Question

The State of Chiapas, Mexico, decided to fund a program for improving reading skills in elementary school students. The first cost is $375,000 now and an update amount of $120,000 every 8 years forever. Determine the perpetual equivalent annual cost at an interest rate of 12 % per year The perpetual equivalent annual cost is determined to be-$[

Answer 1

Cost Break-Up: First Cost = $ 375000, $ 120000 every 8 year into perpetuity, Interest Rate = 12 %

Total Present Value (TPV) = First Cost + Present Value of Periodic Cost = 375000 + 120000 / (1.12)^(8) + 120000 / (1.12)^(16) + 120000 / (1.12)^(24) +......................+ to infinity

Replacing (1.12)^(8) by (1+r), we get:

TPV = 375000 + 120000 / (1+r) + 120000 / (1+r)^(2) +...................+ to infinity

TPV = 375000 + 120000 / r = 375000 + [120000 / {(1.12)^(8)-1}] = $ 456302.8414

Let the equivalent annual cost be $ P

Therefore, 456302.8414 = P x (1/0.12)

P = 456302.8414 x 0.12 = $ 54756.34