Chapter 8, Problem 2M

Summary Introduction

Case summary:

Person C and Person GR are the founders and owners of R Company. This company manufactures and installs heating, ventilation, and cooling units (HVAC) commercially. Both the owners have 50,000 shares of the company’s stock, as per the partnership deed. They wanted to sell their stocks and decided to value their holdings in the company.

R Company has earnings per share of $3.75 and dividends of $48,000 each were paid to the owners of the company. Moreover, there is even a return on equity (ROE) of 17% and the required rate of return is 14%.

Characters in the case:

R Company: The firm that wants to value their stocks.

Person C: Co-owner of Company R.

Person GR: Co-owner of Company R.

To determine: The estimate of stock price on the assumption of growth rate.

Answer to Problem 2M

The estimate of stock price is $41.66.

Explanation of Solution

Given information:

The earnings per share are $3.75, Return on Equity (ROE) is 17%, and the required rate of return is 14%. The earnings per share without the write-off are $1.10. The earnings per share of AC Company is $1.30 and NH Company (both are competitors) is $1.95.

The industry average of earnings per share is $0.96, dividend per share is $0.16, and the rate of return is 11.67%. The industry average ROE is 10% and the dividend paid per share in the current year is $0.96 (refer to the previous problem-computed value).

Formula:

The formula to calculate the industry (competitor’s) earnings per share:

$\text{Industry earnings per share}=\frac{\text{Sum of each earnings per share of competitors}}{\text{Number of competitors}}$

The formula to calculate the industry payout ratio:

$\text{Industry payout ratio}=\frac{\text{Total dividend per share}}{\text{Industry earnings per share}}$

The formula to calculate the industry retention ratio:

$\text{Industry retention ratio}=1-\text{Industry payout ratio}$

The formula to calculate the industry growth rate:

$\text{Industry growth rate}=\text{Total industrial return on equity}\times \text{Industry retention ratio}$

The formula to calculate the total dividends for the next year:

${\text{D}}_1=\text{Current dividend paid}\times \left(1+\text{Industry payout ratio}\right)$

Where,

D₁ refers to the expected dividend per share in the next period.

The formula to calculate the stock price in Year 5:

$\text{Stock price in Year 5}=\frac{\text{Dividend of Year 6}}{\left(\text{Total industry average return}-\text{Industry growth rate}\right)}$

The formula to calculate the current total value of the stock price:

${\text{P}}_o=\frac{{\text{D}}_1}{\left(\text{R}-\text{g}\right)}$

Where,

P_o refers to the price of the stock,

D₁ refers to the expected dividend per share in the next period,

R refers to the required rate of return on its stock,

grefers to the constant rate of growth.

Compute the industry earnings per share:

$\begin{array}{c}\text{Industry earnings per share}=\frac{\text{Sum of each earnings per share of competitors}}{\text{Number of competitors}}\\ =\frac{\$1.30+\$1.95+\$1.10}{3}\\ =\frac{\$4.35}{3}\\ =\$1.45\end{array}$

Hence, the industry earnings per share are $1.45.

Compute the industry payout ratio:

$\begin{array}{c}\text{Industry payout ratio}=\frac{\text{Total dividend per share}}{\text{Industry earnings per share}}\\ =\frac{\$0.16}{\$1.45}\\ =0.1103\end{array}$

Hence, theindustrypayout ratio is 0.1103 or 11.03%.

Compute the industry retention ratio:

$\begin{array}{c}\text{Industry retention ratio}=1-\text{Industry payout ratio}\\ =1-\left(\frac{11.03}{100}\right)\\ =1-0.1103\\ =0.8897\end{array}$

Hence, the industry retention ratio is 0.8897 or 88.97%.

Compute the industry growth rate:

$\begin{array}{c}\text{Industry growth rate}=\text{ Total industrial return on equity}\times \text{Industry retention ratio}\\ =\left(\frac{10}{100}\right)\times \left(\frac{88.97}{100}\right)\\ =0.10\times 0.8897\\ =0.08897\end{array}$

Hence, the industry growth rate of the company is 0.08897 or 8.897%.

Note: The Company has continued to grow at a fast pace in the current five years before the slowdown of the industry growth rate. Compute the total dividends for each of the next 6 years, as a result of the aforementioned growth rate.

Compute the dividend for Year 1:

$\begin{array}{c}{\text{D}}_1=\text{Current dividend paid}\times \left(1+\text{Industry payout ratio}\right)\\ =\$0.96\times \left(1+\frac{11.03}{100}\right)\\ =\$0.96\times \left(1+0.1103\right)\\ =\$0.96\times 1.1103\\ =\$1.065\end{array}$

Hence, the dividend for Year 1 is $1.065.

Compute the dividend for Year 2:

$\begin{array}{c}{\text{D}}_2=\text{Dividend in Year 1}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.065\times \left(1+\frac{11.03}{100}\right)\\ =\$1.065\times \left(1+0.1103\right)\\ =\$1.065\times 1.1103\\ =\$1.18\end{array}$

Hence, the dividend for Year 2 is $1.18.

Compute the dividend for Year 3:

$\begin{array}{c}{\text{D}}_3=\text{Dividend in Year 2}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.18\times \left(1+\frac{11.03}{100}\right)\\ =\$1.18\times \left(1+0.1103\right)\\ =\$1.18\times 1.1103\\ =\$1.31\end{array}$

Hence, the dividend for Year 3 is $1.31.

Compute the dividend for Year 4:

$\begin{array}{c}{\text{D}}_4=\text{Dividend in Year 3}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.31\times \left(1+\frac{11.03}{100}\right)\\ =\$1.31\times \left(1+\mathrm{0.11.03}\right)\\ =\$1.31\times 1.1103\\ =\$1.45\end{array}$

Hence, the dividend for Year 4 is $1.45.

Compute the dividend for Year 5:

$\begin{array}{c}{\text{D}}_5=\text{Dividend in Year 4}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.45\times \left(1+\frac{11.03}{100}\right)\\ =\$1.45\times \left(1+0.1103\right)\\ =\$1.45\times 1.1103\\ =\$1.61\end{array}$

Hence, the dividend for Year 5 is $1.61.

Compute the dividend for Year 6:

$\begin{array}{c}{\text{D}}_6=\text{Dividend in Year 5}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.61\times \left(1+\frac{11.03}{100}\right)\\ =\$1.61\times \left(1+0.1103\right)\\ =\$1.61\times 1.1103\\ =\$1.78\end{array}$

Hence, the dividend for Year 6 is $1.78.

Compute the stock price in Year 5:

$\begin{array}{c}\text{Stock price in Year 5}=\frac{\text{Dividend of Year 6}}{\left(\text{Total industry average return}-\text{Industry growth rate}\right)}\\ =\frac{\$1.78}{\left(\frac{11.67}{100}\right)-\left(\frac{8.897}{100}\right)}\\ =\frac{\$1.78}{\left(0.1167-\text{0}\text{.08897}\right)}\\ =\frac{\$1.78}{0.02773}\\ =\$64.19\end{array}$

Hence, the stock price of Year 5 is $64.19.

Compute the stock price:

$\begin{array}{c}{\text{P}}_o=\left[\begin{array}{l}\frac{{\text{D}}_1}{\left(1+\text{Total industry average return}\right)}+\frac{{\text{D}}_2}{{\left(1+\text{Total industry average return}\right)}^2}\\ +\frac{{\text{D}}_3}{{\left(1+\text{Total industry average return}\right)}^3}+\frac{{\text{D}}_4}{{\left(1+\text{Total industry average return}\right)}^4}\\ +\frac{\left({\text{D}}_5+\text{Stock price in Year 5}\right)}{{\left(1+\text{Total industry average return}\right)}^5}\end{array}\right]\\ =\left[\frac{\$1.065}{1+{\left(\frac{11.67}{100}\right)}^1}+\frac{\$1.18}{1+{\left(\frac{11.67}{100}\right)}^2}+\frac{\$1.31}{1+{\left(\frac{11.67}{100}\right)}^3}+\frac{\$1.45}{1+{\left(\frac{11.67}{100}\right)}^4}+\frac{\left(\$1.61+\$64.19\right)}{1+{\left(\frac{11.67}{100}\right)}^5}\right]\\ =\left[\frac{\$1.065}{\left(1+0.1167\right)}+\frac{\$1.18}{{\left(1+0.1167\right)}^2}+\frac{\$1.31}{{\left(1+0.1167\right)}^3}+\frac{\$1.45}{{\left(1+0.1167\right)}^4}+\frac{\$\text{65}\text{.8}0}{{\left(1+0.1167\right)}^5}\right]\\ =\left[\frac{\$1.065}{1.1167}+\frac{\$1.18}{1.24701}+\frac{\$1.31}{1.39254}+\frac{\$1.45}{1.55505}+\frac{\$\text{65}\text{.8}0}{1.73653}\right]\\ =\left(\$0.95370+\$0.94626+\$0.94072+\$0.93244+\$37.89165\right)\\ =\$41.66\end{array}$

Hence, the stock price is $41.66.