Question

Options are under consideration to meet a 12-period need are shown below. Options have different lives so an adjustment for equivalence is required to perform a valid analysis using engineering economic methods. The interest rate for use is 8.0%.

Options	A	B	C	D
Purchase Cost	65,000	41,000	29,000	19,000
First Year Operating Cost	4,800	6,400	7,500	8,100
Operating Cost Increase Per Period	500	700	900	1,400
Life/Salvage	6/4,000	4/2,000	3/1,500	2/800

a. What is the PW of Option A?    

b. What is the PW of Option B?

c. What is the PW of Option C?

d.What is the PW of Option D?

Answer 1

ANSWER:

A) PW of option a:

i = 8% and n = 12 years

pw = purchase cost + first year operating cost(p/a,i,n) + operating cost per period(p/g,i,n) + salvage value(p/f,i,n) + purchase cost in year 6(p/f,i,n) + salvage value in year 12(p/f,i,n)

pw = -65,000 - 4,800(p/a,8%,12) - 500(p/g,8%,12) + 4,000(p/f,8%,6) - 65,000(p/f,8%,6) + 4,000(p/f,8%,12)

pw = -65,000 - 4,800 * 7.536 - 500 * 34.634 + 4,000 * 0.6302 - 65,000 * 0.6302 + 4,000 * 0.3971

pw = -65,000 - 36,172.8 - 17,317 + 2,520.8 - 40,963 + 1,588.4

pw = -157,864

B) Pw of option b:

i = 8% and n = 4 years

pw = purchase cost + first year operating cost(p/a,i,n) + operating cost per period(p/g,i,n) + salvage value(p/f,i,n) + purchase cost in year 4(p/f,i,n) + salvage value in year 8(p/f,i,n) + purchase cost in year 8(p/f,i,n) + salvage value in year 12(p/f,i,n)

pw = -41,000 - 6,400(p/a,8%,12) - 700(p/g,8%,12) + 2,000(p/f,8%,4) - 41,000(p/f,8%,4) + 2,000(p/f,8%,8) - 41,000(p/f,8%,8) + 2,000(p/f,8%,12)

pw = -41,000 - 6,400 * 7.536 - 700 * 34.634 + 2,000 * 0.735 - 41,000 * 0.735 + 2,000 * 0.5403 - 41,000 * 0.5403 + 2,000 * 0.3971

pw = -41,000 - 48,230.4 - 24,243.8 + 1,470 - 30,135 + 1,080.6 - 22,152.3 + 794.2

pw = -163,887

C) Pw of option c:

i = 8% and n = 3 years

pw = purchase cost + first year operating cost(p/a,i,n) + operating cost per period(p/g,i,n) + salvage value(p/f,i,n) + purchase cost in year 3(p/f,i,n) + salvage value in year 6(p/f,i,n) + purchase cost in year 6(p/f,i,n) + salvage value in year 9(p/f,i,n) + purchase cost in year 9(p/f,i,n) + salvage value in year 12(p/f,i,n)

pw = -29,000 - 7,500(p/a,8%,12) - 900(p/g,8%,12) + 1,500(p/f,8%,3) - 29,000(p/f,8%,3) + 1,500(p/f,8%,6) - 29,000(p/f,8%,6) + 1,500(p/f,8%,9) - 29,000(p/f,8%,9) + 1,500(p/f,8%,12)

pw = -29,000 - 7,500 * 7.536 - 900 * 34.634 + 1,500 * 0.7938 - 29,000 * 0.7938 + 1,500 * 0.6302 - 29,000 * .6302 + 1,500 * 0.5002 - 29,000 * 0.5002 + 1,500 * 0.3971

pw = -29,000 - 56,520 - 31,170.6 + 1,190.7 - 23,020.2 + 945.3 - 18,275.8 + 750.3 - 14,505.8 + 595.65

pw = -170,201

D) Pw of option d:

i = 8% and n = 2 years

pw = purchase cost + first year operating cost(p/a,i,n) + operating cost per period(p/g,i,n) + salvage value(p/f,i,n) + purchase cost in year 2(p/f,i,n) + salvage value in year 4(p/f,i,n) + purchase cost in year 4(p/f,i,n) + salvage value in year 6(p/f,i,n) + purchase cost in year 6(p/f,i,n) + salvage value in year 8(p/f,i,n) + purchase cost in year 8(p/f,i,n) + salvage value in year 10(p/f,i,n) + purchase cost in year 10(p/f,i,n) + salvage value in year 12(p/f,i,n)

pw = -19,000 - 8,100(p/a,8%,12) - 1,400(p/g,8%,12) + 800(p/f,8%,2) - 19,000(p/f,8%,2) + 800(p/f,8%,4) - 19,000(p/f,8%,4) + 800(p/f,8%,6) - 19,000(p/f,8%,6) + 800(p/f,8%,8) - 19,000(p/f,8%,8) + 800(p/f,8%,10) - 19,000(p/f,8%,10) + 800(p/f,8%,12)

pw = -19,000 - 8,100 * 7.536 - 1,400 * 34.634 + 800 * 0.8573 -19,000 * 0.8573 + 800 * 0.735 - 19,000 * 0.735 + 800 * 0.6302 - 19,000 * 0.6302 + 800 * 0.5403 - 19,000 * 0.5403 + 800 * 0.4632 - 19,000 * 0.4632 + 800 * 0.3971

pw = -19,000 - 61,041.6 - 48,487.6 + 685.84 - 16,288.7 + 588 - 13,965 + 504.16 - 11,973.8 + 432.24 - 10,265.7 + 370.56 - 8,880.8 + 317.68

pw = - 187,611