Question

After-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)

Answer 1

Solution Computation of Contribution Margin per unit and Contribution Margin ratio for each model Mountaineering Model Touring Model (a) Selling price per unit (b) Less: Variable cost per unit (c) Contribution Margin per unit (a - b) $180 ($130) $50 $120 ($90) $30 (d) Contribution Margin ratio (c/a) 27.78% 25.00% Required 1.: Desired after-tax targeted income Income tax rate Desired pre-tax targeted income ($48,000/(1-0.40)) $48,000 40% $80,000 Fixed cost of touring model $220,000 Required selling units - Pre-tax targeted Income + Fixed cost Contribution Margin per unit $80,000 + $ 220,000 $30 10,000 units The company must sell 10,000 units of touring model to achieve after-tax income of $48,000. Required 2.: Let assume that the total sales revenue is 'X' at which the Company shall make same profit or loss regardless of the ski model it decided to produce. At Sales revenue 'X', Pre-tax Net profit, if mountaineering model is produced = 'X' x 27.78% - $320,000 Pre-tax Net profit, if touring model is produced = 'X' x 25% - $220,000

Now, Xx 27.78% - $320,000 = 'X' x 25% - $220,000 0.2778 X - $320,000 = 0.25 X - $220,000 (0.2778 -0.25)X = $320,000 - $220,000 0.0278x = $100,000 x = $100,000 / 0.0278 x = $3,597,122 Hence, at sales revenue $3,597,122, the Company shall make same profit or loss regardless of the ski model it decided to produce. Required 3.: We shall calculate the net profit at sales units 12,000 pairs for both the models, as under: Sales Revenue Less: Variable cost Contribution Margin Less: Fixed cost Profit before tax Less: Income tax (40%) Profit after tax Mountaineering Model $2,160,000 ($1,560,000) $600,000 ($320,000) $280,000 ($112,000) $168,000 Touring Model $1,440,000 ($1,080,000) $360,000 ($220,000) $140,000 ($56,000) $84,000 If the Sales Department could guarantee the annual sale of 12,000 pairs of either model, the company should produce Mounteering Model.