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Swanson Brothers, Inc. is putting together a bid for a multi-year state project.

ID: 2428237 • Letter: S

Question

Swanson Brothers, Inc. is putting together a bid for a multi-year state project. The project will have a lifespan of 12 years. If successful, the state will pay Swanson $137387 at the end of each year, increasing the payment by $31278 each subsequent year. The project will have expenses of $35186 per year. Part way through the project, Swanson will need to rent some special equipment at a cost of $3355 per year, with the cost decreasing by 10% each subsequent year. Swanson will make the first payment on the special equipment at the end of year 6 and will need the equipment through the end of year 12.

If Swanson remains on schedule, the company will receive a bonus of $98286 at the end of year 7. (Swanson plans on remaining on schedule.) Calculate the present worth of the project using an interest rate of 2% compounded yearly.

Notes: The first payment and the first year of expenses will occur at the end of year 1.

Explanation / Answer

ANSWER:

N = 12 years

annual benefit = $137,387

gradient increase per year = $31,278

expenses per year = $35,186

renting cost of equipment in year 6 = $3,355

renting cost of equipment in year 7 = renting cost of equipment in year 6 - 10% * renting cost of equipment in year 6 = 3,355 - 10% * 3,355 = 3,355 - 335.5 = $3,019.5

renting cost of equipment in year 8 = renting cost of equipment in year 7 - 10% * renting cost of equipment in year 7 = 3,019.5 - 10% * 3,019.5 = 3,019.5 - 301.95 = $2,717.55

renting cost of equipment in year 9 =  renting cost of equipment in year 8 - 10% * renting cost of equipment in year 8 = 2,717.55 - 10% * 2,717.55 = 2,717.55 - 271.75 = $2,445.79

renting cost of equipment in year 10 =  renting cost of equipment in year 9 - 10% * renting cost of equipment in year 9 = 2,445.79 - 10% * 2,445.79 = 2,445.79 - 244.57 = $2,201.21

renting cost of equipment in year 11 =  renting cost of equipment in year 10 - 10% * renting cost of equipment in year 10 = 2,201.21 - 10% * 2,201.21 = 2,201.21 - 220.12 = $1,981.08

renting cost of equipment in year 12 =  renting cost of equipment in year 12 - 10% * renting cost of equipment in year 12 = 1,981.08 - 10% * 1,981.08 = 1,981.08 - 198.1 = $1,782.97

bonus recieved at year 7 = $98,286

i = 2% and n = 12 years

pw = annual benefit(p/a,i,n) + gradient increase(p/g,i,n) + expenses(p/a,i,n) + renting cost of equipment in 6th year(p/f,i,6) + renting cost of equipment in 6th year(p/f,i,6) + renting cost of equipment in 6th year(p/f,i,6) + renting cost of equipment in 6th year(p/f,i,6) + renting cost of equipment in 6th year(p/f,i,6) + renting cost of equipment in 6th year(p/f,i,6) + renting cost of equipment in 6th year(p/f,i,6) + bonus at year 7(p/f,i,7)

pw = 137,387(p/a,2%,12) + 31,278(p/g,2%,12) -35,186(p/a,2%,12) - 3,355(p/f,2%,6) - 3,019.5(p/f,2%,7) - 2,717.55(p/f,2%,8) - 2,445.79(p/f,2%,9) - 2,201.21(p/f,2%,10) - 1,981.08(p/f,2%,11) - 1,782.97(p/f,2%,12) + 98,286(p/f,2%,7)

pw = 137,387 * 10.575 + 31,278 * 55.671 - 35,186 * 10.575 - 3,355 * 0.888 - 3,019.5 * 0.8706 - 2,717.55 * 0.8535 - 2,445.79 * 0.8368 - 2,201.21 * 0.8203 - 1,981.08 * 0.8043 - 1,782.97 * 0.7885 + 98,286 * 0.8706

pw = $1,457,097.525 + $1,741,277.538 - $372,091.95 - $2,979.24 - $2,628.77 - $2,319.42 - $2,046.63 - $1,805.65 - $1,593.38 - $1,405.87 + $85,567.79

pw = $2,897,071.94