Question

Suppose the City purchases five sidewalk plows worth $20,000 each to be used over 10 years. Determine the annual payments the City is responsible for if the interest rate is constant at 3%. Suppose the benefits of having cleared sidewalks in the neighbourhood these snowplows will be used are estimated at $20,000 each winter, and the annual operating costs are $500 per plow, should the City make this investment? Show your work.

Answer 1

Determine the annual payments the City is responsible for if the interest rate is constant at 3%.

We can calculate the annual payment amount with the help of the mathematical formula:

Annual payment Amount = [P x R x (1+R)^N]/[(1+R)^N-1]
where:
P = $20000, R = 3% or 0.03, and N = 10 years

Based upon the above, the annual payment comes out to be $ 2344.61

And following chart also provide the detail of annual payments and their bifurcation across 10 years:

Year	Annual Payment	Interest cost	Cost of plows recovered	Unrecoverd cost of plows
1	2344.61	600.00	1744.61	18255.39
2	2344.61	547.66	1796.95	16458.44
3	2344.61	493.75	1850.86	14607.58
4	2344.61	438.23	1906.38	12701.20
5	2344.61	381.04	1963.57	10737.63
6	2344.61	322.13	2022.48	8715.15
7	2344.61	261.45	2083.16	6631.99
8	2344.61	198.96	2145.65	4486.34
9	2344.61	134.59	2210.02	2276.32
10	2344.61	68.29	2276.32	0.00

2nd Part of the question:

Annual Cash outflow = Annual payment + Operating cost
Annual Cash outflow = $2344.61 + $500 = $2844.61 (figure A)

Annual benefits expected = $20000 (figure B)

Decision: Figure B > Figure A; hence of course, city should make this investment.