A town with a population of 164,250 persons who live in 39,050 households is considering introducing a recycling program that would require residents to separate paper from their household waste so that it can be sold rather than buried in a landfill like the rest of the town’s waste. Two major benefits are anticipated: revenue from the sale of waste paper and avoided tipping fees (the fee that the town pays the owners of landfills to bury its waste). Aside from the capital costs of specialized collection equipment, household containers, and a sorting facility, the program would involve higher collection costs, inconvenience costs for households, and disposal costs for paper that is collected but not sold. The planning period for the project has been set at eight years, the expected life of the specialized equipment.
The following information has been collected by the town’s sanitation department:
Waste Quantities: Residents currently generate 3.6 pounds of waste per person per day. Over the last 20 years, the daily per capita amount has grown by about 0.02 pounds per year. Small or no increases in the last few years, however, raise the possibility that levels realized in the future will fall short of the trend.
Capital Costs: The program would require an initial capital investment of $1,688,000. Based on current resale values, the scrap value of the capital at the end of eight years is expected to be 20 percent of its initial cost.
Annual Costs: The department estimates that the separate collection of paper will add an average of $6/ton to the cost of collecting household waste. Each ton of paper collected and not sold would cost $4 to return to the landfill.
Savings and Revenues: Under a long-term contract, tipping fees are currently $45 per ton with annual increases equal to the rate of inflation. The current local market price for recycled paper is $22/ton but has fluctuated in recent years between a low of $12 per ton and a high of $32 per ton.
Paper Recovery: The fraction of household waste made up of paper has remained fairly steady in recent years at 32 percent. Based on the experience of similar programs in other towns, it is estimated that between 60 and 80 percent of paper included in the program will be separated from other waste and 80 percent of the paper that is separated will be suitable for sale, with the remaining 20 percent of the collected paper returned to the waste stream for landfilling.
Household Separation Costs: The sanitation department recognized the possibility that the necessity of separating paper from the waste stream and storing it might impose costs on households. An average of 10 minutes per week per household of additional disposal time would probably be needed. A recent survey by the local newspaper, however, found that 80 percent of respondents considered the inconvenience of the program negligible. Therefore, the department decided to assume that household separation costs would be zero.
Discount Rate: The sanitation department has been instructed by the budget office to discount at the town’s real borrowing rate of 6 percent. It has also been instructed to assume that annual net benefits accrue at the end of each of the eight years of the program.
a. Calculate an estimate of the present value of net benefits for the program.
b. How large would annual household separation costs have to be per household to make the present value of net benefits fall to zero?
c. Assuming that household separation costs are zero, conduct a worst-case analysis with respect to the growth in the quantity of waste, the price of scrap paper, and the percentage of paper diverted from the waste stream.
d. Under the worst-case assumptions of part (c), how large would the average yearly household separation costs have to be to make the present value of net benefits fall to zero?
e. Investigate the sensitivity of the present value of net benefits to the price of scrap paper.
f. Implement a Monte Carlo analysis of the present value of net benefits of the program.