Cathy's Towels sells three items (which it purchases from a supplier): bath towels, hand towels, and washcloths in a 4:3:2 mix (thus, a batch of 9 towels has 4 bath towels, 3 hand towels, and 2 washcloths). Each bath towel sells for $10 and costs $4, each hand towel sells for $5 and costs $2; and each washcloth sells for $2.50 and costs $1. The shop's annual fixed expenses are $324,000, and the income tax rate, t, is 40%. How many bath towels must the firm sell at the breakeven point?

Question

Quizplus · Accepted Answer

To find the breakeven point, we need to calculate the total cost and the total revenue. Let B be the number of bath towels sold.

Total cost = (4/9)*($4*B) + (3/9)*($2*B) + (2/9)*($1*B) + $324,000
Total cost = ($16/9)*B + ($6/9)*B + ($2/9)*B + $324,000
Total cost = ($24/9)*B + $324,000
Total cost = $8/3*B + $324,000

Total revenue = ($10*B) + (3/4)*($5*B) + (2/4)*($2.5*B)
Total revenue = $10B + ($15/4)*B + ($5/4)*B
Total revenue = ($45/4)*B

At breakeven, total cost = total revenue:

$8/3*B + $324,000 = ($45/4)*B
(B/12)*($8 + $45) = $324,000
B = 36,000

Therefore, the firm must sell 36,000 bath towels at the breakeven point.

Cathy's Towels Sells Three Items (Which It Purchases from a Supplier)