Question

Globe 10:22 PM KNotes 12 April 2019 at 10:21 PM Determine the capitalize cost at 16% interest of a structure with a first cost of 2,000,000 and an annual operating and maintenance cost of 400,000 (This is a question from Capitalized cost topic under the engineering economy subject, so please include a cashflow diagram and answer it properly and neatly with capitalized cost formulas)

Answer 1

capitalized cost is the present worth of an alternative that will last forever.

working in 1000s

we have

fixed initial cost = 2000

annual maintenance cost = 400

and, we need to discount the cash flows at 16% interest rate,

so,

the present value of the costs

400 1.16 1.62 1.1631.164 2000400

(note: we will now use the formula for the sum of an infinite GP series:

for instance :
a ar + ar + ar+
$= \frac{a}{1-r}$

and in our question , forms the GP series

400 400 400 400 1.16 1.62 1.1631.164

with
400 1.16
and
1.16

so we will solve this series and add 2000 to it to calculate the capitalized cost)

400 2000 + LIT

= 4500

so, the value of the capitalized cost = $ 4,500,000