Bakery pricing: is a price rise worth an 8% drop in sales?
Naledi runs a small bakery in a rented shop in Mogoditshane. Her only fixed monthly costs are P3 600 for rent, water and electricity. Each loaf costs her P4.20 in ingredients and packaging, and she currently bakes and sells 1 800 loaves a month at P7.00 each. Her flour supplier offers two pack sizes: 25 kg bags at P230 each, or 50 kg bags at P420 each. Naledi uses about 900 kg of flour a month. She is considering raising the price of a loaf to P7.50 but expects that this will reduce sales by 8%. Her friend warns her that any price rise will 'chase customers away and lose money', and advises her to keep the price at P7.00.
1. Calculate Naledi's current monthly profit, then her profit if she raises the price to P7.50 and sales fall by 8%. State, with a reason, whether she should raise the price.
Read the worked answer
Current month
- Takings: 1 800 x P7.00 = P12 600
- Ingredients: 1 800 x P4.20 = P7 560
- Fixed costs: P3 600
- Profit = 12 600 - 7 560 - 3 600 = P1 440
With the price rise
- Loaves sold: 1 800 x 0.92 = 1 656
- Takings: 1 656 x P7.50 = P12 420
- Ingredients: 1 656 x P4.20 = P6 955.20
- Profit = 12 420 - 6 955.20 - 3 600 = P1 864.80
Profit rises by P424.80, about 29.5%.
Reason: the money she keeps on each loaf (price minus ingredient cost) rises from P2.80 to P3.30, a rise of 17.9%, while the number of loaves falls by only 8%. Rent is fixed and does not change with the number of loaves, so it cancels out of the comparison. On these estimates she should raise the price.
2. Find the percentage fall in sales at which the two options give exactly the same profit, and use your answer to judge how safe the friend's advice is.
Read the worked answer
Let d be the fraction of sales lost. Equal profit means
1 800(1 - d)(7.50 - 4.20) - 3 600 = 1 440
1 800(1 - d)(3.30) = 5 040
5 940(1 - d) = 5 040
1 - d = 0.8485, so d = 0.1515
Sales would have to fall by about 15.2% before the price rise stopped paying.
Judgement: a fall of 8% is only about half the break-even fall, so the friend's advice ('any rise loses money') is too cautious - the rise is not automatically harmful. Two cautions remain: the margin (about 7 percentage points) is not huge, and the 8% figure is a guess rather than a measurement. Trialling the new price for one month, or asking a sample of regular customers, would make the decision much safer than either rule of thumb.
3. Compare the cost per kilogram of the two flour pack sizes and calculate the monthly saving from the better option. State one assumption behind your answer.
Read the worked answer
- 25 kg bag: 230 / 25 = P9.20 per kg
- 50 kg bag: 420 / 50 = P8.40 per kg
- Saving: P0.80 per kg, about 8.7% cheaper
At 900 kg a month: 900 x 0.80 = P720 a month, or P8 640 a year - half her present monthly profit.
Assumption: the flour in a 50 kg bag is all used before it spoils or is attacked by pests. If a fraction f of the larger bags is wasted, the effective cost per usable kilogram is 8.40 / (1 - f). This only reaches P9.20 when f is about 8.7%, so the large bags remain better value as long as she wastes less than about one kilogram in twelve.