Adding an Evening Welding Section at a Community College
A community college's continuing-education division is considering adding a second evening section of its welding certificate. The section would enroll up to 18 students at $2,800 tuition each. The college would pay a part-time instructor $18,000 for the year, spend $6,000 on consumables, and incur $3,000 in additional utilities. The only suitable lab is currently rented to a local manufacturer for weekend training at $15,000 per year; adding the section would end that rental, and the manufacturer has offered to renew on the same terms. The college has already spent $40,000 on a ventilation upgrade required for either use. Administrators say the program must 'cover its costs.' Enrollment projections are 15 students with probability 0.6 and 12 students with probability 0.4. The existing daytime section is full and uses the same lab on weekdays.
1. Identify the relevant costs and the opportunity cost of adding the section, then compute expected accounting profit and expected economic profit. Show your calculations.
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Relevant explicit costs are the instructor ($18,000), consumables ($6,000), and additional utilities ($3,000), totaling $27,000. The $40,000 ventilation upgrade is sunk and should not enter the decision. The opportunity cost is the $15,000 rental income foregone. Expected revenue is 0.6(15 × $2,800) + 0.4(12 × $2,800) = $25,200 + $13,440 = $38,640. Expected accounting profit is $38,640 − $27,000 = $11,640. Expected economic profit subtracts the opportunity cost: $38,640 − ($27,000 + $15,000) = −$3,360. The section looks profitable on an accounting basis but destroys $3,360 in expected economic value because it uses the lab in a way that is worth more as a rental.
2. Using marginal analysis, should the college add the section? Identify the enrollment threshold at which the section breaks even economically and explain how the probability distribution affects the decision.
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Marginal analysis compares expected incremental benefit with incremental cost, including opportunity cost. Expected revenue is $38,640; incremental cost is $18,000 + $6,000 + $3,000 + $15,000 = $42,000. The expected net economic benefit is −$3,360, so a risk-neutral college should not add the section. The break-even enrollment is $42,000 ÷ $2,800 = 15 students. At 12 students the section loses $8,400; at 15 it breaks even; at 18 it earns $8,400. Because there is a 0.4 probability of only 12 students, the expected value is negative. If the college values workforce development as a separate nonpecuniary benefit worth more than $3,360 in expectation, it could still proceed, but that is not economic profit.
3. Explain how the $40,000 ventilation upgrade and the phrase 'cover its costs' could each lead to a different decision from the one marginal analysis recommends.
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The $40,000 upgrade is a sunk cost: it has already been incurred and does not vary with the decision, so it should be excluded from incremental analysis. If administrators allocate it to the new section and insist that the section 'cover its costs,' they may set a break-even enrollment above the economically relevant 15 students and reject a section that covers all incremental costs. Conversely, the phrase could be read as covering only explicit accounting costs, ignoring the $15,000 foregone rental. That would make the section look profitable by $11,640 and lead to accepting a project that reduces economic value by $3,360. A correct rule should state which costs are included and should treat the rental as an opportunity cost.