Question

We Care Transportation provides local transportation for individuals with special needs in the Western New York area. They are considering purchasing 10 wheel-chair accessible vans that can seat up to 4 passengers each. Each van will cost $63,450 each to purchase. Adapting these vans for wheelchair use will cost 12% of the total purchase price. We Care will hire 10 additional drivers (one per van) at a rate of $15 per hour. They anticipate each driver/van working 8 hours per day for 260 days each year for each of the next 10 years. Additionally, they anticipate spending $4,000 per van each year to keep their fleet in good working condition. We Care will use these new vans for the next 10 years, after which time they will see the donate the vans to local charitable organizations. They anticipate generating $46,000 per van for each of the next 10 years. They estimate the monetary value of this donation to be 15% of the total original cost. Should We Care proceed with this project? Use an annual equivalent worth analysis approach to answer this question and assume that We Care's MARR = 7%

Answer 1

ANSWER:

Purchase price of 1 van = $63,450

purchase price of 10 vans = 10 * $63,450 = $634,500

price of adapting to wheel chair = 12% of purchase price = 12% * $634,500 = $76,140

total initial cost in purchasing = price of adapting to wheel chair + purchase price of 10 vans = $634,500 + $76,140 = $710,640

driver hiring rate = $15 , working hours = 8 , no of days driver will work = 260 , no of drivers = 10

total money paid to drivers per year = driver hiring rate * working hours *  no of days driver will work *  no of drivers

total money paid to drivers per year = $15 * 8 * 260 * 10 = $312,000

additional spending per year per van = $4,000

no of vans = 10

total additional spending per year = $4,000 * 10 = $40,000

revenue genearted per van = $46,000 , no of vans = 10 , no of years =10

total revenue generated = revenue genearted per van * no of vans = $46,000 * 10 = $460,000

donation cost = 15% Of total original cost = 15% * $710,640 = $106,596

i = 7% , n = 10 years

present worth of these investment = total original cost + total money paid to driver each year(p/a,i,n) + additional spending on van per year(p/a,i,n) + revenue generated per year(p/a,i,n) + donation cost(p/f,i,n)

pw = -710,640 - 312,000(p/a,7%,10) - 40,000(p/a,7%,10)+ 460,000(p/a,7%,10) + 106,596(p/f,7%,10)

pw = -710,640 - 312,000 * 7.024 -40,000 * 7.024 + 460,000 * 7.024 + 106,596 * 0.5083

pw = -710,640 - 2,191,488 - 280,960 + 3,231,040 + $54,182.75

pw = $102,134.7

annual worth = r * pw / ( 1 - ( 1+ r) ^ - n)

r = 7% , pw = $102,134.7 , n = 10

annual worth = 7% * 102,134.7 / ( 1 - (1 + 7%) ^ - 10)

anual worth = $26,816.63 / ( 1 - (1.07) ^ -10 )

annual worth = $7,149.432 / ( 1 - 0.5083)

annual worth = $7,149.432 / 0.4916 = $14,541.69

so the annual equivalent worth is $14,541.69