Question

Find the profitability index of a project with the following cash flows using a discount rate of 2%:
Period 0: -1000
Period 1: 707
Period 2: 398
Period 3: 291
Enter your answer in a decimal and round to the hundredths place.

Answer 1

The formula for calculating the profitability index is:

Profitability index = Present value of cash flows / Initial investment

First we will calculate the present value of cash flows:

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 2%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $707 / (1 + 2%)+ $398 / (1 + 2%)² + $291 / (1 + 2%)³

PV = $707 / (1 + 0.02)+ $398 / (1 + 0.02)² + $291 / (1 + 0.02)³

PV = $707 / (1.02)+ $398 / (1.02)² + $291 / (1.02)³

PV = $693.1372+ ($398 / 1.0404) + ($400 / 1.061208)

PV = $693.1372 + $382.54517 + $376.9289

PV = $1452.611

So, required present value is $1452.611

Initial investment = $1000

Now, we will calculate the profitability index as below:

Profitability index = Present value of cash flows / Initial investment

Profitability index = $1452.611 / $1000 = 1.45