Question
In: Economics
The city of Waterbourne has made it a strategic goal to enhance livability in the city....
The city of Waterbourne has made it a strategic goal to enhance livability in the city. The city has decided to undertake a project that will occur in two phases. During the first phase, the city will connect several of the parks with walking paths. During the second phase, the city will add water features or splash fountains to several of the parks.
The initial cost of the project will be $340042. Annual utilities for maintaining the walking paths and keeping them lit during the early evening are estimated to be $11380, with costs increasing by $282 each subsequent year. The paths will require repaving in year 9 at a cost of $43703 and again in year 17 at a cost of $66835.
The water features and splash fountains will be added to the parks at the end of year 9 at a cost of $316585. The water utilities are estimated to be $17520 per year, increasing by 14% each subsequent year. (The first payment for the water utilities will occur at the end of year 9.)
The city has secured a sponsorship from a local business to help pay for part of the project. The city will receive a grant from the business of $118993 per year, increasing by 7% each subsequent year. The city will receive the grant for 7 years. (The city will receive the first grant payment at the end of year 1.)
Using a nominal annual interest rate of 7% compounded annually and a lifespan of 30 years, what is the present worth of the entire project?
Solutions
Expert Solution
i=7% =0.07, t= 30yrs
Investment in year 0 = 340042
Investment in year 9 = repaving + water features = 43703+316585 = 360288
Investment in year 17 = repaving = 66835
utilities for path = 11380 increasing by 282 each year from year 1 to year 30
water utilities = 17520 increasing 14% every year from year 9
Sponsorship starting year 1 = 118993 increasing at 7% uptill 7 yrs
Finding net cash flow for each year
Using formula PV = FV / (1+i)^n for finding present value of any future value
using excel
| Years | Interest | Cash Flow (Future Value) | P/F factor | Present worth | ||||
| Investment | utilities for path | Water utilities | Sponsorship | Net cash flow | ||||
| 0 | -340042.00 | -3,40,042.00 | 1 | -3,40,042.00 | ||||
| 1 | 7.00% | -11,380.00 | 1,18,993.00 | 1,07,613.00 | 0.934579439 | 1,00,572.90 | ||
| 2 | 7.00% | -11,662.00 | 1,27,322.51 | 1,15,660.51 | 0.873438728 | 1,01,022.37 | ||
| 3 | 7.00% | -11,944.00 | 1,36,235.09 | 1,24,291.09 | 0.816297877 | 1,01,458.55 | ||
| 4 | 7.00% | -12,226.00 | 1,45,771.54 | 1,33,545.54 | 0.762895212 | 1,01,881.25 | ||
| 5 | 7.00% | -12,508.00 | 1,55,975.55 | 1,43,467.55 | 0.712986179 | 1,02,290.38 | ||
| 6 | 7.00% | -12,790.00 | 1,66,893.84 | 1,54,103.84 | 0.666342224 | 1,02,685.89 | ||
| 7 | 7.00% | -13,072.00 | 1,78,576.41 | 1,65,504.41 | 0.622749742 | 1,03,067.83 | ||
| 8 | 7.00% | -13,354.00 | -13,354.00 | 0.582009105 | -7,772.15 | |||
| 9 | 7.00% | -360288.00 | -13,636.00 | -17,520.00 | -3,91,444.00 | 0.543933743 | -2,12,919.60 | |
| 10 | 7.00% | -13,918.00 | -19,972.80 | -33,890.80 | 0.508349292 | -17,228.36 | ||
| 11 | 7.00% | -14,200.00 | -22,768.99 | -36,968.99 | 0.475092796 | -17,563.70 | ||
| 12 | 7.00% | -14,482.00 | -25,956.65 | -40,438.65 | 0.444011959 | -17,955.24 | ||
| 13 | 7.00% | -14,764.00 | -29,590.58 | -44,354.58 | 0.414964448 | -18,405.57 | ||
| 14 | 7.00% | -15,046.00 | -33,733.26 | -48,779.26 | 0.387817241 | -18,917.44 | ||
| 15 | 7.00% | -15,328.00 | -38,455.92 | -53,783.92 | 0.36244602 | -19,493.77 | ||
| 16 | 7.00% | -15,610.00 | -43,839.75 | -59,449.75 | 0.338734598 | -20,137.69 | ||
| 17 | 7.00% | -66835.00 | -15,892.00 | -49,977.31 | -1,32,704.31 | 0.31657439 | -42,010.79 | |
| 18 | 7.00% | -16,174.00 | -56,974.14 | -73,148.14 | 0.295863916 | -21,641.89 | ||
| 19 | 7.00% | -16,456.00 | -64,950.52 | -81,406.52 | 0.276508333 | -22,509.58 | ||
| 20 | 7.00% | -16,738.00 | -74,043.59 | -90,781.59 | 0.258419003 | -23,459.69 | ||
| 21 | 7.00% | -17,020.00 | -84,409.69 | -1,01,429.69 | 0.241513087 | -24,496.60 | ||
| 22 | 7.00% | -17,302.00 | -96,227.05 | -1,13,529.05 | 0.225713165 | -25,625.00 | ||
| 23 | 7.00% | -17,584.00 | -1,09,698.84 | -1,27,282.84 | 0.210946883 | -26,849.92 | ||
| 24 | 7.00% | -17,866.00 | -1,25,056.67 | -1,42,922.67 | 0.19714662 | -28,176.72 | ||
| 25 | 7.00% | -18,148.00 | -1,42,564.61 | -1,60,712.61 | 0.184249178 | -29,611.17 | ||
| 26 | 7.00% | -18,430.00 | -1,62,523.65 | -1,80,953.65 | 0.172195493 | -31,159.40 | ||
| 27 | 7.00% | -18,712.00 | -1,85,276.96 | -2,03,988.96 | 0.160930367 | -32,828.02 | ||
| 28 | 7.00% | -18,994.00 | -2,11,215.74 | -2,30,209.74 | 0.150402212 | -34,624.05 | ||
| 29 | 7.00% | -19,276.00 | -2,40,785.94 | -2,60,061.94 | 0.140562815 | -36,555.04 | ||
| 30 | 7.00% | -19,558.00 | -2,74,495.97 | -2,94,053.97 | 0.131367117 | -38,629.02 | ||
| -3,95,633.25 | ||||||||
total present worth of project is -395633.25
showing formula in excel
| Years | Interest | Cash Flow (Future Value) | P/F factor | Present worth | ||||
| Investment | utilities for path | Water utilities | Sponsorship | Net cash flow | ||||
| 0 | -340042 | =C3+D3+E3+F3 | =(1+B3)^-A3 | =H3*G3 | ||||
| 1 | 0.07 | -11380 | 118993 | =C4+D4+E4+F4 | =(1+B4)^-A4 | =H4*G4 | ||
| 2 | 0.07 | =D4-282 | =F4*1.07 | =C5+D5+E5+F5 | =(1+B5)^-A5 | =H5*G5 | ||
| 3 | 0.07 | =D5-282 | =F5*1.07 | =C6+D6+E6+F6 | =(1+B6)^-A6 | =H6*G6 | ||
| 4 | 0.07 | =D6-282 | =F6*1.07 | =C7+D7+E7+F7 | =(1+B7)^-A7 | =H7*G7 | ||
| 5 | 0.07 | =D7-282 | =F7*1.07 | =C8+D8+E8+F8 | =(1+B8)^-A8 | =H8*G8 | ||
| 6 | 0.07 | =D8-282 | =F8*1.07 | =C9+D9+E9+F9 | =(1+B9)^-A9 | =H9*G9 | ||
| 7 | 0.07 | =D9-282 | =F9*1.07 | =C10+D10+E10+F10 | =(1+B10)^-A10 | =H10*G10 | ||
| 8 | 0.07 | =D10-282 | =C11+D11+E11+F11 | =(1+B11)^-A11 | =H11*G11 | |||
| 9 | 0.07 | =-43703-316585 | =D11-282 | -17520 | =C12+D12+E12+F12 | =(1+B12)^-A12 | =H12*G12 | |
| 10 | 0.07 | =D12-282 | =E12*(1+0.14) | =C13+D13+E13+F13 | =(1+B13)^-A13 | =H13*G13 | ||
| 11 | 0.07 | =D13-282 | =E13*(1+0.14) | =C14+D14+E14+F14 | =(1+B14)^-A14 | =H14*G14 | ||
| 12 | 0.07 | =D14-282 | =E14*(1+0.14) | =C15+D15+E15+F15 | =(1+B15)^-A15 | =H15*G15 | ||
| 13 | 0.07 | =D15-282 | =E15*(1+0.14) | =C16+D16+E16+F16 | =(1+B16)^-A16 | =H16*G16 | ||
| 14 | 0.07 | =D16-282 | =E16*(1+0.14) | =C17+D17+E17+F17 | =(1+B17)^-A17 | =H17*G17 | ||
| 15 | 0.07 | =D17-282 | =E17*(1+0.14) | =C18+D18+E18+F18 | =(1+B18)^-A18 | =H18*G18 | ||
| 16 | 0.07 | =D18-282 | =E18*(1+0.14) | =C19+D19+E19+F19 | =(1+B19)^-A19 | =H19*G19 | ||
| 17 | 0.07 | -66835 | =D19-282 | =E19*(1+0.14) | =C20+D20+E20+F20 | =(1+B20)^-A20 | =H20*G20 | |
| 18 | 0.07 | =D20-282 | =E20*(1+0.14) | =C21+D21+E21+F21 | =(1+B21)^-A21 | =H21*G21 | ||
| 19 | 0.07 | =D21-282 | =E21*(1+0.14) | =C22+D22+E22+F22 | =(1+B22)^-A22 | =H22*G22 | ||
| 20 | 0.07 | =D22-282 | =E22*(1+0.14) | =C23+D23+E23+F23 | =(1+B23)^-A23 | =H23*G23 | ||
| 21 | 0.07 | =D23-282 | =E23*(1+0.14) | =C24+D24+E24+F24 | =(1+B24)^-A24 | =H24*G24 | ||
| 22 | 0.07 | =D24-282 | =E24*(1+0.14) | =C25+D25+E25+F25 | =(1+B25)^-A25 | =H25*G25 | ||
| 23 | 0.07 | =D25-282 | =E25*(1+0.14) | =C26+D26+E26+F26 | =(1+B26)^-A26 | =H26*G26 | ||
| 24 | 0.07 | =D26-282 | =E26*(1+0.14) | =C27+D27+E27+F27 | =(1+B27)^-A27 | =H27*G27 | ||
| 25 | 0.07 | =D27-282 | =E27*(1+0.14) | =C28+D28+E28+F28 | =(1+B28)^-A28 | =H28*G28 | ||
| 26 | 0.07 | =D28-282 | =E28*(1+0.14) | =C29+D29+E29+F29 | =(1+B29)^-A29 | =H29*G29 | ||
| 27 | 0.07 | =D29-282 | =E29*(1+0.14) | =C30+D30+E30+F30 | =(1+B30)^-A30 | =H30*G30 | ||
| 28 | 0.07 | =D30-282 | =E30*(1+0.14) | =C31+D31+E31+F31 | =(1+B31)^-A31 | =H31*G31 | ||
| 29 | 0.07 | =D31-282 | =E31*(1+0.14) | =C32+D32+E32+F32 | =(1+B32)^-A32 | =H32*G32 | ||
| 30 | 0.07 | =D32-282 | =E32*(1+0.14) | =C33+D33+E33+F33 | =(1+B33)^-A33 | =H33*G33 | ||
| =SUM(I3:I33) | ||||||||
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