Question
In: Economics
Swanson Brothers, Inc. is putting together a bid for a multi-year state project. The project will...
Swanson Brothers, Inc. is putting together a bid for a multi-year state project. The project will have a lifespan of 10 years. If successful, the state will pay Swanson $124084 at the end of each year, increasing the payment by $34676 each subsequent year. The project will have expenses of $40173 per year. Part way through the project, Swanson will need to rent some special equipment at a cost of $3488 per year, with the cost decreasing by 12% each subsequent year. Swanson will make the first payment on the special equipment at the end of year 4 and will need the equipment through the end of year 10.
If Swanson remains on schedule, the company will receive a bonus of $85023 at the end of year 6. (Swanson plans on remaining on schedule.) Calculate the present worth of the project using an interest rate of 1% compounded yearly.
Notes: The first payment and the first year of expenses will occur at the end of year 1.
Be sure to count the years carefully when calculating the years for the cost of renting the special equipment.
Enter your answer as: 1234
Round your answer. Do not use a dollar sign ("$"), any commas (",") or a decimal point (".").
Solutions
Expert Solution
i=1%=0.01
t =10 yrs
For calculating present we need to multiply respective net cash flow of each year by factor (P/F,i%,t)
1st payment = 124084
2nd payment = 124084 + 34676 = 158760
3rd payment = 158760 + 34676 = 193436...similarly calculate all values for 10 yrs
1st rent = 3488 in 4th yr
5th yr rent = 3488*(1-0.12)=3069.44
6th year rent = 3069.44*(1-0.12)= 2701.107
similarly calculate rent uptill 10th year
Bonus at end of 6th yr= 85023
Calculating net cash flow in each year then multipling the value by their respective factors we get present worth in excel
Adding all values we get final answer.
Using excel
| Years | Interest | Cash Flow (Future Value) | P/F factor | Present worth | ||||
| Payment | Operation Cost | Rent Paid | Bonus | Net cash flow | ||||
| 1 | 1.00% | 1,24,084.00 | -40,173.00 | 83,911.00 | 0.99009901 | 83,080.20 | ||
| 2 | 1.00% | 1,58,760.00 | -40,173.00 | 1,18,587.00 | 0.980296049 | 1,16,250.37 | ||
| 3 | 1.00% | 1,93,436.00 | -40,173.00 | 1,53,263.00 | 0.970590148 | 1,48,755.56 | ||
| 4 | 1.00% | 2,28,112.00 | -40,173.00 | -3,488.00 | 1,84,451.00 | 0.960980344 | 1,77,253.79 | |
| 5 | 1.00% | 2,62,788.00 | -40,173.00 | -3,069.44 | 2,19,545.56 | 0.951465688 | 2,08,890.07 | |
| 6 | 1.00% | 2,97,464.00 | -40,173.00 | -2,701.11 | 85,023.00 | 3,39,612.89 | 0.942045235 | 3,19,930.71 |
| 7 | 1.00% | 3,32,140.00 | -40,173.00 | -2,376.97 | 2,89,590.03 | 0.932718055 | 2,70,105.85 | |
| 8 | 1.00% | 3,66,816.00 | -40,173.00 | -2,091.74 | 3,24,551.26 | 0.923483222 | 2,99,717.65 | |
| 9 | 1.00% | 4,01,492.00 | -40,173.00 | -1,840.73 | 3,59,478.27 | 0.914339824 | 3,28,685.30 | |
| 10 | 1.00% | 4,36,168.00 | -40,173.00 | -1,619.84 | 3,94,375.16 | 0.905286955 | 3,57,022.69 | |
| 23,09,692.16 | ||||||||
showing formula in EXCEL
| Years | Interest | Cash Flow (Future Value) | P/F factor | Present worth | ||||
| Payment | Operation Cost | Rent Paid | Bonus | Net cash flow | ||||
| 1 | 0.01 | 124084 | -40173 | =C3+D3+E3+F3 | =(1+0.01)^-A3 | =H3*G3 | ||
| 2 | 0.01 | =C3+34676 | -40173 | =C4+D4+E4+F4 | =(1+0.01)^-A4 | =H4*G4 | ||
| 3 | 0.01 | =C4+34676 | -40173 | =C5+D5+E5+F5 | =(1+0.01)^-A5 | =H5*G5 | ||
| 4 | 0.01 | =C5+34676 | -40173 | -3488 | =C6+D6+E6+F6 | =(1+0.01)^-A6 | =H6*G6 | |
| 5 | 0.01 | =C6+34676 | -40173 | =E6*(1-0.12) | =C7+D7+E7+F7 | =(1+0.01)^-A7 | =H7*G7 | |
| 6 | 0.01 | =C7+34676 | -40173 | =E7*(1-0.12) | 85023 | =C8+D8+E8+F8 | =(1+0.01)^-A8 | =H8*G8 |
| 7 | 0.01 | =C8+34676 | -40173 | =E8*(1-0.12) | =C9+D9+E9+F9 | =(1+0.01)^-A9 | =H9*G9 | |
| 8 | 0.01 | =C9+34676 | -40173 | =E9*(1-0.12) | =C10+D10+E10+F10 | =(1+0.01)^-A10 | =H10*G10 | |
| 9 | 0.01 | =C10+34676 | -40173 | =E10*(1-0.12) | =C11+D11+E11+F11 | =(1+0.01)^-A11 | =H11*G11 | |
| 10 | 0.01 | =C11+34676 | -40173 | =E11*(1-0.12) | =C12+D12+E12+F12 | =(1+0.01)^-A12 | =H12*G12 | |
| =SUM(I3:I12) | ||||||||
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