Corporate Finance

Free Cash Flow Valuation 
 193

Year Cash flow Rs

0 –1,000,000

1 300,000

2 400,000

3 500,000

4 600,000

Discount rate = 15 percent

1. Calculate the future value of project cash flows at the discount rate of 15 percent.

300000 × 1.15^3 = Rs 456262.50

400000 × 1.15^2 = Rs 529000.0

500000 × 1.15 = Rs 575000

600000

2. Add them
   = Rs 2,160,262.50


3. Calculate the implied return

Investment (1 + r)n= Future value of cash flows

1000000(1 + r)^4 = Rs 2160262.50

r= 21 percent

That is, Modified IRR = 21 percent

Multiple IRRS

In a conventional project a cash outflow is followed by cash inflows. Such projects will have a unique IRR.
Consider the following example. A project requires an outlay of Rs 1 lac. The cash flows from the project are
given here:

Year Cash flow (Rs)

0 (100,000)

1 310,000

2 (220,000)

The project has a cash outflow in the second year. The project has two IRRs:

IRR 1 = 10 percent

IRR 2 = 100 percent

When there is more than one change in sign of cash flows, there will be more than one IRR. The number
of IRRs equals the number of sign changes. There are two ways of tackling the problem.