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Ivan
3 years ago
7

A city government is considering two types of​ town-dump sanitary systems. Design A requires an initial outlay of ​$405 comma 00

0 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.
Business
1 answer:
SIZIF [17.4K]3 years ago
5 0

Answer:

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

Explanation:

<em><u>Desing A </u></em>

F0 405,000

operating and maintenance cost 51,000 for 14 years

Present value of the operating and maintenance cost:

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C = $ 51,000.00

time = 14 years

rate = 0.07

51000 \times \frac{1-(1+0.07)^{-14} }{0.07} = PV\\

PV $446,018.8673

net worth: $ 851,081.87

equivalent annual cost:

PV \div \frac{1-(1+r)^{-time} }{rate} = C\\

PV 851,082

time 14

rate 0.07

851081.87 \div \frac{1-(1+0.07)^{-14} }{0.07} = C\\

C  $ 97,316.904

<u><em>Desing B</em></u>

F0 251,000

operating and maintenance cost 89,000 for 14 years

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C 89,000.00

time 14

rate 0.07

89000 \times \frac{1-(1+0.07)^{-14} }{0.07} = PV\\

PV $778,346.6507

net worth: $ 1,029,346.65

equivalent annual cost:

1029346.65 \div \frac{1-(1+0.07)^{-14} }{0.07} = C\\

C  $ 117,700.580

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