The Oven Decision at 900 Cakes a Month
A bakery in Cumilla sells a standard cake at BDT 320. Hand production costs BDT 200 per cake in materials and labour, with fixed costs of BDT 60,000 per month. A semi-automatic oven would cost BDT 480,000, cut variable cost to BDT 140 per cake, and raise fixed costs to BDT 180,000 per month, including depreciation and the interest on a bank loan. Monthly demand over the past 24 months averaged 900 cakes with a standard deviation of 150 cakes, and demand is approximately normal. Maximum capacity with the oven would be 2,400 cakes. The owner has no cash reserve and would have to borrow the full BDT 480,000.
1. Compute the break-even quantity for each option and the indifference quantity. Which option is better at expected demand, and by how much?
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Contribution per cake: hand = 320 − 200 = BDT 120; oven = 320 − 140 = BDT 180.
Break-even: hand 60,000 ÷ 120 = 500 cakes; oven 180,000 ÷ 180 = 1,000 cakes.
Indifference: 60,000 + 200Q = 180,000 + 140Q → 60Q = 120,000 → Q = 2,000 cakes. Below 2,000 the hand method leaves more profit; above 2,000 the oven wins.
At the expected 900 cakes:
- hand: 900 × 120 − 60,000 = BDT 48,000 profit;
- oven: 900 × 180 − 180,000 = −BDT 18,000 loss.
So the oven is BDT 66,000 a month worse, not better, despite the lower unit cost. Buying it would turn a BDT 48,000 profit into a loss at the same sales volume, while adding BDT 480,000 of debt.
2. Use the mean and standard deviation to assess the risk, and state your recommendation to an owner with no cash reserve.
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For the oven to break even at 1,000 cakes: z = (1,000 − 900) ÷ 150 = 0.67, giving P(demand ≥ 1,000) ≈ 0.25. There is roughly a one-in-four chance the oven even covers its costs in a month, and a 75% chance it adds a loss. For 2,000 cakes, z = (2,000 − 900) ÷ 150 = 7.3, so effectively no chance.
With no cash reserve, a 75% probability of a monthly loss plus a loan instalment is not a risk worth taking: one bad quarter exhausts the buffer while the instalment stays due.
Recommendation: do not buy now. Revisit only when volume is contractually committed. Caveat: the normal model assumes stable demand. If the 24 months show a rising trend or heavy seasonality, the standard deviation misstates risk, so check the trend before quoting the 25% figure.
3. What evidence or change would justify buying the oven? Support your answer with a calculation rather than a general statement.
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Three things, in order of strength:
- A signed contract. A confirmed order above 2,000 cakes a month removes the demand risk the whole calculation rests on.
- A cheaper fixed-cost base. For the oven to merely match the hand method at 900 cakes: 900 × 180 − F = 48,000, so F = BDT 114,000. Fixed cost must fall from 180,000 to about 114,000 - a used or smaller oven, or shared premises. That is a checkable target, not a hope.
- A higher contribution margin. A price rise, or a cheaper supply of materials, widens the gap between BDT 180 and BDT 120 contribution and pulls the indifference point down towards current volume.
'More orders later' justifies nothing: at 900 cakes the oven loses BDT 18,000 a month, and the loan instalment falls due whether or not the orders arrive.