Problem 5.70 Please show complete solution procedure, and include cash flow diag
ID: 1765974 • Letter: P
Question
Problem 5.70
Please show complete solution procedure, and include cash flow diagrams for each machine.
The following costs are associated with three tomato-peeling machines being considered for use in a canning plant. If the canning company uses an interest rate of 12%, which is the best alternative? Use NPW to make your decision. (Note: Consider the least common multiple as the study period.)
Machine A B C
First cost $52,000 $63,000 $67,000
O&M costs $15,000 $9,000 $12,000
Annual benefit $38,000 $31,000 $37,000
Salvage value $13,000 $19,000 $22,000
Useful life (yrs) 4 6 12
Explanation / Answer
The least common multiple life is 12 years, so this will be used as the analysis period.
Machine A
NPW4 = -$52,000 + ($38,000 - $15,000)(P/A, 12%, 4) + $13,000(P/F, 12%, 4)
= -$52,000 + $69,851 + $8,262
= $26,113
NPW12= NPW4 [1 + (P/F, 12%, 4) + (P/F, 12%, 8)]
= $26,113 [1 + (1.12)-4 + (1.12)-8]
= $53,255
Machine B
NPW6 = -$63,000 + ($31,000 - $9,000)(P/A, 12%, 6) + $19,000(P/F, 12%, 6)
= -$63,000 + $90,442 + $9,625
= $37,067
NPW12 = NPW6 [1 + (P/F, 12%, 6)]
= $37,067 [1 + (1.12)-6]
= $55,846
Machine C
NPW12 =-$67,000+($37,000 - $12,000)(P/A, 12%, 12)+$22,000(P/F, 12%, 12)
= -$67,000 + $154,850 + $5,647
= $93,497
Machine C is the correct choice