Chapter 16, Problem 2QP

EBIT, Taxes, and Leverage Repeat p arts (a) and (b) in Problem 1 assuming the company has a tax rate of 35 percent.

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 2QP

Solution: The earnings per share value for recession is $1.79, for normal is $2.99 and for expansion is $3.74. 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
Taxes(35% of EBIT)	$4,830	$8,050	$10,063
Net income	$8,970	$14,950	$18,688
Earnings per share	$1.79	$2.99	$3.74
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. The tax rate is 35%.

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 $8,970, $14,950 and $18,688 respectively. It is given that shares outstanding are 5,000.

Recession:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$8,970}{5,000}\\ =\$1.79\end{array}$

Therefore, the earnings per share for recession is $1.79.

Normal:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$14,950}{5,000}\\ =\$2.99\end{array}$

Therefore, the earnings per share for normal is $2.99.

Expansion:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}}\\ =\frac{\$18,688}{5,000}\\ =\$3.74\end{array}$

Therefore, the earnings per share for expansion is $3.74.

Calculate the percentage change in EPS:

Recession:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{recession}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$1.79-\$2.99\right)}{\$2.99}\\ =\frac{-\$1.2}{\$2.99}\\ =-0.4\text{or}40\%\end{array}$

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

Normal:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{normal}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$2.99-\$2.99\right)}{\$2.99}\\ =0\text{or}0\%\end{array}$

Therefore, the percentage change in EPS is 0%.

Expansion:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{expansion}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$3.74-\$2.99\right)}{\$2.99}\\ =\frac{\$0.75}{\$2.99}\\ =0.25\text{or}25\%\end{array}$

Therefore, the percentage change in EPS is 25%.

Summary Introduction

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

Answer to Problem 2QP

Solution: The earnings per share value for recession is $1.25, for normal is $2.96 and for expansion is $4.02. 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
EBT	$6,720	$15,920	$21,670
Taxes (35% of EBT)	$2,352	$5,572	$7,585
Net income	$4,368	$10,348	$14,086
Earnings per share	$1.25	$2.96	$4.02
Percentage change in EPS	-57.59%	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 $4,368 , $10,348 and $14,086respectively. It is given that shares outstanding are 5,000.

Recession:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share}=\frac{\text{Net income}}{\text{Shares outstanding}-\text{Shares repurchased}}\\ =\frac{\$4,368}{5,000-1,500}\\ =\frac{\$4,368}{3,500}\\ =\$1.25\end{array}$

Therefore, the earnings per share for recession is $1.25.

Normal:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}-\text{Shares repurchased}}\\ =\frac{\$10,348}{5,000-1,500}\\ =\frac{\$10,348}{3,500}\\ =\$2.96\end{array}$

Therefore, the earnings per share for normal is $2.96.

Expansion:

Earnings per share (EPS):

$\begin{array}{c}\text{Earnings per share=}\frac{\text{Net income}}{\text{Shares outstanding}-\text{Shares repurchased}}\\ =\frac{\$14,086}{5,000-1,500}\\ =\frac{\$14,086}{3,500}\\ =\$4.02\end{array}$

Therefore, the earnings per share for expansion is $4.02.

Calculate the percentage change in EPS:

Recession:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{recession}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$1.25-\$2.96\right)}{\$2.96}\\ =\frac{-\$1.71}{\$2.96}\\ =-0.57\text{or}57\%\end{array}$

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

Normal:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{normal}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$2.96-\$2.96\right)}{\$2.96}\\ =0\text{or}0\%\end{array}$

Therefore, the percentage change in EPS is 0%.

Expansion:

$\begin{array}{c}\text{Percentage change in EPS=}\frac{\left({\text{Earnings per share}}_{\text{expansion}}-{\text{Earnings per share}}_{\text{normal}}\right)}{{\text{Earnings per share}}_{\text{normal}}}\\ =\frac{\left(\$4.02-\$2.96\right)}{\$2.96}\\ =\frac{\$1.06}{\$2.96}\\ =0.36\text{or}36\%\end{array}$

Therefore, the percentage change in EPS is 36%.

Conclusion

The percentage change in EPS is same for both with and without taxes,