Chapter 7, Problem 62P

1.

To determine

Calculate contribution margin for a box of praline fudge. Also calculate the contribution margin ratio.

Answer to Problem 62P

Contribution margin per unit and contribution margin ratio are $1.40 and 0.25 respectively.

Explanation of Solution

Contribution margin:

Contribution margin can be defined as the amount obtained after deducting the variable expense from sales revenue. It means the amount of sales left after covering the variable expenses.

Contribution Margin Ratio:

The sales percentage remaining after covering the amount of total variable cost is known as the contribution margin ratio. It is the available sales dollar percentage which will be used to cover the total fixed cost.

Use the following formula to calculate contribution margin:

$Contributionmarginperunit=Sellingpriceperunit-Variable\cos tperunit$

Substitute $5.60 for selling price per unit and $4.20¹ for variable cost per unit in the above formula.

$\begin{array}{c}Contributionmarginperunit=\$5.60-\$4.20\\ =\$1.40\end{array}$

Therefore, the contribution margin per unit is $1.40.

Use the following formula to calculate contribution margin ratio:

$\text{Contribution margin ratio}=\frac{\mathrm{Contribution}marginperunit}{Sellingpriceperunit}$

Substitute $1.40 for contribution margin per unit and $5.60 for selling price per unit in the above formula.

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\$1.40}{\$5.60}\\ =0.25\end{array}$

Therefore, the contribution margin ratio is 0.25.

Working Notes:

1. Calculation of variable cost per unit:

$\begin{array}{c}Variable\text{}\cos t=\left(\begin{array}{l}Pecans+Sugar+Butter+Otheringredients\\ +Box,packingmaterial+Sellingcommission\end{array}\right)\\ =\$0.70+\$0.35+\$1.85+\$0.34+\$0.76+\$0.20\\ =\$4.20\end{array}$

2.

To determine

Compute the break-even point in units and sales dollars.

Answer to Problem 62P

The break-even units and sales dollars are 32,000 units and $179,200.

Explanation of Solution

Break-Even Point:

The point or situation where the amount of total cost is equivalent to total revenue is known as the break-even point. It is the point where there is no loss or no profit.

Break-Even Sales Revenue:

Break-even sales revenue can be evaluated by dividing the total amount of fixed cost by the contribution margin ratio.

Use the following formula to calculate break-even units:

$\text{Break-}\mathrm{even}units=\frac{\text{Total fixed cost}}{\mathrm{Contribution}marginperunit}$

Substitute $44,800² for total fixed cost and $1.40 for contribution margin per unit in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=\frac{\$44,800}{\$1.40}\\ =32,000units\end{array}$

Therefore, break-even quantity is 32,000 units.

Use the following formula to calculate break-even point in sales dollars:

$\text{Break-even sales revenue}=\frac{\text{Total fixed cost}}{\text{Contribution margin ratio}}$

Substitute $44,800² for the total fixed cost and 0.25 for contribution margin ratio in the above formula.

$\begin{array}{c}\text{Break-even sales revenue}=\frac{\$44,800}{0.25}\\ =\$179,200\end{array}$

Therefore, the break-even point in sales dollars is $179,200.

Working Note:

2. Calculation of total fixed cost:

$\begin{array}{c}Total\text{}fixed\cos t=Fixedoverhead\cos t+Fixedsellingandadministrative\cos t\\ =\$32,300+\$12,500\\ =\$44,800\end{array}$

3.

To determine

Calculate last year’s operating income of Company CI.

Answer to Problem 62P

The operating income of Company CI for last year was $4,200.

Explanation of Solution

Operating Income:

The amount of earnings before charging any interest and tax is known as operating income. It is calculated by deducting the amount of expense by the sales revenue.

The following table represents the income statement:

Company PI
Income Statement
	Amount ($)
Sales revenue	196,0003
Less: Variable cost	147,0004
Contribution margin	49,000
Less: Fixed cost	44,8002
Operating income	4,200

Table (1)

Therefore, the operating income of Company CI for last year was $4,200.

Working Note:

3. Calculation of sales:

$\begin{array}{c}Sales=\left(Priceofboxes\times Boxessold\right)\\ =\left(\$5.60\times 35,000\right)\\ =\$196,000\end{array}$

4. Calculation of variable cost:

$\begin{array}{c}\text{Variable cost}=Variable\cos t\mathrm{per}unit\times Unitssold\\ =\left(\$4.20\times 35,000\right)\\ =\$147,000\end{array}$

4.

To determine

Calculate margin of safety in sales dollars.

Answer to Problem 62P

Margin of safety in sales dollars was $16,800.

Explanation of Solution

Margin of Safety:

The number of units sold or the income earned in excess of the break-even sales is known as margin of safety. It is calculated by deducting the break-even sales from the sales revenue.

Use the following formula to calculate the margin of safety in sales dollars:

$\text{Margin of safety}=\text{Sales}-\text{Break-even }sales\text{}revenue$

Substitute $196,000 for sales and $179,200 for break-even sales revenue in the above formula.

$\begin{array}{c}\text{Margin of safety}=\$196,000-\$179,200\\ =\$16,800\end{array}$

Therefore, the margin of safety in sales dollars was $16,800.

5.

To determine

Calculate the new break-even point in units after the change in price. Also recommend that the price should be increased or not.

Explanation of Solution

Use the following formula to calculate break-even units:

$\text{Break-}\mathrm{even}units=\frac{\text{Total fixed cost}}{\mathrm{Contribution}marginperunit}$

Substitute $44,800² for total fixed cost and $2.0⁵ for contribution margin per unit in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=\frac{\$44,800}{\$2.0}\\ =22,400units\end{array}$

Therefore, break-even quantity is 22,400 units.

Use the following formula to calculate new operating income:

$Operatingincome=Sales-Variable\cos t-Fixed\cos t$

Substitute $195,300⁶ for sales, $132,300⁷ for variable cost and $44,800² for fixed cost in the above formula.

$\begin{array}{c}Operatingincome=\$195,300-\$132,300-\$44,800\\ =\$18,200\end{array}$

Therefore, the new operating income will be $18,200.

The new operating income is higher than the previous operating income. It has increased by $14,000$\left(18,200-4,200\right)$. Therefore, it is advisable to raise the price.

Working Note:

5. Calculation of new contribution margin:

$\begin{array}{c}Contributionmarginperunit=Sellingpriceperunit-Variable\cos tperunit\\ =\$6.20-\$4.20\\ =\$2.0\end{array}$

6. Calculation of sales:

$\begin{array}{c}Sales=\left(Priceofboxes\times Boxessold\right)\\ =\left(\$6.20\times 31,500\right)\\ =\$195,300\end{array}$

7. Calculation of variable cost:

$\begin{array}{c}\text{Variable cost}=Variable\cos t\mathrm{per}unit\times Unitssold\\ =\left(\$4.20\times 31,500\right)\\ =\$132,300\end{array}$