Question

The Shirt Works sells a large variety of tee shirts and sweatshirts. Steve Hooper, the owner, is thinking of expanding his sales by hiring high school students, on a commission basis, to sell sweatshirts bearing the name and mascot of the local high school.

These sweatshirts would have to be ordered from the manufacturer six weeks in advance, and they could not be returned because of the unique printing required. The sweatshirts would cost Hooper $23.00 each with a minimum order of 360 sweatshirts. Any additional sweatshirts would have to be ordered in increments of 50.

Since Hooper’s plan would not require any additional facilities, the only costs associated with the project would be the costs of the sweatshirts and the costs of the sales commissions. The selling price of the sweatshirts would be $46.00 each. Hooper would pay the students a commission of $8.00 for each shirt sold.

Required:

1. What level of unit sales and dollar sales is needed to attain a target profit of $11,250?

2. Assume that Hooper places an initial order for 360 sweatshirts. What is his break-even point in unit sales and dollar sales? (Round your intermediate calculations and final answers to the nearest whole number.)

Answer 1

Solution

Shirt Works

1. Determination of the level of unit sales and dollars sales needed to attain a target profit of $11,250:

Desired unit sales = (fixed cost + target profit)/contribution margin per unit

Fixed cost = 0
target profit = 11,250

Contribution margin per unit = sales price – variable costs

= $46 – (23 + 8) = $15 per shirt

desired unit sales = $11,250/$15 = 750 shirts

Desired dollar sales = (fixed cost + target profit)/CM ratio

Fixed cost = 0

Target profit = 11,250

CM ratio = $15/$46 = 32.61%

Desired dollar sales = $11,250/32.61% = $34,500

2. Determination of break-even point in unit sales and sales dollars:

Assuming an initial order for 360 sweatshirts –

Since, minimum order quantity is 360 units, the cost would be a fixed cost.

Fixed cost = $23 x 360 = $8,280

Since, the cost price is treated as fixed cost, the variable cost would comprise only the commission to students.

Hence, variable cost = $8

Contribution margin = $46 - $8 = $38

Now, break-even point in units = fixed cost/CM per unit

= 8,280/38 = 218 units

Break-even point in dollars –

= fixed cost/CM ratio

Fixed cost = $8,280

CM ratio = 38/46 = 82.61%

Break-even point in sales dollars = 8,280/82.61% = $10,023

Hence, break-even point in sales dollars = $10,023