The Profit Margin Puzzle
A small business sells handmade candles. The cost to produce each candle is $4.50, and fixed monthly costs are $2,400. The selling price is $12 per candle. Currently, the business sells 400 candles per month. The owner is considering two changes: (1) increase the selling price by 10%, which is expected to reduce sales volume by 15%, or (2) reduce the selling price by 10%, which is expected to increase sales volume by 20%. The owner wants to know which option yields the higher monthly profit.
1. Calculate the current monthly profit. Then calculate the monthly profit under each proposed change. Which option yields the highest profit?
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Current: Revenue = 400 * $12 = $4,800. Variable cost = 400 * $4.50 = $1,800. Fixed cost = $2,400. Profit = $4,800 - $1,800 - $2,400 = $600.
Option 1: New price = $12 * 1.10 = $13.20. New volume = 400 * 0.85 = 340. Revenue = 340 * $13.20 = $4,488. Variable cost = 340 * $4.50 = $1,530. Profit = $4,488 - $1,530 - $2,400 = $558.
Option 2: New price = $12 * 0.90 = $10.80. New volume = 400 * 1.20 = 480. Revenue = 480 * $10.80 = $5,184. Variable cost = 480 * $4.50 = $2,160. Profit = $5,184 - $2,160 - $2,400 = $624.
Option 2 yields the highest profit: $624, compared to $600 currently and $558 under option 1.
2. Determine the break-even sales volume (in candles) for the current price and for each proposed price. How does the expected sales volume under each option compare to the break-even volume?
Read the worked answer
Break-even volume = Fixed costs / (Price - Variable cost per unit).
Current price: $2,400 / ($12 - $4.50) = $2,400 / $7.50 = 320 candles. Current volume 400 > 320, so profit.
Option 1 price: $2,400 / ($13.20 - $4.50) = $2,400 / $8.70 ≈ 275.86, so 276 candles. Expected volume 340 > 276, so profit.
Option 2 price: $2,400 / ($10.80 - $4.50) = $2,400 / $6.30 ≈ 380.95, so 381 candles. Expected volume 480 > 381, so profit.
All options exceed break-even, but option 2 has the largest margin above break-even (480 - 381 = 99 candles) and yields the highest profit.