Net Present Value and Internal Rate of Return, in short NPV and IRR.
What is the purpose of the NPV and IRR methods of investment analysis,
and how do you calculate NPV and IRR?
The main idea of Net Present Value is very simple: time is money!
The net present value (or “discounted cash flow”) method
takes the time value of money into account, by:
Translating all future cash flows into today’s money
Adding up today’s investment and the present values of all future cash flows
If the net present value of a project is positive,
then it is worth pursuing, as it creates value for the company.
Let’s perform a Net Present Value calculation step-by-step.
What is the present value (PV) of all the cash inflows and cash outflows
of the following project?
Project A requires an investment of $1000 today (in year 0), and is expected to provide
four years’ worth of benefits of nominally $400 per year.
The $1000 of investment is already in today’s money: $1000 today equals $1000 today.
What is the present value of a $400 benefit that we expect one year from now?
To calculate that present value, we need to take the nominal amount of $400 and divide
it by 1 + the weighted average cost of capital.
Weighted average cost of capital (or WACC) is a calculation of a firm's cost of capital
in which each category of capital is proportionately weighted.
The riskier or more uncertain the company and the riskier or more uncertain the project,
the higher the WACC becomes.
Let’s take a fairly high WACC of 20% in this calculation.
1 + 20% equals 1.2.
$400 divided by 1.2 equals $333.
The present value of a nominal amount of $400 one year from now is $333 as today’s equivalent.
What is the present value of a $400 benefit that we expect two years from now?
To calculate that present value, we need to take the nominal amount of $400 and divide
it by 1 + 20%, to the power 2 (as we need to take two steps: from year 2 to year 1,
from year 1 to today).
This is the same as saying $400 divided by 1.2 * 1.2,
or $400 divided by 1.44, which is $278.
The present value of a nominal amount of $400 two years from now is $278 as today’s equivalent.
What is the present value of a $400 benefit that we expect three years from now?
To calculate that present value, we need to take the nominal amount of $400 and divide
it by 1 + 20%, to the power 3 (as we need to take three steps:
from year 3 to year 2, from year 2 to year 1, from year 1 to today).
This is the same as saying $400 divided by 1.2 * 1.2 * 1.2, or $400 divided by 1.728,
which is $231.
The present value of a nominal amount of $400 three years from now
is $231 as today’s equivalent.
What is the present value of a $400 benefit that we expect four years from now?
To calculate that present value, we need to take the nominal amount of $400 and divide
it by 1 + 20%, to the power 4.
This is the same as saying $400 divided by 1.2 * 1.2 * 1.2 * 1.2,
or $400 divided by 2.0736, which is $193.
The present value of a nominal amount of $400 four years from now is $193 as today’s equivalent.
We have now translated all cash flows into today’s equivalent.
To get to NPV, you now simply sum across, and find an NPV of $35.
As the net present value of this project is positive, it is worth pursuing, as it creates
value for the company.
How to calculate the Internal Return of Return (or IRR)?
IRR is the discount rate at which the net present value becomes 0.
In other words, you solve for IRR by setting NPV at 0.
We take the same project A, and write down the formulas to calculate NPV.
Through either trial and error, or the use of the IRR formula in Excel, we will find
that the IRR for project A is 22%.
This IRR of 22% exceeds the Weighted Average Cost of Capital of 20%, so the project is
worth pursuing, as it creates value for the company.
What if we have multiple projects in our company that we want to force rank?
We only have $1000 of investment money to spend,
which project is (financially speaking) the most attractive?
In total, for the full 4 years combined, each of the three projects has $1600 worth of cumulative
benefits, but the timing of these benefits varies: evenly distributed for project A,
high benefits in early years shrinking to lower benefits in later years for project B,
and low benefits in early years growing to higher benefits in later years for project C.
Applying the NPV and IRR methods can help!
We already calculated that at 20% Weighted Average Cost of Capital,
the NPV of project A is $35.
Its IRR is 22%.
For project B, due to the high benefits in early years that don’t get discounted too
much by the time value of money, the NPV is $117, and the IRR is 27%.
For project C, due to the long wait for the bigger benefits to come in, the NPV is negative
at minus $46, and the IRR is 18%.
Project C is not worth pursuing, with negative NPV
and an IRR which is below the Weighted Average Cost of Capital.
Project B is the most attractive.
I hope you enjoyed this short explanation of the Net Present Value
and Internal Rate of Return.
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