Donnelly Corporation manufactures and sells T-shirts imprinted with college name

Question

Donnelly Corporation manufactures and sells T-shirts imprinted with college names and slogans. Last year, the shirts sold for $7.50 each, and the variable cost to manufacture them was $2.25 per unit. The company needed to sell 20,000 shirts to break even. The after-tax net income last year was $5,040. Donnelly's expectations for the coming year include the following:

•The sales price of the T-shirts will be $9. .

•Variable costs to manufacture each unit will increase by 33%. .

•Fixed costs will increase by 10%. .

•The income tax rate of 40% will be unchanged..

If Donnelly Corporation wishes to earn $22,500 in after-tax net income for the coming year, the company sales volume in dollars must be:

  A. $213,750

   B. $207,000

   C. $229,500

   D. $257,625

Explanation / Answer

ok so we need to derive a handy dandy equation to help us out.

we need to find out how much the "fixed costs" are:

(20,000x$7.50) - (20,000x$2.25) = $105,000<<<all other expenses or "fixed costs" as the 20k was the break even point.

we have to assume that the fixed costs have nothing to do with the number of shirts sold. now we need to look at our income BEFORE taxes:

$5,040 x 1.4 = $7,056, as we need to ADD 40% to the net income

so after this, we are making $5.25 for every shirt sold. congrats! now let's find out how many you sold, both before and after the break even point:

$105,000 / $5.25 = 20,000 shirts       $7,056 / $5.25 = 1,344 shirts so 21,344 shirts. quite the business

now its easy. just multiply each item by its respective increase, and put them all together.

T-shirts (S): $9

Manufacturing Costs (Cm): $2.25 x 1.33 = $2.99

Fixed Costs(Cf): $105,000 x 1.10 = $115,500

n: number of T-shirts sold          T: tax

Net Income = [ n x ( S - Cm) - Cf ] x 0.6    the 0.6 comes from taking out 40% for taxes.

use that equation to find n, and then just multiply the number of shirts by the cost per shirt and you'll find you're answer

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