Chapter 9, Problem 4MC

Assume the company’s growth rate declines to the industry average after five years. What percentage of the stock’s value is attributable to growth opportunities?

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. Value per share can be found by the total value of the stock divided by the total number of shares.

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 percentage of the value of the stock attributable to growth opportunity,

$\text{Y}=\text{1}-\text{X}$

Where,

• Y is the percentage of the value of the stock attributable to growth opportunity.
• X is percentage value of the company not attributable to growth opportunity.

$\begin{array}{c}\text{Y}=1-0.8899\\ =0.1101\\ =11.01\%\end{array}$

Working notes:

Calculate the total earnings,

$\begin{array}{c}\text{Total}\text{earnings}=2\times \text{Numbers}\text{of}\text{share}\times \text{EPS}\text{of}\text{the}\text{company}\\ =2\times 150,000\times \$5.35\\ =\$1,605,000\end{array}$

Calculate cash cow value,

$\begin{array}{c}\text{Cash}\text{cow}\text{value}=\frac{\text{Total}\text{earmings}}{\text{Industry}\text{Average}\text{required}\text{return}}\\ =\frac{\$1,605,000}{0.15}\\ =\$10,700,000\end{array}$

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,

$\begin{array}{c}\text{Industry}\text{growth}\text{rate}=\text{Industry}\text{ROE}\times \text{Industry}\text{Retention}\text{Ratio}\\ =0.11\times 0.7087\\ =0.077957\end{array}$

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,

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

Calculate the percentage value of the company not attributable to growth opportunity,

$\begin{array}{c}\text{X}=\frac{\text{Cash}\text{cow}\text{value}}{\text{Present}\text{value}\text{of}\text{the}\text{stock}}\\ =\frac{\$10,700,000}{\$12,023,710.55}\\ =0.8899\end{array}$

Where,

• X is the percentage value of the company not attributable to growth opportunity.

Conclusion

Hence, the percentage of the value of the stock attributable to growth opportunity is 11.01%.