Question

Dorcan Corporation manufactures and sells T-shirts imprinted with college names and slogans. Last year, the shirts sold for $7.68 each, and the variable cost to manufacture them was $2.25 per unit. The company needed to sell 21,800 shirts to break-even. The after tax net income last year was $5,580. Donnelly's expectations for the coming year include the following: The sales price of the T-shirts will be $10. Variable cost to manufacture will increase by one-third. Fixed costs will increase by 10%. The income tax rate of 40% will be unchanged. Based on a $10 selling price per unit, the number of T-shirts Dorcan Corporation must sell to break-even in the coming year is:_______.
a. 19,102 units.
b. 18,602 units.
c. 22,102 units.
d. 24,102 units.

Answer 1

Answer:

b. 18,602 units.

Explanation:

First, we need to use last year's information to determine last year's fixed costs.

Price (P1) = $7.68

Variable costs (VC1) = $2.25

Units sold to break-even (n1) = 21,800

At the break-even point, net income is zero and the fixed cost can be found by:

$N=0 = n_1*(P_1-VC_1) -FC_1\\0=21,800*(\ 7.68-\ 2.25) - FC_1\\FC = \ 118,374$

With information from last, information for the current year can be determined:

Price (P2) = $10.00

Variable costs (VC2) = $2.25 x 1.3333 = $3.00

Fixed cost (FC2) = $118,374 x 1.10 = $130,211.4

The number of units required to break even is:

$N=0 = n_2*(P_2-VC_2) -FC_2\\0=n_2*(\ 10-\ 3) - \ 130,211.4\\n_2 = 18,601.63\ units$

Rounding up to the nearest whole unit, Dorcan Corporation must sell 18,602 units to break-even.