Capstone: Leila’s map-shop decisions

This capstone combines the earlier tools rather than introducing a slogan about business success. A positive cash receipt may use time that has a better alternative. A lower transaction charge may accompany a larger monthly bill. A price increase may improve contribution per order while reducing total orders. Treat these as different decisions with different relevant costs. The teaching walkthroughs use other fictional businesses and different numbers, so you can learn the method before independently calculating Leila’s case. Her exercise responses are submitted for checking; the teaching slides do not disclose their solutions.

The editing opportunity supplies a specific, feasible comparison for time spent on maps. Do not replace it with an imagined wage from work she cannot obtain. Equally, do not assume time is free because Leila does not pay herself a wage. The earlier design work can be used with either service and cannot now be recovered. The laptop is retained for editing whichever option she chooses. These facts explain why some accounting entries will not change this decision. A different resale opportunity, personal preference or future benefit would require revisiting the assumptions rather than silently inserting it into the calculation.

Write the per-order fee as a fixed amount plus a percentage of that order’s price. The word fixed here describes the flat part of a transaction charge; it still varies with the number of orders in a month. Keep it distinct from the monthly charge, which does not vary with orders within the stated range. A bundle is one payment even though it contains three files, so its fixed transaction fee, delivery expense and service time occur once. The monthly charge and maintenance time are avoidable if Leila does not operate next month.

Build two columns before comparing services: recurring monthly consequences and one-off switching consequences. A lower flat transaction charge is only one term. The percentage charge applies to the whole order price, so its importance depends on product mix and prices. The larger monthly fee must also be covered. Switching time displaces available editing just as operating time does, and it uses some of the first month’s capacity. Because reliability and demand are stipulated to be identical, do not invent a customer benefit for one provider. Later, question that assumption explicitly as part of sensitivity analysis.

Keep intermediate calculations to at least four decimal places, and follow each exercise’s requested final precision. A weighted average is useful when the product mix is a planning assumption. If actual counts are known, calculate from those counts instead. An expected 75:25 mix need not be realised exactly in a particular month. Do not call the defined cash surplus a complete accounting profit statement, because the model intentionally excludes many real-world items. Our purpose is to compare stated alternatives consistently, not to imply that running an actual business requires no tax, legal or operational investigation.

First apply the order weights to prices: £2.40 plus £3.60 equals £6. Because the percentage fee is linear and each order has one flat charge, its weighted average is ten pence plus two per cent of six pounds, or twenty-two pence. Convert two minutes to hours by dividing by sixty, then multiply by twenty-four pounds to obtain eighty pence. Finally subtract the fee, delivery and time cost: six minus 0.22 minus 0.18 minus 0.80 equals 4.80. Monthly costs remain separate. An unweighted price average would incorrectly assume equal numbers of the two order types.

Check the time calculation carefully. Fifty orders at two minutes each require one hundred minutes, or five-thirds of an hour. Add one and a half maintenance hours to obtain nineteen-sixths of an hour. At twenty-four pounds per hour, that is seventy-six pounds. Subtracting £76 from the £215 cash surplus gives £139, matching the contribution method. This reconciliation is a powerful error check: the two routes organise the same consequences differently. If they disagree, look for omitted maintenance, inconsistent time units, an incorrect mix or an opportunity cost counted twice.

The complete-allocation method includes the earnings actually received under each plan. Noor’s remaining work hours earn one hundred and sixty-four pounds, while the template business produces two hundred and fifteen pounds after its stated cash outlays. Together they give three hundred and seventy-nine pounds. Compare that with two hundred and forty from using all ten hours for the alternative. The difference is one hundred and thirty-nine. Do not subtract the seventy-six-pound time opportunity cost again from this difference: the forgone earnings have already been reflected in the reduced hours available for the alternative.

Derive the expression instead of memorising a threshold. Revenue is p. Subtract the two-per-cent fee to retain 0.98p. The remaining per-order costs are ten pence of flat fee, eighteen pence of delivery and eighty pence of time, totalling £1.08. At £1.10, the expression is slightly negative; £1.11 makes it positive. This marginal price does not cover the monthly £101 fixed economic costs if charged across the business without enough contribution. Accepting one additional order after commitments are unavoidable and deciding whether to operate for a month are different comparisons.

Calculate the new contribution by subtracting £0.244 fees, £0.18 delivery and £0.80 time from £7.20. To preserve the old result, new total contribution must still cover £101 fixed economic costs and leave £139, so it must equal £240. Divide 240 by 5.976 to find the required expected volume. Then subtract that volume from fifty and divide by fifty to measure the allowed proportional decline. The result says how much loss of demand the model can tolerate. It does not estimate how buyers actually respond to the higher prices or identify a profit-maximising price.

Work from weighted contribution rather than assuming that a ten-per-cent price rise creates a ten-per-cent improvement in surplus. Percentage fees change with prices, while other per-order costs remain fixed under the assumptions. The fixed monthly economic costs remain the same. Compute each scenario separately and compare it with the starting case. Then solve for the exact expected order count needed to match that starting result. Fractional expected counts are allowed for this boundary. A recommendation must distinguish this conditional arithmetic from evidence about which demand scenario is likely.

First calculate each provider’s entire transaction charge at the same order price. For X, thirty pence plus twenty pence gives fifty pence. For Y, ten pence plus thirty pence gives forty pence. Subtract to obtain ten pence saved per order. Multiplying by monthly volume gives total variable savings, from which the eight-pound extra monthly cost must be deducted. At eighty orders, those effects exactly offset. This recurring comparison deliberately excludes a one-off switch, which belongs in a separate calculation. It also assumes no difference in demand, quality or service time.

Value switching time using Rowan’s stated alternative: one and a half hours times twenty pounds is thirty pounds. Add the twenty-pound payment to get fifty pounds. At 180 orders, ten pence per order saves eighteen pounds before the extra eight-pound monthly charge, leaving ten pounds per month. Multiply that recurring advantage by the horizon and subtract the switch once. Do not subtract it every month or omit it entirely. A longer horizon can make a switch attractive, but only if the recurring assumptions hold and the transition fits available capacity. Discounting would be needed if the chosen comparison required it.

Do not mix the higher-price scenario with the service-switching scenario unless explicitly asked to build a new combined case. For this comparison, both services use the original prices, original mix and identical demand. The first-month threshold must include the cash and time cost of switching, while later months should not repeat that one-off cost. The separate 240-order scenario is a planning assumption, not evidence that demand has increased. Your recommendation should state what must remain true over the horizon and whether a small conditional advantage is robust to plausible changes in workload or sales.

The capacity method starts by subtracting all relevant fixed time from available time. For Noor, ten minus one and a half leaves eight and a half hours. Multiplying by sixty gives 510 minutes; dividing by two gives 255 orders. With the additional setup hour, remaining minutes fall to 450, giving 225 orders. Apply the same method independently to Leila’s own figures. A profitable-looking algebraic threshold outside capacity is not an available choice. Meeting it would require a new assumption about labour, service time or available hours, and that change may alter the cost comparison.

A strong brief says what should be done under which conditions and what evidence would change that view. Useful tests might measure service minutes by product, track the realised bundle share or compare customer exposure across periods. Avoid a vague instruction to collect more data without specifying the decision it would inform. If the editing work disappears, identify the new feasible alternative rather than mechanically retaining the old wage or declaring time worthless. Your conclusion should show how assumptions connect to numbers and numbers connect to a decision, while acknowledging questions of rights and wider consequences that the private-return model does not settle.