Two incinerators are being considered by a waste management company. Design A has an initial cost of $2,500,000, has annual operating and maintenance costs of $800,000, and requires overhauls every 5 years at a cost of $1,250,000. Design B is more sophisticated, including computer controls; it has an initial cost of $5,750,000, has annual operating and maintenance costs of $600,000, and requires overhauls every 10 years at a cost of $3,000,000. Using a 5%/year interest rate, determine the capitalized cost for each design and recommend which should be chosen.

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TomShelby TomShelby · Answer 1 · 2019-10-26T19:58:55+02:00

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