The city of Waterbourne has made it a strategic goal to enhance livability in the city. The city has decided to undertak...
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 $381,944. Annual utilities for maintaining the walking paths and keeping them lit during the early evening are estimated to be $13,458, with costs increasing by $214 each subsequent year. The paths will require repaving in year 9 at a cost of $55,214 and again in year 19 at a cost of $74,689.
The water features and splash fountains will be added to the parks at the end of year 9 at a cost of $294,551. The water utilities are estimated to be $18,544 per year, increasing by 13% 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 $137,332 per year, increasing by 2% 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 2% compounded annually and a lifespan of 28 years, what is the present worth of the entire project?
Homework Answers
Using Excel
| Years | Cash Flow | ||||
| Investment | utilities for path | Water utilities | Sponsorship | Net cash flow | |
| 0 | -381944.00 | -3,81,944 | |||
| 1 | -13458 | 137332 | 123874 | ||
| 2 | -13672 | 140079 | 126407 | ||
| 3 | -13886 | 142880 | 128994 | ||
| 4 | -14100 | 145738 | 131638 | ||
| 5 | -14314 | 148653 | 134339 | ||
| 6 | -14528 | 151626 | 137098 | ||
| 7 | -14742 | 154658 | 139916 | ||
| 8 | -14956 | -14956 | |||
| 9 | -349765 | -15170 | -18544 | -383479 | |
| 10 | -15384 | -20955 | -36339 | ||
| 11 | -15598 | -23679 | -39277 | ||
| 12 | -15812 | -26757 | -42569 | ||
| 13 | -16026 | -30236 | -46262 | ||
| 14 | -16240 | -34166 | -50406 | ||
| 15 | -16454 | -38608 | -55062 | ||
| 16 | -16668 | -43627 | -60295 | ||
| 17 | -16882 | -49298 | -66180 | ||
| 18 | -17096 | -55707 | -72803 | ||
| 19 | -74689 | -17310 | -62949 | -154948 | |
| 20 | -17524 | -71132 | -88656 | ||
| 21 | -17738 | -80379 | -98117 | ||
| 22 | -17952 | -90829 | -108781 | ||
| 23 | -18166 | -102636 | -120802 | ||
| 24 | -18380 | -115979 | -134359 | ||
| 25 | -18594 | -131056 | -149650 | ||
| 26 | -18808 | -148094 | -166902 | ||
| 27 | -19022 | -167346 | -186368 | ||
| 28 | -19236 | -189101 | -208337 | ||
| NPW | -10,97,324 | ||||
Showing formula in Excel
| Years | Cash Flow | ||||
| Investment | utilities for path | Water utilities | Sponsorship | Net cash flow | |
| 0 | -381944 | =B3+C3+D3+E3 | |||
| 1 | -13458 | 137332 | =B4+C4+D4+E4 | ||
| 2 | =C4-214 | =E4*1.02 | =B5+C5+D5+E5 | ||
| 3 | =C5-214 | =E5*1.02 | =B6+C6+D6+E6 | ||
| 4 | =C6-214 | =E6*1.02 | =B7+C7+D7+E7 | ||
| 5 | =C7-214 | =E7*1.02 | =B8+C8+D8+E8 | ||
| 6 | =C8-214 | =E8*1.02 | =B9+C9+D9+E9 | ||
| 7 | =C9-214 | =E9*1.02 | =B10+C10+D10+E10 | ||
| 8 | =C10-214 | =B11+C11+D11+E11 | |||
| 9 | =-294551-55214 | =C11-214 | -18544 | =B12+C12+D12+E12 | |
| 10 | =C12-214 | =D12*1.13 | =B13+C13+D13+E13 | ||
| 11 | =C13-214 | =D13*1.13 | =B14+C14+D14+E14 | ||
| 12 | =C14-214 | =D14*1.13 | =B15+C15+D15+E15 | ||
| 13 | =C15-214 | =D15*1.13 | =B16+C16+D16+E16 | ||
| 14 | =C16-214 | =D16*1.13 | =B17+C17+D17+E17 | ||
| 15 | =C17-214 | =D17*1.13 | =B18+C18+D18+E18 | ||
| 16 | =C18-214 | =D18*1.13 | =B19+C19+D19+E19 | ||
| 17 | =C19-214 | =D19*1.13 | =B20+C20+D20+E20 | ||
| 18 | =C20-214 | =D20*1.13 | =B21+C21+D21+E21 | ||
| 19 | -74689 | =C21-214 | =D21*1.13 | =B22+C22+D22+E22 | |
| 20 | =C22-214 | =D22*1.13 | =B23+C23+D23+E23 | ||
| 21 | =C23-214 | =D23*1.13 | =B24+C24+D24+E24 | ||
| 22 | =C24-214 | =D24*1.13 | =B25+C25+D25+E25 | ||
| 23 | =C25-214 | =D25*1.13 | =B26+C26+D26+E26 | ||
| 24 | =C26-214 | =D26*1.13 | =B27+C27+D27+E27 | ||
| 25 | =C27-214 | =D27*1.13 | =B28+C28+D28+E28 | ||
| 26 | =C28-214 | =D28*1.13 | =B29+C29+D29+E29 | ||
| 27 | =C29-214 | =D29*1.13 | =B30+C30+D30+E30 | ||
| 28 | =C30-214 | =D30*1.13 | =B31+C31+D31+E31 | ||
| NPW | =NPV(2%,F4:F31)+F3 | ||||
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