Managerial Accounting Tough Question

Question

Bruce and Company makes a single product. Each unit requires $50 of direct materials. Factory overhead is applied on the 150% of direct labor cost. One-third of the factory overhead is fixed. There is no under- or over-applied factory overhead and company has no beginning or ending inventory. The company reports the following results for February:

Number of units sold
8000
Selling price per unit
$300
Manufacturing cost per unit
$200
Variable selling expenses per unit
$18
Total fixed selling expenses
$50,000
Variable administrative expenses per unit
$32
Total fixed administrative expenses
$240,000

How many units can sales go down before the company incur a loss?
A. 1,375 units
B. 6,625 units
C. 2,500 units
D. 960 units
E. None of above.

 

Answer was A) but I don't get how/why please show help with steps.

Answer 1

Step 1: Calculate Contribution Margin per Unit

Contribution margin per unit is calculated as the selling price per unit minus all variable costs per unit.

Selling Price per Unit: $300

Variable Costs per Unit:

Direct Materials: $50

Direct Labor: (Manufacturing cost per unit - Direct materials - Factory overhead) = ($200 - $50 - Factory overhead)

Factory Overhead: Calculated as 150% of direct labor, where 2/3 is variable

Variable Selling Expenses: $18

Variable Administrative Expenses: $32

Let's find the direct labor and variable portion of the factory overhead:

From the problem, we have:

Manufacturing Cost per Unit = $200

Direct Materials = $50

Factory Overhead is 150% of Direct Labor

Given that Factory Overhead includes a 1/3 fixed component, the variable component of the overhead would be 2/3 of the total overhead.

Given:

Total Manufacturing Cost = Direct Materials + Direct Labor + Factory Overhead

200 = 50 + Direct Labor + 1.5 × Direct Labor 200=50+Direct Labor+1.5×Direct Labor

200 = 50 + 2.5 × Direct Labor

200=50+2.5×Direct Labor

Direct Labor = 150/2.5 = 60

Therefore:

Factory Overhead Total: $60 \times 1.5 = $90

Variable Factory Overhead: $\frac{2}{3} \times 90 = $60

The total variable cost per unit is:

Direct Materials: $50

Direct Labor: $60

Variable Factory Overhead: $60

Variable Selling Expenses: $18

Variable Administrative Expenses: $32

Total Variable Cost per Unit = 50 + 60 + 60 + 18 + 32 = 220

Total Variable Cost per Unit=50+60+60+18+32=220

Contribution Margin per Unit: $300 - 220 = $80

Step 2: Calculate Total Fixed Costs

Total Fixed Selling Expenses: $50,000

Total Fixed Administrative Expenses: $240,000

Fixed Factory Overhead: $\frac{1}{3} \times 90 = $30 \times 8,000 units = $240,000

Total Fixed Costs: $50,000 + $240,000 + $240,000 = $530,000

Step 3: Calculate Break-Even Point

Break-Even Point in Units = Total Fixed Costs / Contribution Margin per Unit

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Break-Even Point in Units = 530,000 / 80 = 6625 units

Conclusion:

The number of units sales can decrease before the company incurs a loss is

8,000−6,625=1,375 units.

Hence, the answer is:

A. 1,375 units