Question

David Davis operates a kiosk in downtown Chicago, at which he sells one style of baseball hat. He buys the hats from a supplier for $36 and sells them for $42. David’s current breakeven point is 33,600 hats per year.

(a1)

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Calculate contribution margin per unit.

Contribution margin per unit

$enter Contribution margin per unit in dollars

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(a2)

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What is David’s current level of fixed costs? (Use the rounded contribution margin per unit calculated in the previous part.)

Current level of fixed costs

$enter current level of fixed costs amount in dollars

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(b)

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Assume that David’s fixed costs, variable costs, and sales price were the same last year, when he made $47,040 in net income. How many hats did David sell last year, assuming a 30% income tax rate? (Use the rounded contribution margin per unit calculated in the previous part.)

enter the number of hats

hats

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(c)

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What was David’s margin of safety last year?

Margin of safety

$enter Margin of safety in dollars

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(d)

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If David wants to earn $84,672 in net income, how many hats must he sell, assuming a 30% tax rate? (Use the rounded contribution margin per unit calculated in the previous part.)

enter the number of hats

hats

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(e)

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How many hats must David sell to break even if his supplier raises the price of the hats to $37 per hat? (Use the rounded contribution margin per unit for computation.)

enter the number of hats

hats

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(g)

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David has decided to increase his sales price to $43 to offset the supplier’s price increase. He believes that the increase will result in a 5% reduction from last year’s sales volume. What is David’s expected net income, assuming a 30% tax rate?

Net income

$enter net income amount in dollars

Answer 1

(a1) Contribution margin per unit is ascertained by reducing variable expenses per unit from selling price per unit.

Selling price per unit = $42
Variable expense per unit (Cost of one hat) = $36

Contribution margin per unit = Selling price per unit - Variable expense per unit = $42 - $36 = $6 per unit

(a2) Current level of fixed costs can be ascertained using the equation for determining the Break-even point in units.

Break-even point in units = 33,600 units

Contribution margin per unit = $6 per unit

Break-even point in units = Fixed costs ÷ Contribution margin per unit

33,600 = Fixed costs ÷ $6
Fixed costs = 33,600 × $6 = $201,600

b) Number of hats David sold last year:

Number of hats sold = (Fixed costs + Income before taxes) ÷ Contribution margin per unit

Fixed costs = $201,600

Income before taxes = Net income × 100 / (100 - Income tax rate) = $47,040 × 100 /(100 - 30) = $67,200

Contribution margin per unit = $6

Number of hats sold = ($201,600 + $67,200) ÷ $6 = 44,800 hats

c) Margin of safety is the difference between current sales and break even sales.

Current sales (last year) = Units sold × Selling price per unit = 44,800 × $42 = $1,881,600

Break even sales = Break even units × Selling price per unit = 33,600 × $42 = $1,411,200

Margin of safety = Current sales - Break even sales = $1,881,600 - $1,411,200 = $470,400

d) Number of hats to be sold earn $84,672 in net income.

Net income before taxes = Net income × 100 / (100 - Income tax rate) = $84,672 × 100 /(100 - 30) = $120,960

Number of hats to be sold to get target income = (Fixed costs + Income before taxes) ÷ Contribution margin per unit
= ($201,600 + $120,960) ÷ $6 = 53,760 units

e)
Price of hats raised to $37 per bat.

Therefore, variable costs per unit = $37
Selling price per unit = $42

Contribution margin = Selling price per unit - Variable expense per unit = $42 - $37 = $5 per unit

Break even sales in units = Fixed costs ÷ Contribution margin per unit = $201,600 ÷ 5 = 40,320 units

g)

Net income is ascertained by reducing fixed costs and income taxes frm contribution margin and income before taxes.

Increased sales price per unit = $43

Variable costs per unit = $37

Sales volume = 5% reduction from last year’s sales volume = 95% of last year's sales volume

Sales volume = 44,800 × 95% = 42,560 units

New contribution margin = $43 - $37 = $6 per unit

Contribution margin = Sales volume - Contribution margin per unit = 42,560 × $6 = $255,360

Income before taxes = Contribution margin - Fixed costs = $255,360 - $201,600 = $53,760

Tax rate = 30%

Net income = Income before taxes × 100% - 30%) = $53,760 × 70% = $37,632