Question

(Engineering Economics Question)

Q. A food processor is considering the purchase of new food processing equipment. using the following data, how many tons of fruit must be processed annually to justify the purchase?

First cost: $78,750

Annual income: $25/ton of processed fruit

Annual operating costs: $5500 in first year, increasing by $800/yr thereafter

Annual property taxes: 8% of first cost

Annual insurance: 4% of first cost, payable at the beginning of each year

Useful life: 10 years

Salvage value @ 10 years: 15% of first cost + $1000

MARR: 4%

Answer 1

ANSWER:

For finding the tons of fruit to be processed annually , we will have to equate the present worth to zero.

pw = initial cost + annual income(p/a,i,n) + aoc(p/a,i,n) + gradient(p/g,i,n) + apt(p/a,i,n) + ai + ai(p/a,i,n) +salvage value(p/f,i,n)

since annual insurance that is ai is at the begining of the period the n will be 9 and the initial insurance will be in year 0.

i = 4% , n = 10 years

initial cost = $78,750 , annual income = $25 * x ( ton of processed fruit) , aoc = $5,500 , gradient = $800

annual property taxes = 8% of first cost = 8% * 78,750 = $6,260

annual insurance = 4% of first cost = 4% * 78,750 = $3,130

salvage value = 15% of first cost + 1000 = 15% * 78,750 + 1000 = $11,737.5 + $1,000 = $12,737.5

pw = -78,750 + 25 * x(p/a,4%,10) - 5500(p/a,4%,10) - 800(p/g,4%,10) - 6260(p/a,4%,10) -3130 -3130(p/a,4%,9) + 12,737.5(p/f,4%,10)

0 = -78,750 +  25 * x * 8.111 - 5500 * 8.111 - 800 *33.881 - 6260 * 8.111 -3,130 - 3,130 * 7.435 + 12,737.5 * 0.6756

0 = -78,750 + 202.775 x - 44,610.5 - 27,104.8 - 50,774.86 - 3,130 - 23,271.55 + 8,605.455

0 = -219,036.3 + 202.775 x

202.775 x = 219,036.3

x = 1080.194

so the no of tons of food to be produced annually will be the next whole number which is 1081