Instructions

$($a$)$ Compute break$-$even point in units using the mathematical equation.

$($b$)$ Compute break$-$even point in dollars using the contribution margin $($CM$)$ ratio.

$($c$)$ Compute the margin of safety percentage assuming actual sales are $$500,000.$

$($d$)$ Compute the sales required in dollars to earn net income of $$165,000.$

Solution

$($a$)$

Required sales $-$ Variable costs $-$ Fixed costs $=$ Net income

$$20Q-$$$9Q-$$$220,000=$$$0$

$$110=$$$220,000$

$Q=20,000$ units

$($b$)$ Unit contribution margin $=$ Unit selling price $-$ Unit variable costs

$$11=$$$20-$$$9$

Contribution margin ratio $=$ Unit contribution margin $$ Unit selling price

$55\%=$$$11$$$20$

Break$-$even point in dollars $=$ Fixed costs $$ Contribution margin ratio

$=$$$220,00055\%$

$=$$$400,000$

$($c$)$

Margin $of$ safety $=\frac{\text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{s}\text{a}\text{l}\text{e}\text{s}-\text{B}\text{r}\text{e}\text{a}\text{k}-\text{e}\text{v}\text{e}\text{n}\text{s}\text{a}\text{l}\text{e}\text{s}}{\text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{s}\text{a}\text{l}\text{e}\text{s}}$

$=\frac{\text{\$}500,000-\text{\$}400,000}{\text{\$}500,000}($a$)$

Required sales $-$ Variable costs $-$ Fixed costs $-$ Net income

$$200-$$$90-$$$220,000=$$$0$

$$110=$$$220,000$

$0=20,000$ units

$($b$)$ Unit contribution margin $-$ Unit selling price $-$ Unit variable cosis

$$11=$$$20-$$$9$

Contribution margin ratio $=$ Unit contribution margin $$ Unit selling price

$5\mathrm{.}5\%-$$$11+$$$20$

Areak$-$even point in dollars $-$ Fixed costs $+$ Contribution margin ratio

$-$$$220,000-55\%$

$-$$$400,000$

$($c$)$

Margin $of$ safety $=\frac{\text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{s}\text{a}\text{l}\text{e}\text{s}-\text{B}\text{r}\text{c}\text{a}\text{k}\text{e}\text{v}\text{e}\text{n}\text{s}\text{a}\text{l}\text{e}\text{s}}{\text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{s}\text{a}\text{l}\text{e}\text{s}}$

$=\frac{\text{\$}500,000-\text{\$}400,000}{\text{\$}500,000}$

$=20\%6$

$($d$)$

Required sales $-$ Variable costs Fixed costs $-$ Net income

$$200-$$$90-$$$220,000=$$$165,000$

$$110=$$$385,000$

$O=35,000$ units

$35,000$ units $$$$20=$$$700,000$ required sales

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QUESTIONS

$($a$)$ What is cost behavior analysis?

$($b$)$ Why is cost behavior analysis important to man$-$

agement?

$($a$)$ Scott Winter asks your help in understanding the

term "activity index." Explain the meaning and

importance of this term for Scott.

$($b$)$ State the two ways that variable costs may be

defined.

Contrast the effects of changes in the activity level on

total fixed costs and on unit fixed costs.

J$.$ P$.$ Alexander claims that the relevant range concept

is important only for variable costs.

$($a$)$ Explain the relevant range concept.

$($b$)$ Do you agree with J$.$ P$\text{'}$s claim? Explain.

"The relevant range is indispensable in cost behavior

analysis." Is this true? Why or why not?

Adam Antal is cVGVVVonfused. He does not understand why

rent on his apartment is a fixed cost and rent on a

Hertz rental truck is a mixed cost. Explain the differ$-$

ence to Adam.

How should mixed costs be classified in CVP analysis?

What approach is used to effect the appropriate

classification?

At the high and low levels of activity during the month,

direct labor hours are $90,000$ and $40,000,$ respectively.

The related costs are $$165,000$ and $$100,000.$ What are

the fixed and variable costs at any level of activity?

"Cost$-$volume$-$profit $($CVP$)$ analysis is based entirely

on unit costs." Do you agree? Explain.

Faye Dunn defines contribution margin as the amount

of profit available to cover operating expenses. Is there

any truth in this definition? Discuss.

$=20\%$

$($d$)$ Required sales $-$ Variable costs $-$ Fixed costs $=$ Net income

$$20Q-$$$9Q-$$$220,000=$$$165,000$

$$11Q=$$$385,000$

$Q=35,000$ units

$35,000$ units $$$$20=$$$700,000$ required sales