Answer:
Desing A: 23,024,370
Desing B: 22,520,274.6
It should purchase desing B as the capitalized cost is lower.
Explanation:
We consider annuity for the overhauls and then, perpetuity to consider this incinerators will last indefinitely.
maintenance cost: 800,000 / 0.05 = 16,000,000
Overhaul:
The company will need to fund 1,250,000 every 5 years. We need to determinate the annuity to obtain this future value:
[tex]FV \div \frac{(1+r)^{time} -1}{rate} = C\\[/tex]
PV 1,250,000
time 5
rate 0.05
[tex]1250000 \div \frac{(1+0.05)^{5} -1}{0.05} = C\\[/tex]
C $ $ 226,218.498
Then at perpetuity:
$ 226,218.498 / 0.05 = 4,524,370
Desing A capitalized cost:
2,500,000 + 16,000,000 + 4,524,370 = 23,024,370
We do the same for Desing B:
investment: 5,750,000
maintenance: 600,000 / 0.05 = 12,000,000
overhaul:
[tex]3000000 \div \frac{1-(1+0.05)^{-10} }{0.05} = C\\[/tex]
C $ 238,513.725
238,513.73/0.05 = 4,770,274.6
Capitalized cost: 5,750,000 + 12,000,000 + 4,770,274.6 = 22,520,274.6