Chapter 16, 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 $1.74, $2.49, and $2.99 respectively and the percentage of change in EPS is -30% and +20 for the recession and expansion periods respectively.

Explanation of Solution

Given information:

Company P has no debt outstanding and its market value is $180,000. The EBIT (earnings before interest and taxes) are expected to be $23,000 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 30%. The tax rate of the company is 35%.

Formula to calculate taxes:

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

Compute taxes for three periods:

$\begin{array}{c}\text{Tax during recession}=\text{EBIT}\times \text{Tax rate}\\ =\$16,100\times 0.35\\ =\$5,635\end{array}$

Hence, the tax during recession is $5,635.

$\begin{array}{c}\text{Tax during normal}=\text{EBIT}\times \text{Tax rate}\\ =\$23,000\times 0.35\\ =\$8,050\end{array}$

Hence, the tax during the normal period is $8,050.

$\begin{array}{c}\text{Tax during normal}=\text{EBIT}\times \text{Tax rate}\\ =\$27,600\times 0.35\\ =\$9,660\end{array}$

Hence, the tax during expansion is $9,660.

Formula to calculate the NI (net income):

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

Compute NI for three periods:

$\begin{array}{c}\text{NI during recession period}=\text{EBIT}-\text{Taxes}\\ =\$16,100-\$5,635\\ =\$10,465\end{array}$

Hence, the NI during recession is $10,465.

$\begin{array}{c}\text{NI during normal period}=\text{EBIT}-\text{Taxes}\\ =\$23,000-8,050\\ =\$14,950\end{array}$

Hence, the NI during normal period is $14,950.

$\begin{array}{c}\text{NI during expansion period}=\text{EBIT}-\text{Taxes}\\ =\$27,600-9,660\\ =\$17,940\end{array}$

Hence, the NI during expansion period is $17,940.

Formula to calculate EPS:

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

Compute EPS:

$\begin{array}{c}\text{EPS at recession period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$10,465}{\$6,000}\\ =\$1.74\end{array}$

Hence, the EPS during recession period is $1.74.

$\begin{array}{c}\text{EPS at normal period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$14,950}{\$6,000}\\ =\$2.49\end{array}$

Hence, the EPS during normal period is $2.49.

$\begin{array}{c}\text{EPS at normal period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$17,940}{\$6,000}\\ =\$2.99\end{array}$

Hence, the EPS during expansion period is $2.99.

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

	Recession	Normal	Expansion
EBIT	$16,100	$23,000	$27,600
Interest	0	0	0
Taxes	5,635	8,050	9,660
NI	$10,465	$14,950	$17,940
EPS	$1.74	$2.49	$2.99
%EPS	–30	NIL	+20

Note:

It is given that 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: The EPS 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.

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

After recapitalization, the EPS under the recession, normal, and expansion periods are $2.02, $3.30, and $4.15 respectively and the percentage of change in EPS is -38.79% and +25.76 for the recession and expansion periods respectively.

Explanation of Solution

Given information:

The company is considering the debt issue of $75,000 with the rate of interest at 7%. At present, outstanding shares of $6,000 exist.

Formula to calculate the share price:

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

Compute the share price:

$\begin{array}{c}\text{Share price}=\frac{\text{Equity }}{\text{Shares outstanding}}\\ =\frac{\$180,000}{6,000}\\ =\$30\end{array}$

Hence, the price of the share is $30.

Formula to calculate the repurchased shares:

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

Compute the repurchased shares:

$\begin{array}{c}\text{Shares repurchased}=\frac{\text{Debt issued}}{\text{Share price}}\\ =\frac{\$75,000}{\$30}\\ =\$2,500\end{array}$

Hence, the repurchased shares are $2,500.

Formula to calculate the payment of interest:

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

Compute the payment of interest:

$\begin{array}{c}\text{Interest payment}=\text{Debt issued}\times \text{ Rate of interest}\\ =\$75,000\times 0.07\\ =\$5,250\end{array}$

Hence, the payment of interest is $5,250.

Formula to calculate taxes:

$\text{Taxes}=\left(\text{EBIT}-\text{Interest}\right)\times \text{Tax rate}$

Compute taxes for the three periods:

$\begin{array}{c}\text{Tax during recession period}=\left(\text{EBIT}-\text{Interest}\right)\times \text{Tax rate}\\ =\left(16,100-5,250\right)\times 0.35\\ =\$3,797.5\end{array}$

Hence, the tax during recession is $3,797.5.

$\begin{array}{c}\text{Tax during normal period}=\left(\text{EBIT}-\text{Interest}\right)\times \text{Tax rate}\\ =\left(23,000-5,250\right)\times 0.35\\ =\$6,212.5\end{array}$

Hence, the tax during normal period is $6,212.5.

$\begin{array}{c}\text{Tax during expansion period}=\left(\text{EBIT}-\text{Interest}\right)\times \text{Tax rate}\\ =\left(27,600-5,250\right)\times 0.35\\ =\$7,822.5\end{array}$

Hence, the tax during expansion period is $7,822.5.

Formula to calculate the NI:

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

Compute NI for three periods:

$\begin{array}{c}\text{NI during recession}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$16,100-5,250-3,797.5\\ =\$7,052.5\end{array}$

Hence, the NI during recession is $6,143.

$\begin{array}{c}\text{NI during normal}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$23,000-5,250-6,212.5\\ =\$11,537.5\end{array}$

Hence, the NI during normal period is $11,537.5.

$\begin{array}{c}\text{NI during recession}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$27,600-5,250-7,822.5\\ =\$14,527.5\end{array}$

Hence, the NI during expansion period is $14,527.5.

Formula to calculate EPS:

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

Compute EPS:

$\begin{array}{c}\text{EPS at recession period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$7,052.5}{\$3,500}\\ =\$2.02\end{array}$

Hence, the EPS at recession period is $2.02.

$\begin{array}{c}\text{EPS at normal period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$11,537.5}{\$3,500}\\ =\$3.30\end{array}$

Hence, the EPS at normal period is $3.30.

$\begin{array}{c}\text{EPS at expansion period}=\frac{\text{Net income}}{\text{Outstanding shares}}\\ =\frac{\$14,527.5}{\$3,500}\\ =\$4.15\end{array}$

Hence, the EPS at expansion period is $4.15.

Note: After recapitalization, $2,500 was recovered from the total outstanding shares of $6,000. Now, the shares outstanding is $6,000-$2,500=$3,500.

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:

$\begin{array}{c}\text{Percentage change in EPS}=\frac{\text{Changes in EPS}}{\text{EPS at normal period}}\times 100\\ =\frac{\$2.02-\$3.30}{\$3.30}\times 100\\ =-\$38.79\end{array}$

Hence, the percentage change in EPS for recession period is -$38.79.

Compute the percentage change in EPS for expansion period:

$\begin{array}{c}\text{Percentage change in EPS}=\frac{\text{Changes in EPS}}{\text{EPS at normal period}}\times 100\\ =\frac{\$4.15-\$3.30}{\$3.30}\times 100\\ =+25.76\end{array}$

Hence, the percentage change is EPS for expansion period is 25.76.

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

	Recession	Normal	Expansion
EBIT	$16,100	$23,000	$27,600
Interest	5,250	5,250	5,250
Taxes	3,797.5	6,212.5	7,822.5
NI	$7,052.5	$11,537.5	$14,527.5
EPS	$2.02	$3.30	$4.15
%EPS	–38.79	NIL	+25.76