Residents of a town take turns driving a water truck to a fire hydrant in a near

Question

Residents of a town take turns driving a water truck to a fire hydrant in a nearby town. They fill the truck with water and then haul it to a storage tank. Last year truck fuel and maintenance cost $3180. This year the residents are seriously considering spending $100,000 to install a pipeline from the nearby town to their storage tank. What rate of return would the residents receive on thir new water supply pipleline if the pipeline is considered to last

A)forever

B)100 years

C)50 years

D)Should the pipleline be installed? Explain

Explanation / Answer

The main idea of the problem is if they spend $100,000 now, then they would save the recurring uniform yearly cost of water transportation of $3180 for the life of the pipeline. a. If the life of the pipeline is forever or infinity, then we can use the formula A = P(i) or, 3180 = 100,000 (i) or, i = 3180/100, 3.18%(answer) b. If they spend $100,000, they will save $3180 every year for the coming 100 years. Doing NPC=NPB: 100,000 = 3180(P/A, i,100), or (P/A, i,100) = 100,00/3180 = 31.446 Now for i=3%, (P/A, 3%,100) = 31.559 Now for i=2.5%, (P/A, 2.5%,100) = 27.655 So the IRR is in between 2.5-3% c. This part is same as the part b. only n = 50 years, that is Doing NPC=NPB: 100,000 = 3180(P/A, i,50), or (P/A, i,50) = 31.559 Now for i=1.75%, (P/A, 1.75%,50) = 33.141 Now for i=2%, (P/A, 2%,50) = 31.424 So the IRR is in between 1.75-2% d. In all cases the internal rate of return is less than 4%, which is the minimum interest that one can earn in this market. So that way the project is not that much lucrative. This is because they can keep the money in an interest bearing account which will pay more than $3180 yearly. However, it is not a loosing project and it will save lot of their personal labor and inconvenience, which was not included in the cost estimates of the project. So I believe, they should go ahead and construct the pipeline anyway.

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