Chapter 14, Problem 1P

a.

Summary Introduction

To determine: Normal EPS and EPS when sales increases by 10%.

Explanation of Solution

Given information: Sales $6 million, Fixed costs $800,000, Variable cost ratio 0.75, loan $600,000, Interest on loan 10%, 20,000 preference share of $3 each and 60,000 common shares, income tax 40%

Calculation:

Particulars	Amount(old)	Amount(new)
Sales	$6,000,000	$6,600,000
Less: Variable costs	($4,500,000)	($4,950,000)
Less: fixed operating costs	($800,000)	($800,000)
EBIT	$700,000	$850,000
Less: interest expense	($60,000)	($60,000)
EBT	$640,000	$790,000
Less: income tax (40%)	($256,000)	($316,000)
EAT	$384,000	$474,000
Less: preferred stock dividends	($60,000)	($60,000)
Earning (common stockholders)	$324,000	$414,000
EPS (60,000 shares)	$5.40	$6.90

b.

Summary Introduction

To determine: DOL (i) by definitional formula (ii) by computational formula

Explanation of Solution

Given information: Sales $6 million, Fixed costs $800,000, Variable cost ratio 0.75, loan $600,000, Interest on loan 10%, 20,000 preference share of $3 each and 60,000 common shares, income tax 40%

Calculation:

1. i. $\text{DOL at "X"}=\left(\frac{\Delta \text{EBIT}}{\text{EBIT}}\right)/\left(\frac{\Delta \text{Sales}}{\text{Sales}}\right)$

   Substituting $6,000,000 as “X”, $150,000 as ∆EBIT, $700,000 as EBIT, $600,000 as ∆Sales and $6,000,000 as Sales in the equation:

   $\begin{array}{c}\text{DOL at \$6,000,000}=\left(\frac{\$150,000}{\text{\$700,000}}\right)/\left(\frac{\$600,000}{\text{\$6,000,000}}\right)\\ =2.143\end{array}$

2. ii. $\text{DOL at "X"}=\frac{\text{Sales}-\text{Variable cost}}{\text{EBIT}}$

   Substituting $6,000,000 as “X”, $6,000,000 as Sales, $4,500,000 as variable cost and $700,000 as EBIT in the equation:

   $\begin{array}{c}\text{DOL at \$6,000,000}=\frac{\text{\$6,000,000}-\text{\$4,500,000}}{\text{\$700,000}}\\ =2.143\end{array}$

3. iii. There is a change of 2.143 percent in EBIT for a one percent change in sales for given sales of $6,000,000 in the same direction.

c.

Summary Introduction

To determine: DFL (i) by definitional formula (ii) by computational formula

Explanation of Solution

Given information: Sales $6 million, Fixed costs $800,000, Variable cost ratio 0.75, loan $600,000, Interest on loan 10%, 20,000 preference share of $3 each and 60,000 common shares, income tax 40%

Calculation:

Substituting $700,000 as “X”, $1.50 as ∆EPS, $5.40 as EPS, $150,000 as ∆EBIT and $700,000 as EBIT in the equation

$\begin{array}{c}\text{DFL at \$700,000}=\left(\frac{\$1.50}{\text{\$5}\text{.40}}\right)/\left(\frac{\$150,000}{\text{\$700,000}}\right)\\ =1.2963\end{array}$

1. i. $\text{DFL at "X"}=\left(\frac{\text{EBIT}}{\text{EBIT}-\text{I}-{\text{D}}_{\text{p}}}\right)/\left(\frac{1}{\text{1}-\text{T}}\right)$

   Substituting $700,000 as “X”, $700,000 as EBIT, $60,000 as I, $60,000 as ${\text{D}}_{\text{p}}$ and 4 as T in the equation

   $\begin{array}{c}\text{DFL at \$700,000}=\left(\frac{\text{\$700,000}}{\text{\$700,000}-\text{\$60,000}-\text{\$60,000}}\right)/\left(\frac{1}{\text{1}-\text{4}}\right)\\ =1.2963\end{array}$

2. ii. There is a change of 1,2963 percent in EPS for a one percent change in EBIT for given EBIT of $700,000 in the same direction.

d.

Summary Introduction

To determine: DCL (i) by definitional formula (ii) by computational formula

Explanation of Solution

Given information: Sales $6 million, Fixed costs $800,000, Variable cost ratio 0.75, loan $600,000, Interest on loan 10%, 20,000 preference shares of $3 each and 60,000 common shares, income tax 40%

Calculation:

1. i. $\text{DCL }=\left(\frac{\Delta \text{EPS}}{\text{EPS}}\right)/\left(\frac{\Delta \text{Sales}}{\text{Sales}}\right)$

Substituting $1.50 as ∆EPS, $5.40 as EPS, $600,000 as ∆Sales and $6,000,000 as Sales in the equation

$\begin{array}{c}\text{DCL }=\left(\frac{\$1.50}{\text{\$5}\text{.40}}\right)/\left(\frac{\$600,000}{\text{\$6,000,000}}\right)\\ =2.778\end{array}$

1. ii. $\text{DCL }=\left(\frac{\text{Sales}-\text{Variable cost}}{\text{EBIT}-\text{I}-{\text{D}}_{\text{p}}}\right)/\left(\frac{1}{1-\text{T}}\right)$

   Substituting $6,000,000 as sales, $ 4,500,000 as variable cost, $700,000 as EBIT, $60,000 as I, $60,000 as ${\text{D}}_{\text{p}}$ and 4 as T in the equation.

   $\begin{array}{c}\text{DCL }=\left(\frac{\text{\$6,000,000}-\text{\$4,500,000}}{\text{\$700,000}-\text{\$60,000}-\text{\$60,000}}\right)/\left(\frac{1}{1-\text{4}}\right)\\ =2.778\end{array}$

2. iii. $\text{DCL }=\text{DOL}\times \text{DFL}$

   Substituting 2.143 as DOL and 1.2963 as DFL in the equation

   $\begin{array}{c}\text{DCL }=\text{2}\text{.143}\times \text{1}\text{.2963}\\ \text{=2}\text{.778}\end{array}$

3. iv. There is a change of 2.778 percent in EPS for one percent change in sale for given sales of $6,000,000 in the same direction.