Question

A city government is considering two types of​ town-dump sanitary systems. Design A requires an initial outlay of ​$405 comma 000 with annual operating and maintenance costs of ​$51 comma 000 for the next 14 ​years; design B calls for an investment of ​$251 comma 000 with annual operating and maintenance costs of ​$89 comma 000 per year for the next 14 years. Fee collections from the residents would again be ​$95 comma 000 per year. The interest rate is 7​%, and no salvage value is associated with either system.

Answer 1

Desing A is a better deal as the equivalent annual cost is lower than desing B

Anywa, bot desing cost are above the city collections thus, it cannot afford the sanitary systems unless it raises taxes

Step-by-step explanation:

Desing A

F0 405,000

operating and maintenance cost 51,000 for 14 years

Present value of the operating and maintenance cost:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C = $ 51,000.00

time = 14 years

rate = 0.07

`51000 * (1-(1+0.07)^(-14) )/(0.07) = PV\\`

PV $446,018.8673

net worth: $ 851,081.87

equivalent annual cost:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 851,082

time 14

rate 0.07

`851081.87 / (1-(1+0.07)^(-14) )/(0.07) = C\\`

C $ 97,316.904

Desing B

F0 251,000

operating and maintenance cost 89,000 for 14 years

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 89,000.00

time 14

rate 0.07

`89000 * (1-(1+0.07)^(-14) )/(0.07) = PV\\`

PV $778,346.6507

net worth: $ 1,029,346.65

equivalent annual cost:

`1029346.65 / (1-(1+0.07)^(-14) )/(0.07) = C\\`

C $ 117,700.580