Chapter 16, Problem 41P

Salem Electronics currently produces two products: a programmable calculator and a tape recorder. A recent marketing study indicated that consumers would react favorably to a radio with the Salem brand name. Owner Kenneth Booth was interested in the possibility. Before any commitment was made, however, Kenneth wanted to know what the incremental fixed costs would be and how many radios must be sold to cover these costs.

In response, Betty Johnson, the marketing manager, gathered data for the current products to help in projecting overhead costs for the new product. The overhead costs based on 30,000 direct labor hours follow. (The high-low method using direct labor hours as the independent variable was used to determine the fixed and variable costs.)

*All depreciation.

The following activity data were also gathered:

Betty was told that a plantwide overhead rate was used to assign overhead costs based on direct labor hours. She was also informed by engineering that if 20,000 radios were produced and sold (her projection based on her marketing study), they would have the same activity data as the recorders (use the same direct labor hours, machine hours, setups, and so on).

Engineering also provided the following additional estimates for the proposed product line:

Upon receiving these estimates, Betty did some quick calculations and became quite excited. With a selling price of $26 and just $18,000 of additional fixed costs, only 4,500 units had to be sold to break even. Since Betty was confident that 20,000 units could be sold, she was prepared to strongly recommend the new product line.

Required:

1. 1. Reproduce Betty’s break-even calculation using conventional cost assignments. How much additional profit would be expected under this scenario, assuming that 20,000 radios are sold?
2. 2. Use an activity-based costing approach, and calculate the break-even point and the incremental profit that would be earned on sales of 20,000 units.
3. 3. Explain why the CVP analysis done in Requirement 2 is more accurate than the analysis done in Requirement 1. What recommendation would you make?

To determine

Ascertain the break-even point and the additional profit for the given proposal.

Explanation of Solution

Contribution Margin Ratio: The contribution margin ratio shows the amount of difference in the actual sales value and the variable expenses in percentage. This margin indicates that percentage which is available for sale above the fixed costs and the profit. The formula for variable cost ratio is shown below:

$\text{Contribution Margin ratio = }\frac{\text{Contribution Margin}}{\text{Sales}}$

Break-Even Point: The break-even point refers to the point of sales at which the firm neither earns a profit nor suffers a loss. It is also known as the point of sales or sales value at which the firm recovers the entire cost of fixed and variable nature.

Break-Even in sales revenue: The break-even in sales revenue refers to the sales volume required to cover the fixed and variable costs and left out with neither profit nor loss.

Compute the variable overhead rate:

$\begin{array}{c}\text{Variable Overhead Cost =}\frac{\text{Materials handling + Power+Machine costs}}{\text{Number of Units}}\\ =\frac{\text{\$18,000}+\$\text{22,000}+\$\text{80,000}}{30,000}\\ =\frac{\$120,000}{30,000}\\ =\$4\end{array}$

The variable overhead rate per direct labor hour is $4.

Compute the unit variable cost:

$\begin{array}{c}\text{Unit Variable Cost }=\text{Unit prime cost }-\text{Unit variable overhead}\\ =\$18+\$4\\ =\$22\end{array}$

The variable cost per unit is $22.

Compute the break-even units:

$\begin{array}{c}\text{Break-even in Units }=\frac{\text{Fixed cost}}{\text{Contribution Margin}}\\ =\frac{\$18,000}{\left(\$26-\$22\right)}\\ =4,500\text{ units}\end{array}$

The break-even unit is 4,500 units.

Compute the additional profit:

$\begin{array}{c}\text{Additional profit }=\text{Contribution Margin}\times \left(\text{Unit sales}-\text{Break-even sales}\right)\\ =\$4\times \left(\text{20,000}-4,500\right)\\ =\$4\times 15,500\\ =\text{\$62,000}\end{array}$

The additional profit is $62,000.

To determine

Compute the break-even point and the incremental profit using the activity based costing.

Explanation of Solution

Compute the unit-based variable overhead cost per unit:

Particulars	Amount ($)
Unit-based variable costs:
Materials handling	$18,000
Power	$22,000
Machine costs	$80,000
Total	$120,000
Machine hours	20000
Pool rate	$6

Table (1)

Compute the unit variable cost:

$\begin{array}{c}\text{Unit Variable Cost }=\text{Unit prime cost }+\text{Unit variable overhead}\\ =\$18+\left(\$6\times \frac{\text{10,000}}{\text{20,000}}\right)\\ =\$18+\$3\\ =\$21\end{array}$

The unit-based variable overhead cost per unit is $21 (X1).

Compute the non-unit-based variable overhead cost per unit:

Particulars	Calculations	Amount ($)
Non-unit-based variable costs:
Engineering (X2)	$\left(\$100,000/5,000\right)$	$20.00
Inspection (X3)	$\left(\$40,000/2,100\right)$	19.05
Setups (X4)	$\left(\$60,000/60\right)$	$1,000

Table (2)

Compute the break-even units:

Substitute the values found in the below equation to compute the break-even point.

$\begin{array}{c}\text{Break-even in Units = }\left(\begin{array}{l}\text{Fixed cost}+\text{Unit-based variable costs}\\ +\text{Non-unit-based variable costs}\end{array}\right)\\ \$26\left(\text{X}1\right)=\text{\$18,000}+\$21\left(\text{X}1\right)+\$20\left(\text{X}2\right)+\$19.05\left(\text{X}3\right)+\$1,000\left(\text{X}4\right)\\ \$26\left(\text{X}1\right)-\$21\left(\text{X}1\right)=\text{\$18,000}+\$20\left(\text{X}2\right)+\$19.05\left(\text{X}3\right)+\$1,000\left(\text{X}4\right)\\ \$5\left(\text{X}1\right)=\text{\$18,000}+\$20\left(\text{X}2\right)+\$19.05\left(\text{X}3\right)+\$1,000\left(\text{X}4\right)\end{array}$

$\begin{array}{c}\text{X}1\text{= }\frac{\text{\$18,000}+\$20\left(\text{X}2\right)+\$19.05\left(\text{X}3\right)+\$1,000\left(\text{X}4\right)}{\$5}\\ =\frac{\text{\$18,000}+\$20\left(1,000\right)+\$19.05\left(1,400\right)+\$1,000\left(40\right)}{\$5}\\ =\frac{\$104,670}{\$5}\\ =20,934\text{ units}\end{array}$

The break-even unit is 20,934 units.

The activity based costing is based on the assumptions that:

• The expected variable cost is realized.
• The depreciation is a fixed cost.

If the depreciation represents no salvage and the expected production is achieved, then the variable cost per unit will increase by $0.90$\left(\frac{\$18,000}{20,000}\right)$. In this scenario, the numerator will decrease by $18,000 and the denominator will decrease by $0.90.

Compute the new break-even units:

$\begin{array}{c}\text{X}1\text{= }\frac{\$104,670-\text{\$18,000}}{\$5-\$0.90}\\ =\frac{\text{\$86,600}}{\text{\$4}\text{.10}}\\ =21,122\text{ units}\end{array}$

The new break-even unit is 21,122 units.

To determine

Describe the reasons for the greater accuracy of CVP analysis done in Requirement 2 than in the CVP analysis done in Requirement 1.

Explanation of Solution

Cost Volume Profit Analysis (CVP Analysis): The Cost volume profit (CVP) analysis is helpful in determining how any type of change in cost determines company’s income.

The reasons for differences in accuracy are:

• The Requirement 2 takes into consideration all the associated costs of the support activities which are ignored by the conventional method.
• The non-unit related costs are viewed as fixed costs in Requirement 1.
• Once these support activity costs are added the analysis tends to be more accurate.