Question

20. An existing public park serving 1.8 Million visitor/year is to be improved. Initial cost is SR 2.25 Million and the annual operating and maintenance cost starts with SR 0.145 Million during the first year and increases 3%/year thereafter. The planning horizon is 20 years, the salvage value is 32% of the initial cost, and the interest rate is 10%. The minimum additional benefits/visit that will justify the facility improvement is closest to: a) SR 0.17 b) SR 0.24 c) SR 0.15 d) SR 0.3

Answer 1

Here,

Initial Cost	2250000
Annual Cost	145000
Growth in AC	3%
Salvage Value	720000	32% of initial cost
Interest Rate	10%
Year	20 years

Present Value of Cost

03-05-2020	Year 0	2250000.00
03-05-2021	Year 1	145000.00
03-05-2022	Year 2	149350.00
03-05-2023	Year 3	153830.50
03-05-2024	Year 4	158445.42
03-05-2025	Year 5	163198.78
03-05-2026	Year 6	168094.74
03-05-2027	Year 7	173137.58
03-05-2028	Year 8	178331.71
03-05-2029	Year 9	183681.66
03-05-2030	Year 10	189192.11
03-05-2031	Year 11	194867.88
03-05-2032	Year 12	200713.91
03-05-2033	Year 13	206735.33
03-05-2034	Year 14	212937.39
03-05-2035	Year 15	219325.51
03-05-2036	Year 16	225905.28
03-05-2037	Year 17	232682.43
03-05-2038	Year 18	239662.91
03-05-2039	Year 19	246852.79
03-05-2040	Year 20	-465741.62
	Net Present Value	3657756.38

Now

If A is the benefit per visit than,

3657756.38 = 1800000*A* (1/(1.1)+1/((1.1)^(2))......1/((1.1)^(20)))

3657756.38/(1800000*A )= (1.1)^(20)* ((1.1)^(19)........+1)

((1.1)^(19)........+1) =( (1.1)^19 - 1)/(1.1-1) = 51.159

So Solving For A = 0.24