Question

fter-Tax Target Income: Profit Analysis

X-Cee-Ski Company recently expanded its manufacturing capacity, which will allow it to produce up to 21,000 pairs of cross-country skis of the mountaineering model or the touring model. The Sales Department assures management that it can sell between 9,000 and 14,000 pairs of either product this year. Because the models are very similar, X-Cee-Ski will produce only one of the two models.

The following information was compiled by the Accounting Department:

	Per-Unit (Pair) Data
		Mountaineering		Touring
Selling price		$180		$120
Variable costs		130		90

Fixed costs will total $320,000 if the mountaineering model is produced but will be only $220,000 if the touring model is produced. X-Cee-Ski is subject to a 40 percent income tax rate.

Required:

1. If X-Cee-Ski Company desires an after-tax net income of $48,000, how many pairs of touring model skis will the company have to sell?
pairs of touring skis

2. Suppose that X-Cee-Ski Company decided to produce only one model of skis. What is the total sales revenue at which X-Cee-Ski Company would make the same profit or loss regardless of the ski model it decided to produce?
$

3. If the Sales Department could guarantee the annual sale of 12,000 pairs of either model, which model would the company produce? (CMA adapted)
Mountaineering model

Answer 1

1.Before-tax income= $48,000/(1 –0.4)= $80,000

Number of pairs of touring model skis to earn $48,000

after-tax income:= ($220,000 + $80,000)/($120 –$90)= 10,000 pairstouring skis

2.Let X= Number of pairs of mountaineering skisand

Y= Number of pairs of touring skis

$180X –$130X –$320,000= $120Y –$90Y –$220,000

$180X –$130X –$100,000= $120Y –$90Y

$180X –$130X –$100,000= $120(180/120)X –$90(180/120)X*

$5X= $100,000

X= 20,000 pairs

Revenue = $180 × 20,000 = $3,600,000

*If total revenue is the same, then 180X = 120Y, or Y = (180/120)X and (180/120)Xcan be substituted for Y.

3.X-Cee-Ski Company would produce and sell 12,000 pairs of the mountaineering skis because they are more profitable.

  

	Mountaineering Model	Touring Model
Sales	$2,160,000	$1,440,000
Less: Variable expenses	1,560,000	1,080,000
Contribution margin	$600,000	$360,000
Less: Fixed expenses	320,000	220,000
Operating income	$280,000	$140,000