Calculate the cost per ton for a 150 ton per day incinerator that costs $25 mill
ID: 2792915 • Letter: C
Question
Calculate the cost per ton for a 150 ton per day incinerator that costs $25 million if it is assumed: (1) the incinerator operates at capacity; (2) the incinerator has a 25 year lifetime; and (3) the incinerator is financed over its lifetime at an interest rate of 5%.
What would be the cost per ton if the interest rate were 7%?
User charges based on some form of unit pricing (pay-as–you-throw) are now being used by some communities to recover the costs of solid waste collection and disposal services. What are the advantages and disadvantages of this approach?
Explanation / Answer
Case 1: Simple Interest Rate
Principal = $25 million
Interest over 25 years = 25 million * 5% * 25 = 31250000
Total Cost = Principal + Interest = 25000000 + 31250000 = 56250000
Total Ton used over 25 years (assuming 365 days in a year & 6 leap years in 25 years) = ((19 * 365) + (6*366)) * 150 = 1369650
So, Cost per ton = 56250000/1369650 = $41.07 [rounded off to 2 decimals]
If Interest Rate is 7%, then Interest over 25 years = 25 million * 7% * 25 = 43750000
Total Cost = Principal + Interest = 25000000 + 43750000 = 68750000
Total Ton used over 25 years (assuming 365 days in a year & 6 leap years in 25 years) = ((19 * 365) + (6*366)) * 150 = 1369650
So, Cost per ton = 68750000/1369650 = $50.20 [rounded off to 2 decimals]
Case 2: Compound Interest Rate
Principal = $25 million
Total Cost with Interest over 25 years = 25000000 * (1 + 5%)25 = 84658873.52 [rounded off to 2 decimals]
Total Ton used over 25 years (assuming 365 days in a year & 6 leap years in 25 years) = ((19 * 365) + (6*366)) * 150 = 1369650
So, Cost per ton = 84658873.52/1369650 = $61.81 [rounded off to 2 decimals]
If Interest Rate is 7%, then Total Cost with Interest over 25 years = 25000000 * (1 + 7%)25 = 135685816.00 [rounded off to 2 decimals]
Total Ton used over 25 years (assuming 365 days in a year & 6 leap years in 25 years) = ((19 * 365) + (6*366)) * 150 = 1369650
So, Cost per ton = 135685816.00/1369650 = $99.07 [rounded off to 2 decimals]
Advantage of Pay as You Throw:
Since it is based on unit costing, so there is incentive for reducing garbage output. Consumers will not throw Reclyable and reusable garbages as that will incur an extra cost for them.
This in turn will increase the recycling rate.
This is also beneficial for people who generates less garbage, in comparison with flat tax. Every person should pay for the amount of garbage produced by them.
Disadvantage:
It may increase illegal dumping of garbages, as consumers might want to get rid of extra payment as per the unit based costing.
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