Credit sales and a zero-profit month
A fictional service business completes 100 identical jobs in one month. Each job is sold for 30 currency units. Variable cash cost is 18 per job and fixed cash operating costs are 1,200 for the month. Every listed cost is paid during the month, and there are no inventories, taxes, depreciation, financing flows or other transactions in this exercise. Only 60 customers pay immediately; the remaining 40 receive invoices and will pay next month. Opening cash is 1,500. The owner sees that the service price exceeds its variable cost and assumes the business must have both positive profit and rising cash. A colleague proposes a new price of 32 while keeping the same fixed and unit-variable-cost model. The exercise asks for a clear distinction between the sales result, the cash balance and the number of jobs needed to cover costs; it is not a forecast that all demand stays unchanged.
1. Calculate this month’s revenue, profit, receivables and closing cash under the stated model.
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Revenue is 100×30=3,000. Variable cost is 100×18=1,800 and total cost is 3,000, so profit is zero. Cash collected is 60×30=1,800; cash paid is 3,000. Closing cash is 1,500+1,800−3,000=300. The unpaid 40 jobs create receivables of 1,200. Zero accrual profit therefore coexists with a 1,200 cash outflow.
2. Find break-even jobs at price 30 and at price 32, keeping the supplied cost model and whole jobs.
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At 30 the unit contribution is 12, so 1,200/12=100 jobs break even. At 32 the contribution is 14, so 1,200/14≈85.71; at least 86 whole jobs are needed. This is a conditional cost calculation, not proof that customers will buy 86 or 100 jobs at the changed price.