Question

What is the equivalent annual cost in years 1 through 10 of a contract that has a first cost of $68,000 in year 0 and annual costs of $16,000 in years 3 through 10? Use an interest rate of 13% per year. The equivalent annual cost is determined to be $

Answer 1

This question has following steps:

1. Calculate the PV of the annual costs from years 3-10 at time 3
2. Discount it to time 0
3. Add the discounted cost to first cost
4. Use the annuity formula to find the PMT for years 1-10

Step 1:

We are given the following information:

PV of an annuity
PMT	$16,000.00
r	13.00%
n	8
frequency	1

We need to solve the following equation to arrive at the required PV

So the PV is $-76780.32

Step 2:

We discount the above calculated PV 2 years back to year 0

We are given the following information

Find PV
r	13.00%
n	2
frequency	1
FV	$76,780.32

We need to solve the following equation to arrive at the required PV

So the PV is $ 60130.26

Step 3:

• Total cost at time 0 = first cost + discounted PV calculated above
• Total cost at time 0 = 68000 + 60130.26
• Total cost at time 0 = ₹ 1,28,130.26

Step 4 now we find the EAC:

We are given the following information:

PV of an annuity
r	13.00%
n	10
frequency	1
PV	$1,28,130.26

We need to solve the following equation to arrive at the required PMT

So the PMT or the equated annual cost is $23,613.07