Question

A project is being started that will cost $70 Million now, and an additional cost of $10 million 8 years from now. After this, there will be maintenance costs of $5 Million every 5 years. Assuming an interest rate of 5% per year compounded quarterly, find the capitalized cost to fund this project.

Answer 1

We have the following information

Initial Cost ($)	70 Million
Additional Cost after 8 Year ($)	10 Million
Periodic Maintenance Cost after every 5 Years ($) after the Additional Cost of $10 Million in 8th year	5 Million

Interest rate = 5% compounded quarterly

No. of interest periods per year, (C) = 4

Effective interest rate (R) = ((1 + (i/C))^C – 1

R = ((1 + (5%/4))⁴ – 1

R = 5.09% compounded annually

Capitalized Cost = 70 + 10(P/F, 5.09%, 8) + 5(A/F, 5.09%, 13)(P/A, 5.09%, n=infinite)

Capitalized Cost = 70 + 10/(1 + 0.0509)⁸ + {5 × [0.0509/((1 + 0.0509)¹³ – 1)] × (1/0.0509)}

Capitalized Cost = 70 + 6.72 + 5.50

Capitalized Cost = $82.22 Million