Question

      A project that requires a 15 percent return has the following expected cash flows.

                        Year     Cash Flow
                            1                              $90,000
                            2                              100,000
                            3                              110,000
                            4                              120,000
                            5                              130,000

            The initial investment is $300,000. Find the profitability index (PI).

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 = 15%, 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 = $90000 / (1 + 15%)+ $100000 / (1 + 15%)² + $110000 / (1 + 15%)³ + $120000 / (1 + 15%)⁴ + $130000 / (1 + 15%)⁵

PV = $90000 / (1 + 0.15)+ $100000 / (1 + 0.15)² + $110000 / (1 + 0.15)³ + $120000 / (1 + 0.15)⁴ + $130000 / (1 + 0.15)⁵

PV = $90000 / (1.15)+ $100000 / (1.15)² + $110000 / (1.15)³ + $120000 / (1.15)⁴ + $130000 / (1.15)⁵

PV = $78260.87+ ($100000 / 1.3225) + ($110000 / 1.520875) + ($120000 / 1.74900625) + ($130000 / 2.0113571)

PV = $78260.87 + $75614.37 + $72326.78 + $68610.39 + $64632.98

PV = $359445.39

So, required present value is $359445.39

Initial investment = $300000

Now, we will calculate the profitability index as below:

Profitability index = Present value of cash flows / Initial investment

Profitability index = $359445.39 / $300000 = 1.198