{\text{n}+\text{1}}={\text{D}}_{\text{n}}\left(\text{1}+\text{G}\right)\\ =\$1,029,902.97\left(1+0.1263\right)\\ =\$1,159,979.72\end{array}$

Calculate the value of the dividend in the five year,

$\begin{array}{c}\text{Value}\text{of}\text{the}\text{stock}=\frac{{\text{D}}_{\text{5}}\left(\text{1}+\text{Industry}\text{growth}\text{rate}\right)}{\left(\text{Industry}\text{return}-\text{Industry}\text{growth}\text{rate}\right)}\\ =\frac{\$1,159,979.97\left(1.1263\right)}{\left(0.15-0.077957\right)}\\ =\frac{\$1,306,485.44}{0.072043}\\ =\$18,134,800.605\end{array}$

Calculate the present value of the stock,

$\begin{array}{c}\text{PV}=\left(\begin{array}{l}\frac{{\text{D}}_{\text{1}}}{{\left(\text{1}+\text{R}\right)}^{\text{n}}}+\frac{{\text{D}}_{\text{2}}}{{\left(\text{1}+\text{R}\right)}^{\text{n}+\text{1}}}+\frac{{\text{D}}_{\text{3}}}{{\left(\text{1}+\text{R}\right)}^{\text{n}+\text{2}}}+\frac{{\text{D}}_{\text{4}}}{{\left(\text{1}+\text{R}\right)}^{\text{n}+\text{3}}}\\ +\frac{{\text{D}}_5+\text{Stock}\text{value}\text{in}\text{year}\text{5}}{{\left(\text{1}+\text{R}\right)}^{\text{n}+4}}\end{array}\right)\\ =\left(\begin{array}{l}\frac{\$720,832}{\left(1+0.15\right)}+\frac{\$811,873.0816}{{\left(1+0.15\right)}^2}+\frac{\$914,412.65}{{\left(1+0.15\right)}^3}+\frac{\$1,029,902.97}{{\left(1+0.15\right)}^4}\\ +\frac{\$1,159,979.72+\$18,134,800.605}{{\left(1+0.15\right)}^5}\end{array}\right)\\ =\left(\begin{array}{l}\$626,810.43+\$613,892.69+\$601,241.16\\ +\$588,850.37+\$9,592,915.9\end{array}\right)\\ =\$12,023,710.55\end{array}$

Conclusion

Hence, estimated stock price is $40.8.