Chapter 13, Problem 6QP

a)

Summary Introduction

To compute: The highest EPS and the lowest EPS.

Introduction:

The leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 6QP

The highest EPS is in the all-equity plan and the lowest EPS is in Plan II.

Explanation of Solution

Given information:

Company C is comparing two various capital structures: Plan I and Plan II. The first plan will result in $8,500 shares of stock and $361,000 in debt. The second plan will result in $12,000 shares of stock and $228,000 in debt. The rate of interest on debt is 10%. The EBIT is $61,000. The plan of equity will result in the stock outstanding of $18,000 shares.

Formula to calculate the payment of interest:

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

Compute the payment of interest:

$\begin{array}{c}\text{Interest payment under Plan I}=\text{Debt issued}\times \text{ Rate of interest}\\ =\$361,000\times 0.10\\ =\$36,100\end{array}$

Hence, the payment of interest under Plan I is $36,100.

Compute the payment of interest:

$\begin{array}{c}\text{Interest payment under Plan II}=\text{Debt issued}\times \text{ Rate of interest}\\ =\$228,000\times 0.10\\ =\$22,800\end{array}$

Hence, the payment of interest under Plan II is $22,800.

Formula to calculate the NI (Net Income):

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

Compute NI for each plan:

$\begin{array}{c}\text{NI for Plan I}=\text{EBIT}-\text{Interest}\\ =\$61,000-36,100\\ =\$24,900\end{array}$

Hence, the net income under Plan I is $24,900.

$\begin{array}{c}\text{NI for Plan II}=\text{EBIT}-\text{Interest}\\ =\$61,000-22,800\\ =\$38,200\end{array}$

Hence, the net income under Plan II is $38,200.

Formula to compute the EPS:

$\text{Earnings per share}=\frac{\text{EBIT}}{\text{Outstanding shares}}$

Compute the EPS:

$\begin{array}{c}\text{Earnings per share under Plan I}=\frac{\text{NI}}{\text{Outstanding shares}}\\ =\frac{\$24,900}{8,500\text{ shares}}\\ =\$2.93\end{array}$

Hence, the EPS for plan I is $2.93.

$\begin{array}{c}\text{Earnings per share under Plan II}=\frac{\text{NI}}{\text{Outstanding shares}}\\ =\frac{\$38,200}{12,000\text{ shares}}\\ =\$3.18\end{array}$

Hence, the EPS for plan II is $3.18.

$\begin{array}{c}\text{Earnings per share under Plan III}=\frac{\text{NI}}{\text{Outstanding shares}}\\ =\frac{\$61,000}{18,000\text{ shares}}\\ =\$3.39\end{array}$

Hence, the EPS for plan III is $3.39.

Table showing the income statement under each plan:

	I	II	All-equity
EBIT	$61,000	$61,000	$61,000
Interest	36,100	22,800	0
NI	$24,900	$38,200	$61,000
EPS	$2.93	$3.18	$3.39

Hence, the all-equity plan has the highest EPS and the lowest EPS is in Plan II.

b)

Summary Introduction

To calculate: The break-even level of EBIT for Plan I and Plan II compared to the all-equity plan and identify whether any one of the plans is greater than the other with a reason.

Introduction:

The leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 6QP

The break-even level of EBIT is $68,400 for both the plans compared to the all-equity plan.

Explanation of Solution

The break-even level of EBIT happens, when the plans of capitalization lead to same EPS. Thus, the formula to compute EPS is as follows:

Formula to calculate the break-even level of EBIT:

$\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}$

Where,

R_DD denotes the payment of interest.

The above equation computes the payment of interest (R_DD) and subtracts it from EBIT, which gives the net income. The net income divided by outstanding shares gives the EPS. The interest is zero for all-equity plan. To compute the break-even level of EBIT for Plan I and all-equity plan, set the equations equalizing each other.

Equation to solve for break-even level of EBIT under Plan I:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}-0.10\left(\$361,000\right)}{\$8,500}\end{array}$

Equation to solve for break-even level of EBIT under all equity plan:

$\begin{array}{c}\text{EPS}=\frac{\text{EBIT}}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}}{\$18,000}\end{array}$

Solve the above two equations:

$\begin{array}{c}\frac{\text{EBIT}}{\$18,000}=\frac{\text{EBIT}-0.10\left(\$361,000\right)}{\$8,500}\\ \$8,500\text{EBIT}=\$18,000\text{EBIT}-\$649,800,000\\ -\$18,000\text{EBIT}+\$8,500\text{EBIT}=-\$649,800,000\end{array}$

$\begin{array}{c}-\$9,500\text{EBIT}=-\$649,800,000\\ \text{EBIT}=\$68,400\end{array}$

Hence, the break-even level of EBIT between Plan I and all-equity plan is $68,400.

Equation to solve for break-even level of EBIT under Plan II:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}-0.10\left(\$228,000\right)}{\$12,000}\end{array}$

Solve the above equation with the equation of all-equity plan:

$\begin{array}{c}\frac{\text{EBIT}}{\$18,000}=\frac{\text{EBIT}-0.10\left(\$228,000\right)}{\$12,000}\\ \$12,000\text{EBIT}=\$18,000\text{EBIT}-\$410,400,000\\ -\$18,000\text{EBIT}+\$12,000\text{EBIT}=-\$410,400,000\end{array}$

$\begin{array}{c}-\$6,000\text{EBIT}=-\$410,400,000\\ \text{EBIT}=\$68,400\end{array}$

Hence, the break-even level of EBIT between Plan II and all-equity plan is $68,400.

c)

Summary Introduction

To calculate: The EBIT to identify the identical EPS under Plan I and Plan II.

Introduction:

The leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 6QP

Ignoring the taxes, the EPS will be identical for both the firms, when EBIT is $68,400.

Explanation of Solution

Equation to solve for break-even level of EBIT under Plan I:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}-0.10\left(\$361,000\right)}{\$8,500}\end{array}$

Equation to solve for break-even level of EBIT under Plan II:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}-0.10\left(\$228,000\right)}{\$12,000}\end{array}$

Solve the above two equations:

$\begin{array}{c}\frac{\text{EBIT}-0.10\left(\$361,000\right)}{\$8,500}=\frac{\text{EBIT}-0.10\left(\$228,000\right)}{\$12,000}\\ \$12,000\text{EBIT}-\$193,800,000=\$8,500\text{EBIT}-\$433,200,000\\ -\$8,500\text{EBIT}+\$12,000\text{EBIT}=-\$239,400,000\end{array}$

$\begin{array}{c}\$3,500\text{EBIT}=-\$239,400,000\\ \text{EBIT}=\$68,400\end{array}$

Hence, the break-even level of EBIT between two plans is $68,400.

d)

Summary Introduction

To calculate: The highest EPS and the lowest EPS, the break-even level of EBIT of Plan I and Plan II compared to the all-equity plan, and the EBIT to identify the identical EPS under Plan I and Plan II, if the corporate rate of tax is 35%.

Introduction:

The leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 6QP

With taxes, again EPS is highest in the all-equity plan and the lowest in Plan II. The break-even level of EBIT is $68,400 for both the plans compared to the all-equity plan. The EPS will be identical for both the firms, when EBIT is $68,400.

Explanation of Solution

Formula to calculate the payment of interest:

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

Compute the payment of interest:

$\begin{array}{c}\text{Interest payment under Plan I}=\text{Debt issued}\times \text{ Rate of interest}\\ =\$361,000\times 0.10\\ =\$36,100\end{array}$

Hence, the payment of interest under Plan I is $36,100.

Compute the payment of interest:

$\begin{array}{c}\text{Interest payment under Plan II}=\text{Debt issued}\times \text{ Rate of interest}\\ =\$228,000\times 0.10\\ =\$22,800\end{array}$

Hence, the payment of interest under Plan II is $22,800.

Formula to calculate the taxes:

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

Compute taxes for each plan:

$\begin{array}{c}\text{Tax under Plan I}=\left(\text{EBIT}-\text{Interest}\right)\left(\text{Tax rate}\right)\\ =\left(\$61,000-\$36,100\right)\left(0.35\right)\\ =\$8,715\end{array}$

Hence, the tax for Plan I is $8,715.

$\begin{array}{c}\text{Tax under Plan II}=\left(\text{EBIT}-\text{Interest}\right)\left(\text{Tax rate}\right)\\ =\left(\$61,000-\$22,800\right)\left(0.35\right)\\ =\$13,370\end{array}$

Hence, the tax for Plan II is $13,370.

$\begin{array}{c}\text{Tax under all-equity plan}=\left(\text{EBIT}-\text{Interest}\right)\left(\text{Tax rate}\right)\\ =\left(\$61,000-\$0\right)\left(0.35\right)\\ =\$21,350\end{array}$

Hence, the tax for all-equity plan is $21,350.

Formula to calculate the NI (Net Income):

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

Compute NI for each plan:

$\begin{array}{c}\text{NI for Plan I}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$61,000-\$36,100-\$8,715\\ =\$16,185\end{array}$

Hence, the net income under Plan I is $16,185

$\begin{array}{c}\text{NI for Plan II}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$61,000-22,800-\$13,370\\ =\$24,830\end{array}$

Hence, the net income under Plan II is $24,830.

$\begin{array}{c}\text{NI for all-equity plan}=\text{EBIT}-\text{Interest}-\text{Taxes}\\ =\$61,000-\$0-\$39,650\\ =\$21,350\end{array}$

Hence, the net income under all-equity plan is $21,350.

Formula to compute the EPS:

$\text{Earnings per share}=\frac{\text{NI}}{\text{Outstanding shares}}$

Compute the EPS:

$\begin{array}{c}\text{Earnings per share under Plan I}=\frac{\text{NI}}{\text{Outstanding shares}}\\ =\frac{\$16,185}{8,500\text{ shares}}\\ =\$1.90\end{array}$

Hence, the EPS for plan I is $1.90.

$\begin{array}{c}\text{Earnings per share under Plan II}=\frac{\text{NI}}{\text{Outstanding shares}}\\ =\frac{\$24,830}{12,000\text{ shares}}\\ =\$2.07\end{array}$

Hence, the EPS for plan II is $2.07.

$\begin{array}{c}\text{Earnings per share under all-equity plan}=\frac{\text{NI}}{\text{Outstanding shares}}\\ =\frac{\$39,650}{18,000\text{ shares}}\\ =\$2.20\end{array}$

Hence, the EPS for all-equity plan is $2.20.

Table showing the income statement under each plan:

	I	II	All-equity
EBIT	$61,000	$61,000	$61,000
Interest	36,100	22,800	0
Taxes	8,715	13,370	21,350
NI	$16,185	$24,830	$21,350
EPS	$1.90	$2.07	$2.20

Hence, the all-equity plan has the highest EPS and the lowest EPS is in Plan II.

Formula to calculate the break-even level of EBIT:

$\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)\left(1-T_c\right)}{\text{Outstanding shares}}$

Where,

R_DD denotes the payment of interest,

T_C is the corporate tax rate.

Note: The above equation is equal to the equation used before, except the addition of taxes.

Equation to solve for break-even level of EBIT under Plan I:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)\left(1-T_c\right)}{\text{Outstanding shares}}\\ =\frac{\left(\text{EBIT}-0.10\left(\$361,000\right)\right)\left(1-0.35\right)}{\$8,500}\end{array}$

Equation to solve for break-even level of EBIT under all equity plan:

$\begin{array}{c}\text{EPS}=\frac{\text{EBIT}\left(1-T_C\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}\left(1-0.35\right)}{\$18,000}\end{array}$

Solve the above two equations:

$\begin{array}{c}\frac{\text{EBIT}\left(1-0.35\right)}{\$18,000}=\frac{\left(\text{EBIT}-0.10\left(\$361,000\right)\right)\left(1-0.35\right)}{\$8,500}\\ \text{\$5,525 EBIT}=\left(\$11,700\text{EBIT}-\$422,370,000\right)\\ \$6,175\text{EBIT}=\$422,370,000\\ \text{EBIT}=\$68,400\end{array}$

Hence, the break-even level of EBIT between Plan I and all-equity plan is $68,400.

Equation to solve for break-even level of EBIT under Plan II:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}-0.10\left(\$228,000\right)\left(1-0.35\right)}{\$12,000}\end{array}$

Solve the above equation with the equation of all-equity plan:

$\begin{array}{c}\frac{\text{EBIT}\left(1-0.35\right)}{\$18,000}=\frac{\text{EBIT}-0.10\left(\$228,000\right)\left(1-0.35\right)}{\$12,000}\\ \$7,800\text{EBIT}=\$11,700\text{EBIT}-\$266,760,000\\ \text{EBIT}=\$68,400\end{array}$

Hence, the break-even level of EBIT between Plan II and all-equity plan is $68,400.

Equation to solve for break-even level of EBIT under Plan I:

$\begin{array}{c}\text{EPS}=\frac{\left(\text{EBIT}-R_{D}D\right)}{\text{Outstanding shares}}\\ =\frac{\text{EBIT}-0.10\left(\$361,000\right)\left(1-0.35\right)}{\$8,500}\end{array}$

Solve the above equation with the equation of Plan II:

$\begin{array}{c}\frac{\text{EBIT}-0.10\left(\$361,000\right)\left(1-0.35\right)}{\$8,500}=\frac{\text{EBIT}-0.10\left(\$228,000\right)\left(1-0.35\right)}{\$12,000}\\ \$7,800\text{EBIT}-\text{\$125,970,000}=\text{\$5,525EBIT}-\$281,580,000\\ \$2,275\text{EBIT}=\$155,610,000\\ \text{EBIT}=\$68,400\end{array}$

Hence, the break-even level of EBIT between Plan I and Plan II is $68,400.