Answer:
Machine I
capitalized cost: 230,271.28
EAC: $ 27,047.58
Machine II
EAC: $ 27,377.930
As Machine I cost per year is lower it is better to purchase that one.
Annual deposits to purchase Machine I in 20 years: $ 1,396.770
return of machine I with savings of 28,000 per year: 10.51%
Explanation:
WE calculate the present worth of each machine and then calculate the equivalent annual cost:
MACHINE 1
Operating cost:
C 18,000
time 20
rate 0.1
PV $153,244.1470
Salvage value:
Maturity $20,000.0000
time 20.00
rate 0.1
PV 2,972.87
Total: -80,000 cost - 153,244.15 annual cost + 2,972.87 salvage value:
Total: 230,271.28
Present worth $(230,271.28)
time 20
rate 0.1
C -$ 27,047.578
Fund to purchase in 20 years:
FV $80,000.00
time 20
rate 0.1
C $ 1,396.770
IF produce a 28,000 savings:
we must solve using a financial calcualtor for the rate at which the capitalized cost equals 28,000
PV $230,271.28
time 20
rate 0.105126197
C $ 28,000.000
rate of 0.105126197 = 10.51%
<u>Machine II</u>
100,000 cost
25,000 useful life
15,000 operating cost during 10 years
20,000 for the next 15 years
Present value of the operating cost:
C 15,000
time 10
rate 0.1
PV $92,168.5066
C 20,000
time 15
rate 0.1
PV $152,121.5901
in the timeline this is at the end of the 10th year we must discount as lump sum for the other ten years:
Maturity $152,121.5901
time 10.00
rate 0.1
PV 58,649.46
salvage value
Maturity $25,000.0000
time 25.00
rate 0.1
PV 2,307.40
Total cost: 100,000 + 92,168.51 + 58,649.46 - 2,307.40 = $248,510.57
PV $248,510.57
time 25
rate 0.1
C $ 27,377.930