Question

Fifteen families live in Willow Canyon. Although several water wells have been drilled, none hasproduced water. The residents take turns driving a water truck to a fill station in a nearby town. The water is hauled to a storage tank in Willow Canyon. Last year truck and water expenses totaled $6200. What rate of return would the Willow Canyon residents receive on a new water supply pipeline costing $100,000 that would replace the truck? The pipeline is considered to lastA)ForeverB)100 yearsC)50 yearsD)Would you recommend the pipeline be installed? Explain. Consider non-economic terms, too.

Answer 1

Initial Investment, P = $100, 000

Recurring Cost, A=$6200

(a) Calculate the internal rate of return for infinite life,

A= P(i)

6200=100000(i)

i = 6200/100000

i =6.2%

(b) Calculate the internal rate of return for 100 years,

P = A(P/A, i, 100)

100000 = 6200 (P/A, i, 100)

(P/A, i, 100) = 16.129

For i = 6%

(P/A,6%,100) = 16.618

For i = 7%

(P/A ,7%,100) = 14.269

i = [(6 - 7) / (16.618 - 14.269)] (16.129 - 16.618) +6

i = 6.2%

Thus, IRR = 6.2%

(c) Calculate the internal rate of return for 50 years,

P = A(P/A ,i , 50)

100000 = 6200 (P/A, i, 50)

(P/A, i, 50) = 16.129

For i = 6%

(P/A, 6%, 100) = 15.762

For i = 5%

(P/A , 5%, 100) = 18.256

i = [(5 - 6) / (18.256 - 15.762)] (16.129-15.762) + 6

i = 5.853%

Thus, IRR = 5.853%

(d)

In all cases internal rate of return is greater than 4%, which is minimum interest rate that one can earn. So they should consider to install the pipeline.