Two Copier Leases, One Binding Year
The manager of a university photocopy unit must choose between two leased machines before the new academic year. Machine A costs ₹4,200 a month to lease and ₹0.45 per page in toner and maintenance; it can print up to 30,000 pages a month. Machine B costs ₹7,800 a month and ₹0.28 per page, with a ceiling of 55,000 pages. Last year the unit printed 42,000 pages, and the registrar's office expects a 12% rise after a new hostel block opens. The unit charges students ₹1.00 per page and cannot refuse work. A one-year lease is binding, and switching mid-year would cost two months' rent as penalty.
1. At what monthly volume do the two leases cost the same? Interpret the figure for the manager.
Read the worked answer
Set the monthly costs equal, with x = pages printed:
- Machine A: 4,200 + 0.45x
- Machine B: 7,800 + 0.28x
4,200 + 0.45x = 7,800 + 0.28x 0.17x = 3,600 x = 21,176.47, i.e. about 21,176 pages.
Interpretation: below roughly 21,200 pages a month, the low-fixed-cost machine A wins; above it, the per-page saving on B repays its higher rent. The important point is that this crossover (21,176) is below A's capacity ceiling (30,000), so the crossover is actually reachable. If the indifference point had fallen above A's ceiling, the comparison would have been meaningless, because A could never have served those volumes anyway. The number is therefore a genuine decision threshold, not a formality, and the manager should compare it with the realistic monthly range rather than with a single annual average.
2. Using the expected demand, which machine should be leased? Show the cost comparison and name one non-cost factor that could overturn the choice.
Read the worked answer
Expected demand = 42,000 × 1.12 = 47,040 pages.
- Machine A: 4,200 + (0.45 × 47,040) = 4,200 + 21,168 = ₹25,368
- Machine B: 7,800 + (0.28 × 47,040) = 7,800 + 13,171.20 = ₹20,971.20
B is cheaper by ₹4,396.80. More decisively, A is infeasible: 47,040 pages exceed its 30,000-page ceiling, and since the unit cannot refuse work, unmet demand would have to be outsourced at retail rates - a cost the comparison above ignores. With ₹1.00 per page of revenue (₹47,040), B also leaves the healthier margin. Lease B.
Non-cost factors worth weighing: B carries ₹3,600 more fixed cost each month, which hurts if printing is seasonal (vacation months); a single high-volume machine is also a single point of failure, so the manager should check B's service-level agreement and downtime cover. Print quality or finishing attachments could matter more than ₹4,000 for examination material, but neither is likely to reverse a decision driven by a hard capacity ceiling.
3. The registrar warns that demand may instead fall 20% below last year's figure. Does the recommendation change? Explain with numbers, and state the condition under which it would.
Read the worked answer
Revised demand = 42,000 × 0.80 = 33,600 pages.
- A still cannot serve this: 33,600 > 30,000. Even using A to its limit, the unit would pay 4,200 + (0.45 × 30,000) = ₹17,700 for only 30,000 pages, then pay again to outsource 3,600 pages.
- B at 33,600 pages = 7,800 + (0.28 × 33,600) = 7,800 + 9,408 = ₹17,208, and it covers the whole job.
So the recommendation does not change: B is cheaper and the only feasible single machine. The recommendation would flip only if monthly volume fell to about 21,176 pages or fewer - roughly half of last year's 42,000 - a collapse far deeper than the 20% scenario.
One caution: fixed costs are monthly, not annual. If demand is lumpy, the honest method is a twelve-month series, because in low-print vacation months A would indeed be cheaper. The manager should model monthly volumes and consider whether a short-term sub-lease or seasonal outsourcing can cover the gap months rather than locking a full year of high fixed cost.