Question

The cash flows associated with a project are shown below. The interest rate varies from year to year as shown.

EOY	Cash Flow
0	$0
1	$600
2	$-300
3	$700
4	$0
5	$1,000

Interest Period	Interest Rate
EOY 0 to EOY 1	10%/yr
EOY 1 to EOY 2	10%/yr
EOY 2 to EOY 3	8%/yr
EOY 3 to EOY 4	8%/yr
EOY 4 to EOY 5	12%/yr

Determine the amount required to create an equivalent uniform annual series of cash flows. $_________

Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is ±3%

Answer 1

First we need present values of all cash flows,

PV(CF1) = 600/1.1

PV(CF2) = -300/1.1²

PV(CF3) = 700/1.1³

PV(CF4) = 0/1.08⁴

PV(CF5) = 1000/1.12⁵

Adding all these, we get a Net Present Value or NPV of $1,420.63009 (you can use excel to solve this, or a financial calculator)

Now, if all cash flows are same, lets call the annual cash flow as X.

The new formula for NPV would look like:

Taking X out and solving for X, we get $370.74492 or $371 (rounded-up)

This means that the values of the cash flows is the same if amount is $371 for all five years.