Question

Karl runs a store that sells small and large space heaters. The large heaters sell for $250 each with unit variable costs of $120, while the small space heaters sell for $80 each with unit variable costs of $30. Currently, the small space heaters amount to 2,100 of the 2,800 units sold. The fixed costs of the store are $126,000. How many small space heaters and small space hearters must Karl sell to break even?

Answer 1

Answer: Karl must sell 1350 small heaters and 450 large heaters to break even.

We follow these steps to arrive at the answer:

No.                                               Small Large     Total

1 Selling Price per unit                     80  250  

2 Variable Cost per unit                  30   120  

3 Number of units sold              2100   700       2800

4 Sales mix                                  3      1  

5 Total sales (1*3)                  168000   175000  

6 Total Variable Cost (2*3)   63000    84000  

7 Contribution Margin (5-6)  105000     91000      196000

Next we compute the Weighted Average Contribution Margin as follows:

$\mathbf{WACM per unit = \frac{Total Contribution Margin}{Total number of units sold}}$

$\mathbf{WACM per unit= \frac{196000}{2800} = 70}$

Now, Break even point (BEP) is computed as

$\mathbf{BEP = \frac{Total Fixed Costs}{WACM per unit}}$

$\mathbf{BEP = \frac{126000}{70} = 1800 units}$

Since the large and small heaters are sold in the 3:1 ratio, we can find the number of large and small heaters to be sold in order to achieve the break even point at 1800 units.

$No. of small heaters = BEP * \frac{3}{4}$

$No. of small heaters = 1800 * \frac{3}{4} = 1350 units$

$No. of large heaters = BEP * \frac{1}{4}$

$No. of large heaters = 1800 * \frac{1}{4} = 450 units$