Answer and Explanation :
As per the data given in the question,
Present value = Amount ÷ (1 + r)^n
Machine A
Year Amount Discount Factor PV
1 $5,000 1.05 $4,761.90
2 $5,000 $4,535.15
3 $5,000 $4,319.19
Total $13,616.24
Now
Present value of salvage value =$2,000 ÷ 1.05^3 = $1,727.68
Present worth of Machine A is
= -$12,500 - $13,616.24 + $1,727.68
= -$24,388.56
Similarly Present worth of Machine B = -$15,000 - $4,000 ÷ 1.05 -$4,000 ÷ (1.05)^2 - $4,000 ÷ 1.05^3 - $4,000 ÷ 1.05^4 + $1,500 ÷ 1.05^4
=-$24,658.94
Based on the comparison between Machine A and Machine B
Machine A is better because it has higher present worth
Annual worth:
For machine A = -$12,500(A/PA,5%,3) -$5,000+$2,000(A/F,5%,3)
=-$12,500 × 0.367 - $5,000 + $2,000 × 0.317
= -$8,953.5
For Machine B:
= -$15,000(A/P,5%,4) - $4,000 + $1,500(A/F,5%,4)
= -$7,882.16
Based on the comparison between Machine A and Machine B
Machine B is better because it has higher annual worth
Capitalized cost:
Machine A :
= -$12,500+$2,000(P/F,5%,3) - $5,000 ÷ 0.05
= -$12,500 + $2,000 × 0.86 - $5,000 ÷ 0.05
= -$110,772
Machine B :
=-$15,000(P/F,5%,4) - $4000 ÷ 0.05
=-$15,000 × 0.82 - $4,000 ÷ 0.05
= -$93,765.9
Based on the comparison between Machine A and Machine B
Machine B is better because it has lower capitalized cost
