Chapter 16, Problem 1QP

a)

Summary Introduction

To determine: The earnings per shares and percentage change in earnings per share under given scenarios.

Introduction:

Earnings per share are the fraction of a firm’s profits allocated to every outstanding share of common stock. Earnings per share are used as an indicator to determine the firm’s profitability.

Answer to Problem 1QP

Solution: The earnings per share value for recession is $2.75, for normal is $4.60 and for expansion is $5.75. The percentage change in earnings per share value for recession is -40%, for normal is 0% and for expansion is 25%.

Explanation of Solution

Calculate the earnings per share (EPS) for the three economic scenarios before any debts issued:

Particulars	Recession	Normal	Expansion
EBIT	$13,800	$23,000	$28,750
Less: Interest	$0	$0	$0
Net income	$13,800	$23,000	$28,750
Earnings per share	$2.76	$4.60	$5.75
Percentage change in EPS	-40%	0%	25%

NOTE:

Calculate the earnings before interest and taxes (EBIT):

It is given that earnings before interest and taxes (EBIT) value is $23,000 when the condition is normal. If there is recession, EBIT will be 40% lower and during expansion it will be 25% higher.

Recession:

Earnings before interest and taxes (EBIT):

$\begin{array}{c}\text{Earnings before interest and taxes=EBIT}\times \left(1-{\text{EBIT rate}}_{\text{recession}}\right)\\ =\$23,000\times \left(1-40\%\right)\\ =\$23,000\times 0.6\\ =\$13,800\end{array}$

Therefore, the earnings before interest and taxes for recession is $13,800.

Expansion:

Earnings before interest and taxes (EBIT):

$\begin{array}{c}\text{Earnings before interest and taxes=EBIT}\times \left(1+{\text{EBIT rate}}_{\text{Expansion}}\right)\\ =\$23,000\times \left(1+25\%\right)\\ =\$23,000\times 1.25\\ =\$28,750\end{array}$

Therefore, the earnings before interest and taxes for expansion is $28,750.

Calculate the earnings per share (EPS):

The net income value for recession, normal and expansion are $6,720, $15,920 and $21,670 respectively. It is given that shares outstanding are 5,000.

Recession:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$13,800}{5,000}\\ =\$2.76\end{array}$

Therefore, the earnings per share for recession is $2.76.

Normal:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$23,000}{5,000}\\ =\$4.60\end{array}$

Therefore, the earnings per share for normal is $4.60.

Expansion:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$28,750}{5,000}\\ =\$5.75\end{array}$

Therefore, the earnings per share for expansion is $5.75.

Calculate the percentage change in EPS:

Recession:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{recession}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$2.76-\$4.60\right)}{\$4.60}\\ =\frac{-\$1.84}{\$4.60}\\ =-0.4\text{or}40\%\end{array}$

Therefore, the percentage change in EPS is -40%.

Normal:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{normal}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$4.60-\$4.60\right)}{\$4.60}\\ =0\text{or}0\%\end{array}$

Therefore, the percentage change in EPS is 0%.

Expansion:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{expansion}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$5.75-\$4.60\right)}{\$4.60}\\ =\frac{\$1.15}{\$4.60}\\ =0.25\text{or}25\%\end{array}$

Therefore, the percentage change in EPS is 25%.

b)

Summary Introduction

To determine: The earnings per shares and percentage change in earnings per share when company goes through recapitalization.

Answer to Problem 1QP

Solution: The earnings per share value for recession is $1.92, for normal is $4.55 and for expansion is $6.19. The percentage change in earnings per share value for recession is -57.79%, for normal is 0% and for expansion is 36.12%.

Explanation of Solution

When company goes through recapitalization, then it will have to repurchase.

Calculate the share price:

It is given that the market value is $295,000 and shares outstanding are 5,000.

$\begin{array}{c}\text{Share price}=\frac{\text{Market value}}{\text{Shares outstanding}}\\ =\frac{\$295,000}{5,000}\\ =\$59\end{array}$

Therefore, the share price is $59.

Calculate the shares repurchased:

It is given that the company is considering issuing $88,500 debts.

$\begin{array}{c}\text{Share repurchased}=\frac{\text{Debt issued}}{\text{Shares price}}\\ =\frac{\$88,500}{\$59}\\ =1,500\text{shares}\end{array}$

Therefore, the shares repurchased are 1,500.

Calculate the interest payment for each year:

It is given that the company is considering issuing $88,500 debts and interest payment is 8%.

$\begin{array}{c}\text{Interest payment}=\text{Debts issued}\times \text{Interest rate}\\ =\text{\$88,500}\times \text{8\%}\\ =\text{\$7,080}\end{array}$

Therefore, the interest payment is $7,080.

Now, calculate the earnings per share.

Particulars	Recession	Normal	Expansion
EBIT	$13,800	$23,000	$28,750
Less: Interest	$7,080	$7,080	$7,080
Net income	$6,720	$15,920	$21,670
Earnings per share	$1.92	$4.55	$6.19
Percentage change in EPS	-57.79%	0%	36.12%

NOTE:

Calculate the earnings before interest and taxes (EBIT):

It is given that earnings before interest and taxes (EBIT) value is $23,000 when the condition is normal. If there is recession, EBIT will be 40% lower and during expansion it will be 25% higher.

Recession:

Earnings before interest and taxes (EBIT):

$\begin{array}{c}\text{Earnings before interest and taxes=EBIT}\times \left(1-{\text{EBIT rate}}_{\text{recession}}\right)\\ =\$23,000\times \left(1-40\%\right)\\ =\$23,000\times 0.6\\ =\$13,800\end{array}$

Therefore, the earnings before interest and taxes for recession is $13,800.

Expansion:

Earnings before interest and taxes (EBIT):

$\begin{array}{c}\text{Earnings before interest and taxes=EBIT}\times \left(1+{\text{EBIT rate}}_{\text{Expansion}}\right)\\ =\$23,000\times \left(1+25\%\right)\\ =\$23,000\times 1.25\\ =\$28,750\end{array}$

Therefore, the earnings before interest and taxes for expansion is $28,750.

Calculate the earnings per share (EPS):

The net income value for recession, normal and expansion are $13,800, $23,000 and $28,750 respectively. It is given that shares outstanding are 5,000.

Recession:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share}=\frac{\text{Net income}}{\text{Shares outstanding}-\text{Shares repurchased}}\\ =\frac{\$6,720}{5,000-1,500}\\ =\frac{\$6,720}{3,500}\\ =\$1.92\end{array}$

Therefore, the earnings per share for recession is $1.92.

Normal:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}-\text{Shares repurchased}}\\ =\frac{\$15,920}{5,000-1,500}\\ =\frac{\$15,920}{3,500}\\ =\$4.55\end{array}$

Therefore, the earnings per share for normal is $4.55.

Expansion:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}-\text{Shares repurchased}}\\ =\frac{\$21,670}{5,000-1,500}\\ =\frac{\$21,670}{3,500}\\ =\$6.19\end{array}$

Therefore, the earnings per share for expansion is $6.19.

Calculate the percentage change in EPS:

Recession:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{recession}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$1.92-\$4.55\right)}{\$4.55}\\ =\frac{-\$2.63}{\$4.55}\\ =-0.57\text{or}57\%\end{array}$

Therefore, the percentage change in EPS is -57%.

Normal:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{normal}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$4.55-\$4.55\right)}{\$4.55}\\ =0\text{or}0\%\end{array}$

Therefore, the percentage change in EPS is 0%.

Expansion:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{expansion}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$6.19-\$4.55\right)}{\$4.55}\\ =\frac{\$1.64}{\$4.55}\\ =0.36\text{or}36\%\end{array}$

Therefore, the percentage change in EPS is 36%,