Alpine Thrills Ski Company recently expanded its manufacturing capacity. The firm will now be able to produce up to 32,000 pairs of cross-country skis of either the mountaineering model or the touring model. The sales department assures management that it can sell between 26,000 and 30,000 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 $ 149.00 $ 137.00
Variable costs per unit 87.70 87.70
Fixed costs will total $622,400 if the mountaineering model is produced but will be only $526,200 if the touring model is produced. Alpine Thrills Ski Company is subject to a 50 percent income tax rate.

Required:

Compute the contribution-margin ratio for the touring model. (Round your final answer to 2 decimal places.)

If Alpine Thrills Ski Company desires an after-tax net income of $41,620, 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.)

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.)

Suppose the variable cost per unit of touring skis decreases by 15 percent, and the total fixed cost of touring skis increases by 15 percent. Compute the new break-even point. (Do not round intermediate calculations. Round your final answer up to nearest whole unit.)

Answer:

35.98%

12,362 pairs

$2.53

9,688 pairs

Explanation:

As per the data given in the question,

1)

As we know that

Contribution margin ratio = (Contribution margin per unit) ÷ (Selling price per unit) × 100

where,

Contribution margin per unit = Selling price per unit - variable cost per unit\

So,

Selling price = $137.00

Variable cost = $87.70

Contribution Margin = $137.00 - $87.70 = $49.30

Contribution margin ratio = $49.30 ÷ $137.00

= 35.98%

2)

Net Income after tax = $41,620

Income Before tax = $41,620 ÷ 50%

= $83,240

Now Pairs of touring skis will be sold by company = (Income before tax + fixed cost) ÷ Contribution Margin

= ($83,240 + $526,200) ÷ $49.30

= 12,362 pairs

3)

Break-even of mountaineering model

= Fixed cost ÷ (Selling price per unit - variable cost per unit)

= $622,400  ÷ ($149 - $87.70)

= $10,153

Now Let Variable cost be Y

$10,153 = $526,200 ÷ ($137 - Y)

Y = $85.17

Therefore, Variable cost per unit decreased by

= ($87.70 - $85.17)

= $2.53

4)

New Fixed cost

= Fixed cost × increased percentage

= $526,200 × 1.15

= $605,130

New variable cost per unit

= $87.70 × 0.85

= $74.54

New Break-even point = New Fixed cost ÷ Contribution Margin

= $605,130 ÷ ($137-$74.54)

= 9,688 pairs

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