Chapter 8, Problem 2M

Summary Introduction

Case summary:

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

R Company has earnings per share of $3.15 and the dividends of $45,000 each were paid to the owners of the company. Moreover, there is even 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 $35.98.

Explanation of Solution

Given information:

The earnings per share are $3.15, Return on equity (ROE) is 17%, and the required rate of return is 14%. The earnings per share without the write-off is $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 earning per share is $0.96, dividend per share is $0.18, and the rate of return is 11.67%. The industry average ROE is 9.59% and the dividend paid per share in the current year is $0.90 (Refer the previous problem-computed value).

Formulae:

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:

$\begin{array}{c}\text{Industry payout ratio}=\frac{\text{Total dividend per share}}{\text{Industry earnings per share}}\\ =\frac{\$0.18}{\$1.45}\\ =0.1241\end{array}$

Hence, theindustrypayout ratio is 0.1241 or 12.41%.

Compute the industry retention ratio:

$\begin{array}{c}\text{Industry retention ratio}=1-\text{Industry payout ratio}\\ =1-\left(\frac{12.41}{100}\right)\\ =1-0.1241\\ =0.8759\end{array}$

Hence, the industry retention ratio is 0.8759 or 87.59%.

Compute the industry growth rate:

$\begin{array}{c}\text{Industry growth rate}=\text{ Total industrial return on equity}\times \text{Industry retention ratio}\\ =\left(\frac{9.59}{100}\right)\times \left(\frac{87.59}{100}\right)\\ =0.0959\times 0.8759\\ =\text{0}\text{.0839}\end{array}$

Hence, the industry growth rate of the company is 0.0839 or 8.39%.

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

Compute the dividend for Year 1:

$\begin{array}{c}{\text{D}}_1=\text{Current dividend paid}\times \left(1+\text{Industry payout ratio}\right)\\ =\$0.90\times \left(1+\frac{12.14}{100}\right)\\ =\$0.90\times \left(1+0.1241\right)\\ =\$0.90\times 1.1241\\ =\$1.01\end{array}$

Hence, the dividend for Year 1 is $1.01.

Compute the dividend for Year 2:

$\begin{array}{c}{\text{D}}_2=\text{Dividend in Year 1}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.01\times \left(1+\frac{12.14}{100}\right)\\ =\$1.01\times \left(1+0.1241\right)\\ =\$1.01\times 1.1241\\ =\$1.13\end{array}$

Hence, the dividend for Year 2 is $1.13.

Compute the dividend for Year 3:

$\begin{array}{c}{\text{D}}_3=\text{Dividend in Year 2}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.13\times \left(1+\frac{12.14}{100}\right)\\ =\$1.13\times \left(1+0.1241\right)\\ =\$1.13\times 1.1241\\ =\$1.27\end{array}$

Hence, the dividend for Year 3 is $1.27.

Compute the dividend for Year 4:

$\begin{array}{c}{\text{D}}_4=\text{Dividend in Year 3}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.27\times \left(1+\frac{12.14}{100}\right)\\ =\$1.27\times \left(1+0.1241\right)\\ =\$1.27\times 1.1241\\ =\$1.42\end{array}$

Hence, the dividend for Year 4 is $1.42.

Compute the dividend for Year 5:

$\begin{array}{c}{\text{D}}_5=\text{Dividend in Year 4}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.42\times \left(1+\frac{12.14}{100}\right)\\ =\$1.42\times \left(1+0.1241\right)\\ =\$1.42\times 1.1241\\ =\$1.60\end{array}$

Hence, the dividend for Year 5 is $1.60.

Compute the dividend for Year 6:

$\begin{array}{c}{\text{D}}_6=\text{Dividend in Year 5}\times \left(1+\text{Industry payout ratio}\right)\\ =\$1.60\times \left(1+\frac{12.14}{100}\right)\\ =\$1.60\times \left(1+0.1241\right)\\ =\$1.60\times 1.1241\\ =\$1.79\end{array}$

Hence, the dividend for Year 6 is $1.79.

Compute the stock price in Year 5:

$\begin{array}{c}\text{Stock price in Year 5}=\frac{\text{Dividend of Year 6}}{\left(\text{Total industry average return}-\text{Industry growth rate}\right)}\\ =\frac{\$1.79}{\left(\frac{11.67}{100}\right)-\left(\frac{8.39}{100}\right)}\\ =\frac{\$1.79}{\left(0.1167-0.0839\right)}\\ =\frac{\$1.79}{0.0328}\\ =\$54.57\end{array}$

Hence, the stock price of Year 5 is $54.57.

Compute the stock price:

$\begin{array}{c}{\text{P}}_o=\left[\begin{array}{l}\frac{{\text{D}}_1}{\left(1+\text{Total industry average return}\right)}+\frac{{\text{D}}_2}{{\left(1+\text{Total industry average return}\right)}^2}\\ +\frac{{\text{D}}_3}{{\left(1+\text{Total industry average return}\right)}^3}+\frac{{\text{D}}_4}{{\left(1+\text{Total industry average return}\right)}^4}\\ +\frac{\left({\text{D}}_5+\text{Stock price in Year 5}\right)}{{\left(1+\text{Total industry average return}\right)}^5}\end{array}\right]\\ =\left[\frac{\$1.01}{1+{\left(\frac{11.67}{100}\right)}^1}+\frac{\$1.13}{1+{\left(\frac{11.67}{100}\right)}^2}+\frac{\$1.27}{1+{\left(\frac{11.67}{100}\right)}^3}+\frac{\$1.42}{1+{\left(\frac{11.67}{100}\right)}^4}+\frac{\$1.60+\$54.57}{1+{\left(\frac{11.67}{100}\right)}^5}\right]\\ =\left[\frac{\$1.01}{\left(1+0.1167\right)}+\frac{\$1.13}{{\left(1+0.1167\right)}^2}+\frac{\$1.27}{{\left(1+0.1167\right)}^3}+\frac{\$1.42}{{\left(1+0.1167\right)}^4}+\frac{\$56.17}{{\left(1+0.1167\right)}^5}\right]\\ =\left[\frac{\$1.01}{1.1167}+\frac{\$1.13}{1.24701}+\frac{\$1.27}{1.39254}+\frac{\$1.42}{1.55505}+\frac{\$56.17}{1.73653}\right]\\ =\left(\$0.90445+\$0.90616+\$0.91200+\$0.91315+\$32.34611\right)\\ =\$35.98\end{array}$

Hence, the stock price is $35.98.