Chapter 7, Problem 54P

Basu Company produces two types of sleds for playing in the snow: basic sled and aerosled. The projected income for the coming year, segmented by product line, follows:

The selling prices are $30 for the basic sled and $60 for the aerosled. (Round break-even packages and break-even units to the nearest whole unit.)

Required:

1. 1. Compute the number of units of each product that must be sold for Basu to break even.
2. 2. Assume that the marketing manager changes the sales mix of the two products so that the ratio is five basic sleds to three aerosleds. Repeat Requirement 1.
3. 3. CONCEPTUAL CONNECTION Refer to the original data. Suppose that Basu can increase the sales of aerosleds with increased advertising. The extra advertising would cost an additional $195,000, and some of the potential purchasers of basic sleds would switch to aerosleds. In total, sales of aerosleds would increase by 12,000 units, and sales of basic sleds would decrease by 5,000 units. Would Basu be better off with this strategy?

To determine

Calculate break-even units for basic sled and aerosled.

Answer to Problem 54P

Break-even quantity for basic sled and aerosled are 47,850 units and 19,140 units respectively.

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.

The package of basic sled and aerosled is given below:

Product	Price ($) A	Unit Variable Cost ($) B	Unit Contribution Margin ($) C $\left(A-B\right)$	Sales Mix D	Package Unit Contribution Margin ($) $\left(C\times D\right)$
Basic sled	30	103	20	55	100
Aerosled	60	254	35	25	70
Total					170

Table (1)

Use the following formula to calculate break-even quantity:

$\text{Break-}\mathrm{even}quantity=\frac{\text{Total fixed cost}}{\mathrm{Contribution}margin}$

Substitute $1,626,900⁶ for total fixed cost and $170 for contribution margin in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=\frac{\$1,626,900}{\$170}\\ =9,570units\end{array}$

Therefore, break-even quantity is 9,570 units.

Use the following formula to calculate break-even quantity for basic sled:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 9,570 units for number of units and 5⁵ for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=9,570\times 5\\ =47,850\text{units}\end{array}$

Therefore, the break-even quantity for basic sled is 47,850 units.

Use the following formula to compute break-even point for aerosled:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 9,570 units for number of units and 2⁵ for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=9,570\times 2\\ =19,140\text{units}\end{array}$

Therefore, the break-even motorcycle helmet is 19,140 units.

Working Note:

1. Calculation of units sold of basic sled:

$\begin{array}{c}Units\text{}sold=\frac{Sales}{Sellingprice}\\ =\frac{\$3,000,000}{\$30}\\ =100,000\text{}\mathrm{units}\end{array}$

2. Calculation of units sold of aerosled:

$\begin{array}{c}Units\text{}sold=\frac{Sales}{Sellingprice}\\ =\frac{\$2,400,000}{\$60}\\ =40,000\text{}\mathrm{units}\end{array}$

3. Calculation of variable cost per unit for basic sled:

$\begin{array}{c}Variable\cos tperunit=\frac{Totalvariable\text{}\cos t}{\mathrm{Units}sold}\\ =\frac{\$1,000,000}{100,000\mathrm{units}}\\ =\$10perunit\end{array}$

4. Calculation of variable cost per unit for aerosled:

$\begin{array}{c}Variable\cos tperunit=\frac{Totalvariable\text{}\cos t}{\mathrm{Units}sold}\\ =\frac{\$1,000,000}{40,000\mathrm{units}}\\ =\$25perunit\end{array}$

5. Calculation of sales mix:

Ratio for basic sled:

$\begin{array}{c}Ratio=\frac{Numberofbasicsled}{Totalnumberofitems}\\ =\frac{100,000}{140,000}\\ =\frac{5}{7}\end{array}$

Ratio for aerosled:

$\begin{array}{c}Ratio=\frac{Numberofaerosled}{Totalnumberofitems}\\ =\frac{40,000}{140,000}\\ =\frac{2}{7}\end{array}$

The sales mix ratio for basic sled and aerosled is 5:2.

6. Calculation of total fixed cost:

$\begin{array}{c}Total\text{}fixed\cos t=Totaldirect\cos t+Commonfixed\cos t\\ =\$1,428,000+\$198,900\\ =\$1,626,900\end{array}$

To determine

Calculate the break-even units for basic sled and aerosled if the sales mix is 5:3.

Answer to Problem 54P

Break-even quantity for basic sled and aerosled are 39,680 units and 23,808 units respectively.

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.

The package of basic sled and aerosled is given below:

Product	Price ($) A	Unit Variable Cost ($) B	Unit Contribution Margin ($) C $\left(A-B\right)$	Sales Mix D	Package Unit Contribution Margin ($) $\left(C\times D\right)$
Basic sled	30	103	20	5	100
Aerosled	60	254	35	3	105
Total					205

Table (1)

Use the following formula to calculate break-even quantity:

$\text{Break-}\mathrm{even}quantity=\frac{\text{Total fixed cost}}{\mathrm{Contribution}margin}$

Substitute $1,626,900⁶ for total fixed cost and $205 for contribution margin in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=\frac{\$1,626,900}{\$205}\\ =7,936units\end{array}$

Therefore, break-even quantity is 7,936 units.

Use the following formula to calculate break-even quantity for basic sled:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 7,936 units for number of units and 5 for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=7,936\times 5\\ =39,680\text{units}\end{array}$

Therefore, the break-even quantity for basic sled is 39,680 units.

Use the following formula to compute break-even point for aerosled:

$\text{Break-}\mathrm{even}quantity=\text{Number of }units\times \text{Sales mix}$

Substitute 7,936 units for number of units and 3 for sales mix in the above formula.

$\begin{array}{c}\text{Break-}\mathrm{even}quantity=7,936\times 3\\ =23,808\text{units}\end{array}$

Therefore, the break-even motorcycle helmet is 23,808 units.

To determine

State whether the strategy is profitable.

Explanation of Solution

Particulars	Amount ($)
Increase in contribution margin of aerosled	420,0007
Decrease in contribution of basic sled	(100,000)8
Increase in total contribution margin	320,000
Less: Additional fixed cost	195,000
Increase in income	125,000

Table (1)

The strategy will earn Person B $125,000. Therefore, the strategy is beneficial for Person B.

Working Notes:

7. Calculation of increase in contribution margin of aerosled:

$\begin{array}{c}Increasein\text{}contributionmargin=Increaseinquantity\times Unitcontributionmargin\\ =12,000\times \$35\\ =\$420,000\end{array}$

8. Calculation of decrease in contribution margin of basic sled:

$\begin{array}{c}Decreasein\text{}contributionmargin=Decreaseinquantity\times Unitcontributionmargin\\ =5,000\times \$20\\ =\$100,000\end{array}$