Question

1. A new bridge with a 100-year life is expected to have an initial cost of Birr 20 million. This bridge must be resurfaced every five years, at a cost of Birr 1 million. The annual inspection and operating costs are estimated to be Birr 50 000. Determine the present-worth cost of the bridge using the capitalized equivalent approach (i.e., take the life of the bridge as infinite). The interest rate is 10% per year, compounded annually.

Answer 1

The present worth of non-recurring cost	20M
The recurring of $1 M cost equivalent

=

A_i=(1000,000)(A/F),10%,5)

A_i=$1000,000 X 0.163797748=$163,797 per year

There are two annual cost

A₁=$163,797, A₂=$50,000

Capitalized equivalent=($163,797+$50,000 )/0.10=$2,137,970

                                                 

Present Worth Cost=$20,000,000 +2,137,970=$22137,970