Question

2. Two firms propose to dispose of all of the waste currently entering the City of Columbia landfill. Each proposal is to handle the waste stream for 10 years. The current estimate is for about 220,000 tons of trash per year. Both firms’ minimum acceptable rate of return is 5 percent. Firm #1: Wants $3 million dollars up front and will bill the City at $32/ton of waste for the 10-year period. Firm #2: Wants $1.5 million up front and will bill the City at $35/ton for the first five years and $40/ton for the last five years.

Which firm would be a better deal for the City? Support your answer quantitatively

Answer 1

Based on the information shared above: -

Firm #1, will charge $32/ton for 220,000 tons of trash. Thus Firm #1, will charge $32 X 220,000 = $7,040,000 for the next 10 years in addition to $3,000,000 upfront.

Firm #2, will charge:

(i) $35/ton for 220,000 tons of trash for Years 1 to 5. Thus, Firm #2, will charge $35 X 220,000 = $7,700,000 for the Years 1 to 5

(ii) $40/ton for 220,000 tons of trash for Years 6 to 10. Thus Firm #2, will charge $40 X 220,000 = $8,800,000 for the Years 6 to 10

In the table below, are the cash outflows by the City and Present Value of future payments in present value terms: -

Years	Firm #1	Firm #2	PV Factor @ 5%	PV of Future Cash Payments
				Firm #1	Firm #2
1	7,040,000	7,700,000	0.9524	6,704,762	7,333,333
2	7,040,000	7,700,000	0.9070	6,385,488	6,984,127
3	7,040,000	7,700,000	0.8638	6,081,417	6,651,550
4	7,040,000	7,700,000	0.8227	5,791,825	6,334,809
5	7,040,000	7,700,000	0.7835	5,516,024	6,033,151
6	7,040,000	8,800,000	0.7462	5,253,356	6,566,695
7	7,040,000	8,800,000	0.7107	5,003,197	6,253,996
8	7,040,000	8,800,000	0.6768	4,764,949	5,956,186
9	7,040,000	8,800,000	0.6446	4,538,047	5,672,558
10	7,040,000	8,800,000	0.6139	4,321,949	5,402,437
Total Outlay over 10 Years				54,361,014	63,188,843
Initial Payment				3,000,000	1,500,000
Total Payment for the Project				57,361,014	64,688,843

Thus, from the table above,

a) Firm #1 is charging a total of $57,361,014 in Present value terms

b) Firm #2 is charging a total of $64,688,843 in Present value terms

Therefore, for the City Firm #1, is more cost effective.