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23 May, 02:51

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.

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  1. 23 May, 05:07
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    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.
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