Chapter 21, Problem 4BP

1.

To determine

Compute the break-even point in dollar sales for year 2015.

Explanation of Solution

Break-Even Point: It is the point of sales at which entity neither earns a profit nor suffers a loss. It can also be said that the point of sales at which sales value of the entity recovers the entire cost of fixed and variable nature is called break-even point

$\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}$

Given, 20,000 units sold for $750,000, variable costs incurred is $600,000, and fixed costs are $200,000. Contribution margin ratio is 20% (Working note 1).

Compute the break-even point in dollar sales for year 2015:

$\begin{array}{c}\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}\\ =\frac{\$200,000}{20\%}\\ =\$1,000,000\end{array}$

Therefore, the break-even point in dollar sales for year 2015 is $1,000,000.

Working note1: Compute the contribution margin ratio

Sales price per unit $\left(\$750,000÷20,000\text{units}\right)$ (A)	$37.50
Variable costs per unit $\left(\$600,000÷20,000\text{units}\right)$	$30
Contribution margin per unit (B)	$7.50
Contribution margin ratio $\left[\left(\text{B}\right)\text{÷}\left(\text{A}\right)\right]\times 100\%$	20%

Table (1)

2.

To determine

Compute the predicted break-even point in dollar sales for 2016 assuming the machine is installed and there is no change in the unit selling price.

Explanation of Solution

Break-Even Point: It is the point of sales at which entity neither earns a profit nor suffers a loss. It can also be said that the point of sales at which sales value of the entity recovers the entire cost of fixed and variable nature is called break-even point

$\text{Break-even point }\left(\$\right)\text{ = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}$

Fixed costs are $350,000 (refer working note 2) and contribution margin ratio is 60% (refer working note 3).

Compute the predicted break-even point in dollar sales for 2016:

$\begin{array}{c}\text{Break-even point }\left(\$\right)\text{ = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}\\ =\frac{\$350,000}{60\%}\\ =\$583,333\end{array}$

Therefore, the predicted break-even point in dollar sales for 2016 is $583,333 (rounded off to next dollar).

Working note 2: Compute the predicted fixed costs for 2016.

Fixed cost in 2015	$200,000
Add: Increase in the fixed costs	$150,000
Predicted fixed costs for 2016	$350,000

Table (2)

Working note 3: Compute the predicted contribution margin ratio for 2016.

Predicted sales price per unit (no change in sales price)	$37.50
Predicted variable costs per unit $\left(\$30\times 50\%\right)$	$15
Predicted contribution margin ratio $\left[(\$37.50-\$15)÷\$37.50\right]$	60%

Table (3)

3.

To determine

Prepare a forecasted contribution margin income statement for 2016.

Explanation of Solution

Prepare a forecasted contribution margin income statement for 2016:

Contribution margin income statement: It is a kind of income statement which reports the sales, variable costs, contribution margin, fixed costs, and net profit.

Prepare a forecasted contribution margin income statement for 2016:

Company R
Forecasted Contribution Margin Income Statement
For Year Ended December 31, 2016
Sales $\left(20,000\times \$37.50\right)$	$750,000
Less: Variable costs $\left(20,000\times \$15\right)$	300,000
Contribution margin $\left(20,000\times \left(\$37.50-\$15\right)\right)$	450,000
Less: Fixed costs	350,000
Income before income taxes	$100,000

Table (4)

4.

To determine

Compute the sales level required in both dollars and units to earn $200,000 of target pre-tax income in 2016 with machine installed and no change in unit sale price.

Explanation of Solution

Fixed costs are $350,000 (refer working note 2), target operating revenue is $200,000 and average contribution margin ratio is 60% (refer working note 3).

Required sales in dollars:

$\begin{array}{c}\text{Break-even sales volume }\left(\text{\$}\right)\text{ =}\frac{\text{ Fixed costs}+\text{Target Operting Income}}{\text{Contribution margin ratio}}\\ \text{=}\frac{\$350,000+\$200,000}{60\%}\\ =\frac{550,000}{60\%}\\ =\$916,667\end{array}$

Required sales in units:

Selling price per unit is $37.50 and required sales in dollars are $916,667.

$\begin{array}{c}\text{Required sales in units}\text{=}\frac{\$916,667}{\$37.50}\\ =24,445\text{units}\end{array}$

Therefore, the sales level required in both dollars and units to earn $200,000 are $916,667 (rounded off to next dollar) and 21,667 units (rounded off to next unit) respectively.

5.

To determine

Prepare the forecasted contribution margin income statement that shows the results at the sales level computed in part 4.

Explanation of Solution

Prepare the forecasted contribution margin income statement that shows the results at the sales level computed in part 4:

Company R
Forecasted Contribution Margin Income Statement
For Year Ended December 31, 2016
Sales $\left(24,445\text{units}\times \$37.50\right)$	$916,688
Variable costs $\left(24,445\text{ units}\times \$15\right)$	366,675
Contribution margin $\left(21,667\text{ units}\times \$30\right)$	550,013
Fixed costs (refer working note 2)	350,000
Income before income taxes	$200,013

Table (5)

Therefore, forecasted pre-tax income for the year 2016 is $200,013.