The Dooley Co.manufactures two products,Baubles and Trinkets.The following are projections for the coming year: How many Baubles will be sold at the break-even point,assuming that the facilities are jointly used and the sales mix will remain constant?

Question

Quizplus · Accepted Answer

To find the break-even point, we need to use the contribution margin per unit for each product.

Contribution margin per Bauble = Selling Price per Bauble - Variable Cost per Bauble = $90 - $60 = $30 
Contribution margin per Trinket = Selling Price per Trinket - Variable Cost per Trinket = $50 - $20 = $30

At the break-even point, the total contribution margin will equal the total fixed costs. Let's call the number of Baubles sold "B" and the number of Trinkets sold "T". Then we have:

$30B + $30T = $210,000

We also know that the sales mix (the ratio of Baubles sold to Trinkets sold) will remain constant. Let's call this ratio "x:Baubles". Then:

T = xB

Substituting this into the equation above, we get:

$30B + $30(xB) = $210,000

Simplifying:

$30B(1+x) = $210,000

B = $210,000 / $30(1+x)

We don't know the value of "x", but we can at least find the minimum number of Baubles we need to sell to break even. Let's assume the worst-case scenario: we sell only Baubles (i.e. x=0). Then:

B = $210,000 / $30 = 7,000

So we need to sell at least 7,000 Baubles to break even.

Notice that if we sell any Trinkets at all, the ratio of Baubles to Trinkets will be greater than 0:1, which means the actual break-even point will be lower than 7,000 Baubles.

Let's try using the other extreme scenario: we sell only Trinkets (i.e. x=infinity). Then:

B = $210,000 / $30(infinity+1) = $0

This doesn't make sense -- we can't break even by selling zero Baubles. But it does tell us something useful: if we sell mostly Trinkets, then the break-even point will be very low.

The true break-even point will lie somewhere in between these two extremes. We can solve for the value of "x" by looking at the sales mix:

x:Baubles = 3500/6000 = 7/12

This means that for every 7 Baubles we sell, we sell 5 Trinkets. Now we can solve for the number of Baubles we need to sell:

B = $210,000 / $30(1+7/12) = 6,600

Therefore, the answer is (C) 6,600.