Question

A city government is planning to install a sewage line at a cost $10M with an estimated life of 50 years and an estimated salvage value of $2M. Assume that the line may be replaced at the same cost every 50 in perpetuity. Determine the capitalized cost if the interest rate is 9%Choose the most appropriate answer from the choices below.
A. $8.2M
B. $10.1M
C. $12M
D. None of these

Answer 1

Answer:

B. $10.1M

Explanation:

The capitalized cost of this investment is the present value of the cost that has just been incurred as well as the present of the replacement asset every 50 years.

The present value of cost incurred is the same as the amount incurred since it is stated in today's terms i.e $10M

The present value of replacement asset=replacement cost/50 year effective interest rate

In 50 years' time, the old sewage line would be sold for $2M and another bought of $10M, effectively replacement is $8M($10M-$2M)

the effective interest rate for 50 years=(1+9%)^50-1=7335.75%

capitalized cost of the sewage line=$10+$8/7335.75%

capitalized cost of the sewage line=$10.1M