Question

Adam Granger operates a kiosk in downtown Chicago, at which he sells one style of baseball hat. He buys the hats from a supplier for $16 and sells them for $22. Adam’s current breakeven point is 20,250 hats per year.

Assume that Adam’s fixed costs, variable costs, and sales price were the same last year, when he made $28,350 in net income. How many hats did Adam sell last year, assuming a 30% income tax rate? (correct answer is 27,700 - already figured out that step)

What was Adam’s margin of safety last year? Margin of Safety $_____

If Adam wants to earn $51,030 in net income, how many hats must he sell, assuming a 30% tax rate?
# of Hats: _____

How many hats must Adam sell to break even if his supplier raises the price of the hats to $17 per hat?
# of Hats: _____

Adam has decided to increase his sales price to $23 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 Adam’s expected net income, assuming a 30% tax rate?
Net Income: $_______

Answer 1

1. Number of hats sold by Adam last year=27000(Note)

Note:

Adam’s Current Break-Even Point=20250 units

Current Contribution per unit=$22-$16=$6 per unit

Therefore Current Fixed Cost=$ 6 *20250=$121500

Current Year’s Fixed Cost =Last Year’s Fixed Cost

Therefore Last Year’s Fixed Cost=$ 121500

Last Year Net Income=$ 28350

Therefore last year Income before taxes=$28350/0.7=$ 40500

Last year contribution= Net Income before taxes+ Fixed cost

=$ 40500+$ 121500=$ 162000

Therefore number of units sold=Total Contribution/Contribution per unit

   =$ 162000/$ 6=27000 units

2. Adam’s Margin of Safety last year=$148500 (Note)

Note:

Last year’s Actual Sales=27000 units

Last year’s Break-Even point=20250 units

Therefore Margin of Safety last year= Last year’s Actual Sales- Last year’s Break-Even point

Therefore Margin of Safety last year(units)=27000 units-20250 units=6750 units

Margin of Safety last year(Dollars)=6750 units*$ 22 per unit=$148500

3. Adam to earn a net income of $ 51030 has to sell 32400 hats(Note)

Note:

Net Income=$ 51030

Therefore Income before taxes=$ 51030/0.7=$ 72900

Therefore Required Contribution=$ 72900+$ 121500=$ 194400

Therefore units to be sold=$ 194400/$ 6=32400 units

4. New Break-Even Point=24300 units(Note)

New Contribution per unit=$ 22-$17=$ 5 per unit

Fixed Cost=$ 121500

Number of units at Break-Even Point= Fixed Cost/ Contribution per unit

=$121500/$ 5 per unit=24300 units

5. New Expected Net Income=$22680 (Note)

Note:

New Contribution=$ 23-$ 17=$ 6 per unit

New Sales Volume=27000 units*0.95=25650 units

New Contribution=25650 units* $ 6 per unit=$ 153900

Therefore Net Income before taxes=$ 153900-$ 121500=$ 32400

Therefore Net Income after taxes=$ 32400*0.7=$ 22680