Kareem's Kandle Kitchen: Break-Even, a New Fixed Cost and a Hotel Deal
Kareem's Kandle Kitchen makes scented candles. His fixed monthly costs (rent, insurance, equipment) total $450. Each candle costs $6.50 in wax, wick, jar and scent, and sells for $11.00.
From next month Kareem must pay a farmers' market stall fee of $120 per month. It is a fixed cost; the selling price and the unit cost are unchanged.
Separately, a hotel has offered to buy candles, but only at a unit price of $10.50. Kareem has worked out that this bulk order would let him buy jars in larger quantities, saving $0.50 per candle on packaging. Everything else stays the same.
Kareem wants the business to break even within the first two months at the market, and to make a monthly profit of at least $900 after that. Working alone, he can produce at most 400 candles a month by hand. He is inclined to accept the hotel deal because 'a lower price is always worse', but he has not yet done the arithmetic.
1. Write expressions for monthly cost and revenue before the stall fee, find the break-even number of candles, and calculate the profit at 250 candles.
Read the worked answer
Let n = number of candles made and sold in a month.
Cost: C = 450 + 6.50n (fixed cost plus variable cost) Revenue: R = 11.00n
Break-even: R = C 11n = 450 + 6.50n 11n − 6.50n = 450 4.50n = 450 n = 100 candles
The $4.50 is the contribution per candle: each sale contributes $4.50 towards the $450 of fixed costs, so 450 ÷ 4.50 = 100 candles are needed to cover them. Below 100 he makes a loss; above 100 each candle adds $4.50 of profit.
Profit at 250 candles Revenue = 250 × 11 = $2,750 Cost = 450 + 250 × 6.50 = 450 + 1,625 = $2,075 Profit = 2,750 − 2,075 = $675
Check: (250 − 100) × 4.50 = 675. The two methods agree.
2. Including the $120 stall fee, find the new break-even number of candles and the number needed to make $900 profit. Is Kareem's target achievable within his 400-candle capacity?
Read the worked answer
Fixed costs become 450 + 120 = $570. Contribution per candle is unchanged at $4.50.
New break-even 570 ÷ 4.50 = 126.67 → he must round up: 127 candles At 126 candles profit = 4.50 × 126 − 570 = 567 − 570 = −$3, so 126 is a small loss. Rounding up matters here.
Candles for $900 profit Profit = 4.50n − 570 = 900 4.50n = 1,470 n = 326.67 → 327 candles
At 327 candles: revenue = 3,597, cost = 570 + 2,125.50 = 2,695.50, profit = $901.50. ✓
Capacity check 327 of 400 = 81.75% of his maximum output.
The target is achievable, but only just. He has 73 candles of headroom, and any month with illness, a wax shortage or a rainy market day where sales fall below 327 breaks the target. The first two months are also fine - 127 is well inside 400 - so the break-even requirement is comfortable; the $900 profit requirement is the tight constraint, not capacity.
3. Evaluate the hotel offer using contribution, and advise Kareem whether to accept it.
Read the worked answer
Contribution under the hotel deal New unit cost = 6.50 − 0.50 = $6.00 New price = $10.50 Contribution per candle = 10.50 − 6.00 = $4.50 - exactly the same as before.
What this means Break-even and target volumes do not change: still 127 candles to break even and 327 to make $900, because profit = 4.50n − 570 whatever the mix. At full capacity of 400 candles, profit is 4.50 × 400 − 570 = $1,230 under either arrangement.
What does change is revenue and risk:
- Revenue at 400 candles falls from 400 × 11.00 = $4,400 to 400 × 10.50 = $4,200.
- The hotel order is a guaranteed volume, while market sales are uncertain. A guaranteed 400 units at $4.50 contribution beats a market that might only sell 200 units ($330 profit).
Advice Kareem's instinct that 'a lower price is always worse' is wrong: what matters is the contribution per candle, and here it is unchanged because the cost saving exactly offsets the price cut. Accept the hotel deal only if it commits to a volume above 327 candles; if the hotel wants fewer, the guaranteed order may still be worth it for stability, but he should keep market sales running alongside it. If the hotel wanted $10.00 with the same $6.00 cost, contribution would fall to $4.00 and break-even would rise to 570 ÷ 4.00 = 143 candles - that would be a deal to refuse.