Question

1. The Wilcox Company sells two products, A and B, with contribution margin ratios of 40 and 30 percent and selling prices of $5 and $2.50 a unit. Fixed costs amount to $72,000 a month. Monthly sales average 30,000 units of product A and 40,000 units of product B.

Required:

a.

Assuming that three units of product A are sold for every four units of product B, calculate the dollar sales volume necessary to break even.

b.

As part of its cost accounting routine, Wilcox Company assigns $36,000 in fixed costs to each product each month. Calculate the break-even dollar sales volume for each product.

c.

Wilcox Company is considering spending an additional $9,700 a month on advertising, giving more emphasis to product A and less emphasis to product B. If its analysis is correct, sales of product A will increase to 40,000 units a month, but sales of product B will fall to 32,000 units a month. Recalculate the break-even sales volume, in dollars, at this new product mix. Should the proposal to spend the additional $9,700 a month be accepted?

Answer 1

Answer

a. Sales mix = 3 units of A : 4 units of B

So, as mentioned in the question, 30,000 units of product A and 40,000 units of product B can be taken as sales mix.

Break even dollar sales volume is asked here.

Break even dollar sales volume = Fixed cost / Contribution margin ratio

Since, there are two kinds of products, we can't consider the contribution margin ratio of a single product. We should calculate weighted average contribution margin ratio. Here is the workings:

		Product A	Product B	Total
Number of units		30,000	40,000	70,000
Selling price per unit		$5	$2.5
Total sales	Number of units*selling price	30,000*5 = $150,000	40,000*2.5 = $100,000	$250,000
Contribution margin ratio		40%	30%
Total contribution margin	Total sales*contribution margin ratio	150,000*40% = $60,000	100,000*30% = $30,000	$90,000

So, total contribution margin for product A $ B = $90,000

Weighted average contribution margin ratio = Total contributon margin / total sales = 90,000/250,000 = 0.36 or 36%

fixed cost = $72,000

So, break even dollar sales volume = 72,000 / 0.36 = $200,000

b. Break even dollar sales volume for each product

	Product A	Product B
Contribution margin ratio	40% or 0.4	30% or 0.3

Fixed cost = $36,000 for each product

Break even dollar sales volume = fixed cost / contribution margin ratio

1. For product A = 36,000 / 0.4 = $90,000

2. For product B = 36,000 / 0.3 = $120,000

c.If advertising is adopted, fixed cost will increase by $9,700

Sales mix also changed. Let's calculate new weighted average contribution margin ratio.

		Product A	Product B	Total
Number of units		40,000	32,000	72,000
Selling price		$5	$2.5
Total sales	seling price*number of units	5*40,000 = $200,000	2.5*32,000 = $80,000	$280,000
Contribution margin ratio (contribution margin ratio for individual products won't change)		40%	30%
Total contribution margin	Total sales*contribution margin ratio	200,000*40% = $80,000	80,000*30% = $24,000	$104,000

Weighted contribution margin ratio = Total contribution margin / total sales = 104,000/280,000 = 0.3717 or 37.14%

Fixed cost = 72,000 + 9,700 = $81,700

Break even sales volume in dollars = 81,700 / 0.3714 = $219,978

Decision on advertising proposal

The break even sales volume in dollars was $200,000 before accepting this proposal. But after accepting this, it has increased to $219,978, which means the company has to increase it's sales by $19,978 to attain the break even(or to attain no profit no loss condition). But due to advertising, the gross sales has increased from $250,000 to $280,000. An increase of $30,000 sales is enough to compensate the increase in break even sales of $19,978. SO, THE ADVERTISING PROPOSAL CAN BE ACCEPTED.