Question

2) S&P Supply sells only two products, Product S and Product P.

	Product S	Product P
Selling price per unit	$25	$50
Variable cost per unit	$20	$30
Fixed costs			$225,000

a) What is the firm’s breakeven sales in dollars, assuming a sales (revenue) mix of 20% Product S and 80% Product P?

b). Suppose the firm generated the amount of sales in dollars needed to break even, assuming a sales mix of 20% Product S and 80% Product P. If the firm’s actual sales mix was 25% Product S and 75% Product P, total profits would be:

CHOOSE ONE: POSITIVE NEGATIVE ZERO

c.) If the firm’s actual profits were $90,000 with a revenue mix of 20% Product S and 80% Product P, what was total revenue from Product P?

Answer 1

Solution

S&P Supply

1. Determination of the firm’s breakeven sales in dollars, assuming a sales mix of 20% and 80% of products S and P, respectively:

Break-even sales in dollars = fixed cost/weighted average CM ratio

Weighted average contribution,

	Product S	Product P
Sales price per unit	$25	$50
Variable cost	$20	$30
Contribution margin per unit	$5	$20

Weighted average unit contribution margin

= [(unit CM of Product S x sales proportion) + (unit CM of Product P x sales proportion)]

= [($5 x 0.20) + ($20 x 0.8)] = $17 per unit

Break-even point in units = fixed cost/ (weighted average selling price – weighted average variable cost)

Weighted average selling price= (25 x 0.2) + (50 x 0.8) = $45

Weighted average variable cost = (20 x 0.2) + (30 x 0.8) = $28

Break-even sales in units = $225,000 / ($45 -$28) = 13,235 units (rounded to nearest whole number)

Break even sales in dollars –

Proportion of Product S in break-even sales in units = 13,235 x 0.2 = 2,647

Proportion of Product P in break-even sales in units = 13,235 x 0.8 = 10,588

Break-even sales in dollars = (2,647 x $25) + (10,588 x $50) = $595,575

1. Assuming actual sales mix – Product S and Product P – 25% : 75%

Weighted average contribution margin = [($5 x 0.25) + ($20 x 0.75)] = $16.25 per unit

Break-even sales in units = $225,000/$16.25 =13,846 units

Break-even sales in units of Product S = 13,846 x 0.25 = 3,462

Break-even sales in units of Product P = 13,486 x 0.75 = 10,384

Break even sales in dollars –

Break-even sales in dollars = (3,462 x $25) + (10,384 x $50) = $605,750

Comparison of break-even points for the two mentioned sales mixes – (20%, 80%) and (25%, 75%) indicates that the break-even point in sales dollars is higher for 25% ; 75%. A higher break-even point indicates higher level of fixed cost and decrease in profits. Hence, profits would be NEGATIVE if the firm’s actual sales mix is 25%: 75%. Of S and P.

1. Actual profits = $90,000

Revenue mix = S:P = 20% : 80%

Total revenue from Product P is calculated as follows,

Total contribution= fixed cost + profit = $225,000 + $90,000 = $315,000

total number of units sold = Total contribution /weighted average contribution margin

Weighted average unit contribution margin

= [(unit CM of Product S x sales proportion) + (unit CM of Product P x sales proportion)]

= [($5 x 0.20) + ($20 x 0.8)] = $17 per unit

total number of units sold = 315,000/$17 = 18,529 (rounded to nearest whole number)

share of P = 18,529 x 80% = 14,823 units

Total Revenue from Product P = 14,823 x $50 = $741,160