Break-even and loss probability for a new Mandalay bakery outlet
A Mandalay bakery is evaluating a new outlet near a busy market. Annual fixed costs are estimated at 18,000,000 MMK for rent, salaries and insurance. Each loaf sells for 2,000 MMK and the variable cost is 1,200 MMK. Market research suggests annual demand will be normally distributed with a mean of 25,000 loaves and a standard deviation of 4,000 loaves. The outlet needs one year's notice to exit the lease, so the owner wants a risk assessment before signing. The bank will lend the fit-out cost only if the probability of making a loss is below 20%. The owner also wants to know the margin of safety and whether a shorter lease, which would cut fixed costs by 2,000,000 MMK but increase later rent, changes the risk picture.
1. Calculate the break-even volume, expected annual profit, and margin of safety in loaves and as a percentage of expected demand.
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Contribution per loaf = selling price - variable cost = 2,000 - 1,200 = 800 MMK. Break-even volume = fixed costs / contribution per loaf = 18,000,000 / 800 = 22,500 loaves. Expected profit = (expected demand x contribution) - fixed costs = (25,000 x 800) - 18,000,000 = 20,000,000 - 18,000,000 = 2,000,000 MMK. Margin of safety in loaves = expected demand - break-even volume = 25,000 - 22,500 = 2,500 loaves. Margin of safety percentage = 2,500 / 25,000 = 10%. This is a thin buffer: demand only needs to be 10% below the mean for the outlet to make a loss. The calculation assumes the selling price and variable cost are constant and that demand is the only uncertain variable.
2. Estimate the probability that the outlet makes a loss in the first year and advise whether the bank's 20% criterion is met. Show the standard normal calculation.
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A loss occurs when demand is below the break-even volume of 22,500 loaves. Let D be annual demand, with mean 25,000 and standard deviation 4,000. z = (22,500 - 25,000) / 4,000 = -2,500 / 4,000 = -0.625. Using the standard normal distribution, P(Z < -0.625) is approximately 0.2660, or 26.6%. So the estimated probability of a loss is about 26.6%. This is above the bank's 20% threshold, so on the stated criterion the outlet does not qualify. The conclusion depends on the normal distribution assumption and on the reliability of the demand estimate. If the owner believes demand is skewed or if the standard deviation is understated, the true loss probability could be higher. The bank may also require a sensitivity test at, say, 20,000 loaves, which would be a loss of (20,000 x 800) - 18,000,000 = -2,000,000 MMK.
3. The owner can reduce fixed costs by 2,000,000 MMK by signing a shorter lease. Recalculate the loss probability and discuss whether the decision should be based only on this statistic.
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New fixed costs = 18,000,000 - 2,000,000 = 16,000,000 MMK. New break-even volume = 16,000,000 / 800 = 20,000 loaves. z = (20,000 - 25,000) / 4,000 = -1.25. P(Z < -1.25) is approximately 0.1056, or 10.6%. This meets the bank's 20% criterion. However, the decision should not rest only on the loss probability. The shorter lease may reduce fixed costs now but expose the owner to higher rent later, renewal risk or relocation costs. A lower break-even point improves downside protection, but the expected profit also changes: expected profit becomes (25,000 x 800) - 16,000,000 = 4,000,000 MMK. The owner should compare the present value of the rent savings with the future rent increase, consider the reliability of the demand estimate, and ask whether the bank's 20% rule is the only relevant risk measure. A sensitivity analysis using a lower mean demand, for example 22,000 loaves, would show how fragile the conclusion is.