A regional municipality is studying a water supply plan for the area to the end

Question

A regional municipality is studying a water supply plan for the area to the end of the year 2050. To satisfy the water demand, one suggestion is to construct a pipeline from a distant lake. It is now the end of 2010. Construction would start in the year 2015 (five years from now) and take five years to complete at a cost of $20 million per year. Annual maintenance and repair costs are expected to be $2 million and will start the year follow- ing project completion (all costs are based on current estimates). From a predicted infla- tion rate of 3 percent per year, and the real MARR, city engineers have determined that a MARR of 7 percent per year is appropriate. Assume that all cash flows take place at the end of the year and that there is no salvage value at the end of 205:5. (a) Find the present worth of the project. (b) Construct a sensitivity graph showing the effects of 5 percent and 10 percent increases and decreases in the construction costs, maintenance costs, and inflation rate. To which is the present worth most sensitive?

Explanation / Answer

Present Value(PV) of cash flow=((Cash flow)/(1+i)^N) i=discount rate=MARR=7%=0.07(Nominal Rate) N=Year of cash flow Year wise cash flow and PV of cash flows are given below Inflation Rate=3%=1.03 Inflation Adjusted cash flow=(Cash flow)*(1+0.03)^N N=Year of cash flow N A B=A*(1.03^N) C=B/(1.07^N) Year Cash flow without inflation adjustment(million $) Inflation Adjusted Cash flow($ million) Present Value(PV) of Cash flow 2010 0 $0 $0 $0 2011 1 $0 $0 $0 2012 2 $0 $0 $0 2013 3 $0 $0 $0 2014 4 $0 $0 $0 2015 5 $20 23.18548149 16.53092786 2016 6 $20 23.88104593 15.91294925 2017 7 $20 24.59747731 15.31807264 2018 8 $20 25.33540163 14.74543442 2019 9 $20 26.09546368 14.19420322 2020 10 $2 2.687832759 1.36635788 2021 11 $2 2.768467741 1.315279081 2022 12 $2 2.851521774 1.26610977 2023 13 $2 2.937067427 1.218778563 2024 14 $2 3.02517945 1.173216748 2025 15 $2 3.115934833 1.129358178 2026 16 $2 3.209412878 1.08713918 2027 17 $2 3.305695265 1.046498463 2028 18 $2 3.404866122 1.007377026 2029 19 $2 3.507012106 0.969718071 2030 20 $2 3.612222469 0.933466928 2031 21 $2 3.720589143 0.898570969 2032 22 $2 3.832206818 0.86497953 2033 23 $2 3.947173022 0.832643847 2034 24 $2 4.065588213 0.801516974 2035 25 $2 4.187555859 0.771553723 2036 26 $2 4.313182535 0.742710593 2037 27 $2 4.442578011 0.714945711 2038 28 $2 4.575855351 0.688218769 2039 29 $2 4.713131012 0.662490964 2040 30 $2 4.854524942 0.637724947 2041 31 $2 5.000160691 0.613884762 2042 32 $2 5.150165511 0.590935799 2043 33 $2 5.304670477 0.568844741 2044 34 $2 5.463810591 0.547579517 2045 35 $2 5.627724909 0.527109255 2046 36 $2 5.796556656 0.507404236 2047 37 $2 5.970453356 0.488435853 2048 38 $2 6.149566956 0.470176569 2049 39 $2 6.334053965 0.452599875 2050 40 $2 6.524075584 0.435680253 2051 41 $2 6.719797852 0.419393141 2052 42 $2 6.921391787 0.403714893 2053 43 $2 7.129033541 0.388622747 2054 44 $2 7.342904547 0.374094794 2055 45 $2 7.563191683 0.360109942 SUM $103.978830 Present Worth of the project=(Sum of PV)= $103.978830 million Present Worth of the project $103,978,829.69

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