Calculating Working Capital with Net Present Value (NPV) and Internal Rate of Return (IRR)

A piece of equipment costing $100,000 is purchased for a future investment project. Working capital increases by $30,000 initially, and is then recovered after the completion of the project. The project has a 7 years life and 8.3% required return compounded monthly. The cash flow information is as follows:

Graphical Representation of the Cash Flows

Calculate:

1) Net Present Value
2) Internal Rate of Return
3) Payback Period
4) Profitability Index

Solution:

First we create a financial timeline. The numbers from 0-7 below are the Years.

|0______|1______|2______|3_____|4______|5_______|6______|7________|

In your calculator, type in 2nd -> CF

CFO = -130,000
CO1 = 45000
FO1 = 3 (means cash flow for 3 years)
CO2 = 85000
FO2 = 3
CO3 = -20,000
FO3 = 1

CPT -> NPV

I = 8.3% (this is the company's required rate of return)

1) NPV -> CPT = -$+$145,420
2) IRR -> CPT = 35.84%

3) Profitability Index = (NPV + Initial Investment) \ Initial Investment
Profitability Index = (145,420 + 100,000) / 100,000 = 2.45

4) Payback Period

Payback Period = 2 + 40000 / 45000
Payback Period = 2.89 Years

Analysis of Solutions

Should we take up this Investment?

1) The rules of NPV?

- If an investment has a Positive NPV, then go ahead and do it!
- If an investment has a Negative NPV, then do not invest in it!

Therefore, since the NPV is +$145,420, this investment is GOOD!

2) The rules of IRR?

- If the IRR exceeds the required return, go ahead and do the project!
- If the IRR is below the required return, the project should NOT be done.

Since the achieved IRR of 35.84% is greater than the required rate of return of 8.3%, this investment is GOOD!

3) Rules of Profitability Index

- If PI > 1, Good Investment
- If PI < 1, Bad Investment

Since in this investment the Profitability Index of 2.45 is greater than 1, this investment is GOOD!