Question

What is the present value of costs for a 30-year project that has annual maintenance costs of $1.1 million per year, but also requires additional major maintenance costing $9 million every ten years?

You may assume major maintenance is needed after 10 years and 20 years but not after 30 years (at the end of the project). Assume a discount rate of 8% and that all costs are incurred at the end each year.

Enter your answer in the box below in units of million $.

Answer 1

i = 8%

n = 30 years

PV of costs = P

P = (1.1/(1 + 8%) + 1.1/(1 + 8%)² + .... + 1.1/(1 + 8%)³⁰)

+ (9/(1 + 8%)¹⁰ + 9/(1 + 8%)²⁰ + 9/(1 + 8%)³⁰)

Using compound factor tables for i = 8% and n = 30

P = 11.258 x 1.1 + 6.994

P = $ 19.3778 mn