Chapter 7, Problem 2CC

Summary Introduction

Case summary:

Person C and Person GR are the founder and owners of the R Company. This company commercially produces and installs heating, ventilation, and cooling units (HVAC). 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 holding in the company.

The R Company has earnings per share of $4.85 and dividends of $75,000 each were paid to the owners of the company. Moreover, there is even the Return on equity (ROE) of 17% and required rate of return is 14%.

Characters in the case:

R Company: The firm wants to value their stocks.

Person C: Co-owner of Company R.

Person GR: Co-owner of Company R.

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

Answer to Problem 2CC

The estimate of stock price is $41.33.

Explanation of Solution

Given information:

The earnings per share are $4.85, Return on equity (ROE) is 17%, and required rate of return is 14%. The earnings per share without of written off are $0.54. The earnings per share of AC Company are $0.84 and NH Company (both are competitors) is $1.34.

The industry average of earning per share is $0.54, dividend per share is $0.49, and return is 11.67%.The industry average ROE is 15% and the dividend per share paid in the current year is $1.5 (Refer 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 of next year:

${\text{D}}_1=\text{Current dividend paid}\times \left(1+\text{Growth rate}\right)$

Where,

D₁ refers to the next period expected dividend per share.

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 next period expected dividend per share.

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

grefers to the constant rate of growth.

Compute the industry earnings per share:

$\begin{array}{c}\text{Industry earnings per share}=\frac{\text{Sum of each earnings per share of competitors}}{\text{Number of competitors}}\\ =\frac{\$0.84+\$1.34+\$0.54}{3}\\ =\frac{\$2.72}{3}\\ =\$0.91\end{array}$

Hence, the industry earnings per share are $0.91.

Compute the industry payout ratio:

$\begin{array}{c}\text{Industry payout ratio}=\frac{\text{Total dividend per share}}{\text{Industry earnings per share}}\\ =\frac{\$0.49}{\$0.91}\\ =\text{0}\text{.5384}\end{array}$

Hence, the industry payout ratio is 0.5384 or 53.84%.

Compute the industry retention ratio:

$\begin{array}{c}\text{Industry retention ratio}=1-\text{Industry payout ratio}\\ =1-\left(\frac{53.84}{100}\right)\\ =1-0.5384\\ =\text{0}\text{.4616}\end{array}$

Hence, the industry retention ratio is 0.4616 or 46.16%.

Compute the industry growth rate:

$\begin{array}{c}\text{Industry growth rate}=\text{ Total industrial return on equity}\times \text{Industry retention ratio}\\ =\left(\frac{15}{100}\right)\times \left(\frac{46.16}{100}\right)\\ =0.15\times 0.4616\\ =\text{0}\text{.0692}\end{array}$

Hence, the industry growth rate of the company is 0.0692 or 6.92%.

Note: The Company has continued to grow in the current pace for 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:

$\begin{array}{c}{\text{D}}_1=\text{Current dividend paid}\times \left(1+\text{Growth rate}\right)\\ =\$1.5\times \left(1+\frac{11.74}{100}\right)\\ =\$1.5\times \left(1+\text{0}\text{.1174}\right)\\ =\$1.5\times 1.1174\\ =\$1.68\end{array}$

Hence, the dividend for Year 1 is $1.68.

Compute the dividend for Year 2:

$\begin{array}{c}{\text{D}}_2=\text{Dividend in Year 1}\times \left(1+\text{Growth rate}\right)\\ =\$1.68\times \left(1+\frac{11.74}{100}\right)\\ =\$1.68\times \left(1+\text{0}\text{.1174}\right)\\ =\$1.68\times 1.1174\\ =\$1.87\end{array}$

Hence, the dividend for Year 2 is $1.87.

Compute the dividend for Year 3:

$\begin{array}{c}{\text{D}}_3=\text{Dividend in Year 2}\times \left(1+\text{Growth rate}\right)\\ =\$1.87\times \left(1+\frac{11.74}{100}\right)\\ =\$1.87\times \left(1+0.1174\right)\\ =\$1.87\times 1.1174\\ =\$2.09\end{array}$

Hence, the dividend for Year 3 is $2.09.

Compute the dividend for Year 4:

$\begin{array}{c}{\text{D}}_4=\text{Dividend in Year 3}\times \left(1+\text{Growth rate}\right)\\ =\$2.09\times \left(1+\frac{11.74}{100}\right)\\ =\$2.09\times \left(1+0.1174\right)\\ =\$2.09\times 1.1174\\ =\$2.34\end{array}$

Hence, the dividend for Year 4 is $2.34.

Compute the dividend for Year 5:

$\begin{array}{c}{\text{D}}_5=\text{Dividend in Year 4}\times \left(1+\text{Growth rate}\right)\\ =\$2.34\times \left(1+\frac{11.74}{100}\right)\\ =\$2.34\times \left(1+0.1174\right)\\ =\$2.34\times 1.1174\\ =\$2.61\end{array}$

Hence, the dividend for Year 5 is $2.61.

Compute the dividend for Year 6:

$\begin{array}{c}{\text{D}}_6=\text{Dividend in Year 5}\times \left(1+\text{Industry Growth rate}\right)\\ =\$2.61\times \left(1+\frac{6.92}{100}\right)\\ =\$2.61\times \left(1+\text{0}\text{.0692}\right)\\ =\$2.61\times 1.0692\\ =\$2.79\end{array}$

Hence, the dividend for Year 6 is $2.79.

Compute the stock price in Year 5:

$\begin{array}{c}\text{Stock price in Year 5}=\frac{\text{Dividend of Year 6}}{\left(\text{Total industry average return}-\text{Industry growth rate}\right)}\\ =\frac{\$2.79}{\left(\frac{11.67}{100}\right)-\left(\frac{6.92}{100}\right)}\\ =\frac{\$2.79}{\left(0.1167-0.0692\right)}\\ =\frac{\$2.79}{0.0475}\\ =\$58.74\end{array}$

Hence, the stock price of Year 5 is $58.74.

Compute the stock price:

$\begin{array}{c}{\text{P}}_o=\left[\begin{array}{l}\frac{{\text{D}}_1}{\left(1+\text{Total industry average return}\right)}+\frac{{\text{D}}_2}{{\left(1+\text{Total industry average return}\right)}^2}\\ +\frac{{\text{D}}_3}{{\left(1+\text{Total industry average return}\right)}^3}+\frac{{\text{D}}_4}{{\left(1+\text{Total industry average return}\right)}^4}\\ +\frac{\left({\text{D}}_5+\text{Stock price in Year 5}\right)}{{\left(1+\text{Total industry average return}\right)}^5}\end{array}\right]\\ =\left[\frac{\$1.68}{1+{\left(\frac{11.67}{100}\right)}^1}+\frac{\$1.87}{1+{\left(\frac{11.67}{100}\right)}^2}+\frac{\$2.09}{1+{\left(\frac{11.67}{100}\right)}^3}+\frac{\$2.34}{1+{\left(\frac{11.67}{100}\right)}^4}+\frac{\left(\$2.61+\$58.74\right)}{1+{\left(\frac{11.67}{100}\right)}^5}\right]\\ =\left[\frac{\$1.68}{\left(1+0.1167\right)}+\frac{\$1.87}{{\left(1+0.1167\right)}^2}+\frac{\$2.09}{{\left(1+0.1167\right)}^3}+\frac{\$2.34}{{\left(1+0.1167\right)}^4}+\frac{\$\text{61}\text{.35}}{{\left(1+0.1167\right)}^5}\right]\\ =\left[\frac{\$1.68}{1.1167}+\frac{\$1.87}{1.24701}+\frac{\$2.09}{1.39254}+\frac{\$2.34}{1.55505}+\frac{\$\text{61}\text{.35}}{1.73653}\right]\\ =\left(\$1.50443+\$\text{1}\text{.49958}+\$\text{1}\text{.50085}+\$\text{1}\text{.50477}+\$\text{35}\text{.32907}\right)\\ =\$\text{41}\text{.33}\end{array}$

Hence, the stock price is $41.33.