Question

INCREMENTAL COST ANALYSIS

A county’s recycling program collected 46,280 tons of recyclable refuse this year. The cost of the program includes five vehicles that can partly process the recyclables. The county does not have the depreciation information for these trucks; but they estimate annual maintenance costs of up to $10,000 for each truck. The fuel expense totaled $69,000 this year. The county also hires fifty workers in the program. The annual personnel expense this year was $1.5 million. Other expenses this year included office expenses of $15,000, overhead of $189,000, and miscellaneous expenses of $150,000. Recently, a small nearby city asked the county to provide recycling services. The city offered a fixed fee of $6.00 for every ton of recyclable material pickup. It is estimated that there will be 3,500 tons of pickup during the next year from the city. County analysts studied the proposal. They reckoned that, to add 3,500 tons of pickup, the county did not need new vehicles or new hiring. Office and miscellaneous expenses would also remain the same, but the fuel consumption and the overhead would increase. Treating fuel and overhead as variable costs and others as fixed costs, calculate the incremental cost and the marginal cost for the county. Should the county accept the city’s offer? Discuss in detail the logic of your decision. Explain explicitly any assumption you make.

Answer 1

Here the relevant expenses are fuel consumption and the overhead which will increase.

Now fuel consumption costs per ton = 69,000/46,280 tons = $1.4909 per ton

Overhead costs per ton = 189,000/46,280 tons = $4.0838 per ton

Thus total relevant cost here = (1.4909+4.0838)*3,500 tons

= $19,511.67.

Revenue from 3,500 tons = 3500*$6 per ton

= $21,000

Thus incremental cost = $19,511.67 for 3500 tons and marginal cost = 19,511.67/3500 = $5.5748 per ton

As incremental revenue of $21,000 is greater than incremental costs of $19,511.67 the county should accept the offer.

The assumption that I have made is that depreciation is nil for the vehicles and hence it has not been accounted for.