Question

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.

Answer 1

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:

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

PV 1,250,000

time 5

rate 0.05

$1250000 \div \frac{(1+0.05)^{5} -1}{0.05} = C$

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:

$3000000 \div \frac{1-(1+0.05)^{-10} }{0.05} = C$

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