Question

A cash flow series is increasing geometrically at the rate of 9% per year. The initial payment at EOY 1 is $5,500, with increasing annual payments ending at EOY 20. The interest rate is 13 % compounded annually for the first seven years and 5 % compounded annually for the remaining 13 years. Find the present amount that is equivalent to this cash flow

Answer 1

The present value of the payments for the first 7 years should be calculated using the interest rate of 13% compounded annually, while the present value of the payments for the remaining 13 years should be calculated using the interest rate of 5% compounded annually.

Step-by-step explanation:

To find the present amount that is equivalent to the given cash flow series, we need to calculate the present value of each individual payment and then sum them up.

Step 1: Calculate the present value of the payments for the first 7 years using the interest rate of 13% compounded annually:

1. 
   
3. Use the formula for present value: PV = FV / (1 + r)t, where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years.
4. 
   
6. Calculate the present value for each payment and sum them up:

Year 1 payment: PV = $5,500 / (1 + 0.13)1 = $5,500 / 1.13 = $4,867.26

Year 2 payment: PV = $5,500 / (1 + 0.13)2 = $5,500 / 1.1449 = $4,805.61

Repeat this calculation for years 3 to 7.

Step 2: Calculate the present value of the payments for the remaining 13 years using the interest rate of 5% compounded annually:

Use the same formula and calculations as in step 1 for years 8 to 20.

Step 3: Sum up all the present values from steps 1 and 2 to find the present amount that is equivalent to the cash flow series.