Chapter 13, Problem 2QP

a)

Summary Introduction

To calculate: The EPS (Earnings per share) under the three scenarios before the debt issue and the changes in EPS while the economy expands a recession

Introduction:

The EPS is the part of the profit of a firm that is allocated to every outstanding share of common stock. It indicates the profitability of the company.

Answer to Problem 2QP

The EPS under the recession, normal, and expansion periods are $0.70, $1.08, and $1.30 respectively and the percentage of change in EPS is -35% and +20% for the recession and expansion periods respectively.

Explanation of Solution

Given information:

Company K has no debt outstanding and its market value is $125,000. The EBIT (Earnings before interest and taxes) are expected to be $10,400 at normal economic conditions. If the economy condition is strong, then EBIT will increase to 20% and if the economy enters into recession, then it will decrease to 35%. The outstanding shares are $6,250.

Formula to calculate taxes:

$\text{Taxes}=\text{EBIT}\times \text{Tax rate}$

Compute taxes for three periods:

$\begin{array}{c}\text{Tax during recession}=\text{EBIT}\times \text{Tax rate}\\ =\$6,760\times 0.35\\ =\$2,366\end{array}$

Hence, the tax during recession is $2,366.

$\begin{array}{c}\text{Tax during normal}=\text{EBIT}\times \text{Tax rate}\\ =\$10,400\times 0.35\\ =\$3,640\end{array}$

Hence, the tax during normal period is $3,640.

$\begin{array}{c}\text{Tax during normal}=\text{EBIT}\times \text{Tax rate}\\ =\$12,480\times 0.35\\ =\$4,368\end{array}$

Hence, the tax during expansion is $4,368.

Formula to calculate the NI (Net Income):

$\text{NI}=\text{EBIT}-\text{Taxes}$

Compute NI for three periods:

$\begin{array}{c}\text{NI during recession period}=\text{EBIT}-\text{Taxes}\\ =\$6,760-2,366\\ =\$4,394\end{array}$

Hence, the net income during recession is $4,394.

$\begin{array}{c}\text{NI during normal period}=\text{EBIT}-\text{Taxes}\\ =\$10,400-3,640\\ =\$6,760\end{array}$

Hence, the net income during normal period is $6,760.

$\begin{array}{c}\text{NI during expansion period}=\text{EBIT}-\text{Taxes}\\ =\$12,480-\text{ 4368}\\ =\$8,112\end{array}$

Hence, the net income during expansion period is $8,112.

Formula to calculate EPS:

$\text{EPS}=\frac{\text{NI (Net income)}}{\text{Outstanding shares}}$

Compute EPS:

$\begin{array}{c}\text{EPS at recession period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$4,394}{\$6,250}\\ =\$0.70\end{array}$

Hence, EPS during recession period is $0.70.

$\begin{array}{c}\text{EPS at normal period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$6,670}{\$6,250}\\ =\$1.08\end{array}$

Hence, EPS during normal period is $1.08.

$\begin{array}{c}\text{EPS at expansion period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$8,112}{\$6,250}\\ =\$1.30\end{array}$

Hence, EPS during expansion period is $1.30.

Table showing the income statement for the three possible periods of economy with the EPS and percentage change in EPS:

	Recession	Normal	Expansion
EBIT	$6,760	$10,400	$12,480
Interest	0	0	0
Taxes	$2,366	$3,640	$4,368
NI	$4,394	$6,760	$8,112
EPS	$0.70	$1.08	$1.30
%ΔEPS	–35%	NIL	20%

Note:

According to the given information, during the recession period, the EBIT will decrease to 35% and during the expansion period, EBIT will increase to 25%.

b)

Summary Introduction

To calculate: EPS (Earnings per share) under the three scenarios before the debt issue and the changes in EPS while the economy expands a recession by assuming that the firm undergoes the planned recapitalization

Answer

After recapitalization, the EPS under the recession, normal, and expansion periods are $0.45, $1.02, and $1.35 respectively and the percentage of change in EPS is -55.88% and +32.35% for the recession and expansion periods respectively.

Explanation of Solution

Given information:

The company is considering the debt issue of $42,000 with the rate of interest at 6%. At present, the outstanding shares of $6,250 exist.

Formula to calculate the share price:

$\text{Share price}=\frac{\text{Equity }}{\text{Shares outstanding}}$

Compute the share price:

$\begin{array}{c}\text{Share price}=\frac{\text{Equity }}{\text{Shares outstanding}}\\ =\frac{\$125,000}{\$6,250}\\ =\$20\end{array}$

Hence, the price of the share is $20.

Formula to calculate the repurchased shares:

$\text{Shares repurchased}=\frac{\text{Debt issued}}{\text{Share price}}$

Compute the repurchased shares:

$\begin{array}{c}\text{Shares repurchased}=\frac{\text{Debt issued}}{\text{Share price}}\\ =\frac{\$42,000}{\$20}\\ =\$2,100\end{array}$

Hence, the repurchased shares are $2,100.

Formula to calculate the payment of interest:

$\text{Interest payment}=\text{Debt issued}\times \text{ Rate of interest}$

Compute the payment of interest:

$\begin{array}{c}\text{Interest payment}=\text{Debt issued}\times \text{ Rate of interest}\\ =\$42,000\times 0.06\\ =\$2,520\end{array}$

Hence, the payment of interest is $2,520.

Formula to calculate the NI (Net Income):

$\text{NI}=\text{EBIT}-\text{Interest}-\text{Taxes}$

Compute NI for three periods:

$\begin{array}{c}\text{NI during recession}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$6,760-\$2,520-\$2,366\\ =\$1,874\end{array}$

Hence, the net income during recession is $1,874.

$\begin{array}{c}\text{NI during normal period}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$10,400-2,520-\$3,640\\ =\$4,240\end{array}$

Hence, the net income during normal period is $4,240.

$\begin{array}{c}\text{NI during recession}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$12,480-\$2,520-\$4,368\\ =\$5,592\end{array}$

Hence, the net income during expansion period is $5,592.

Formula to calculate EPS:

$\text{EPS}=\frac{\text{NI (Net income)}}{\text{Outstanding shares}}$

Compute EPS:

$\begin{array}{c}\text{EPS at recession period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$1,874}{\$4,150}\\ =\$0.45\end{array}$

Hence, the EPS at recession period is $0.45.

$\begin{array}{c}\text{EPS at normal period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$4,240}{\$4,150}\\ =\$1.02\end{array}$

Hence, the EPS at normal period is $1.02.

$\begin{array}{c}\text{EPS at expansion period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$5,592}{\$4,150}\\ =\$1.35\end{array}$

Hence, the EPS at expansion period is $1.35.

Note: After recapitalization, $2,100 was recovered from the total outstanding shares of $6,250. Now, the shares outstanding is $6,250-$2,100 = $4,150.

Formula to calculate the percentage change in EPS:

$\text{Percentage change in EPS}=\frac{\text{Changes in EPS}}{\text{EPS at normal period}}\times 100$

Compute the percentage change in EPS for recession period:

$\begin{array}{c}\text{Percentage change in EPS}=\frac{\text{Changes in EPS}}{\text{EPS at normal period}}\times 100\\ =\frac{\$0.45-\$1.02}{\$1.02}\times 100\\ =-\$55.88\%\end{array}$

Hence, the percentage change in EPS for recession period is -$55.88%.

Compute the percentage change in EPS for expansion period:

$\begin{array}{c}\text{Percentage change in EPS}=\frac{\text{Changes in EPS}}{\text{EPS at normal period}}\times 100\\ =\frac{\$1.35-\$1.02}{\$1.02}\times 100\\ =+32.35\end{array}$

Hence, the percentage change is EPS for expansion period is 32.35.

Table showing the income statement for the three possible periods of economy under the planned recapitalization with EPS and percentage change in EPS:

	Recession	Normal	Expansion
EBIT	$6,760	$10,400	$12,480
Interest	$2,520	$2,520	$2,520
Taxes	$2,366	$3,640	$4,368
NI	$1,874	$4,240	$5,592
EPS	$0.45	$1.02	$1.35
%ΔEPS	–55.88%	NIL	32.35%