Question

Alpine Thrills Ski Company recently expanded its manufacturing capacity. The firm will now be able to produce up to 25,000 pairs of cross-country skis of either the mountaineering model or the touring model. The sales department assures management that it can sell between 19,000 and 23,000 units of either product this year. Because the models are very similar, the company will produce only one of the two models.

The following information was compiled by the accounting department.

	Model
	Mountaineering				Touring
Selling price per unit	$	142.00			$	130.00
Variable costs per unit		84.20				84.20

Fixed costs will total $594,400 if the mountaineering model is produced but will be only $505,200 if the touring model is produced. Alpine Thrills Ski Company is subject to a 45 percent income tax rate.

1. Compute the contribution-margin ratio for the touring model.

2.  If Alpine Thrills Ski Company desires an after-tax net income of $38,120, how many pairs of touring skis will the company have to sell? (Do not round intermediate calculations. Round your final answer to the nearest whole unit.)

3. How much would the variable cost per unit of the touring model have to change before it had the same break-even point in units as the mountaineering model? (Round your intermediate calculations and final answer to 2 decimal places.)

4. Suppose the variable cost per unit of touring skis decreases by 20 percent, and the total fixed cost of touring skis increases by 20 percent. Compute the new break-even point. (Do not round intermediate calculations. Round your final answer up to nearest whole unit.)

5. Suppose management decided to produce both products. If the two models are sold in equal proportions, and total fixed costs amount to $534,800, what is the firm’s break-even point in units? (Do not round intermediate calculations and round your final answer up to nearest whole number.)

Answer 1

1. Contribution margin ratio for the Touring Model : $ ( 130 - 84.20 ) / $ 130 = 35.23 %

2. Pretax net income required = $ 38,120 / ( 1 - 0.45 ) = $ 69,309

Number of pairs of touring skis required to be sold to earn $ 69,309 = $ ( 505,200 + 69,309 ) / $ 45.8 = 12,543.86 or 12,544 units.

3. Break-even point for the Mountaineering Model = $ 594,400 / $ 57.8 = 10,284 units

Contribution margin per unit for Touring Model needs to be = $ 505,200 / 10,284 = $ 49.12

130 - V = 49.12

or V = $ 80.88 per unit

Decrease in variable cost per pair of the Touring Model required = $ 84.20 - $ 80.88 = $ 3.32.

4. New fixed cost if the Touring Model is produced = $ 606,240

New variable cost per unit of Touring Model : $ 67.36

New break-even point = $ 606,240 / $ ( 130 - 67.36 ) = 9,678.16 or 9,679 units