Are the Weighted Average Cost of Capital and the Internal Rate of Return the same thing?
Well, they are related, but not the same.
Let me show you how that works, in words, in formulas, and in numbers.
I assume you already know the basics of how Net Present Value works.
If you don’t, then please watch that video first!
The Weighted Average Cost of Capital 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.
Internal Rate of Return is the discount rate at which the net present value of all cash
flows from a particular project is equal to 0.
Both the Weighted Average Cost of Capital and the Internal Rate of Return are elements
of the Net Present Value calculation, but serve a different function!
Here’s how WACC comes in.
You start off quantifying the nominal cash flows over the years for your project.
You take the WACC, which in most companies is a non-negotiable number determined by the
corporate finance department.
You use the WACC to calculate present values of the estimated project cash flows.
The last step is to calculate the Net Present Value (or NPV)
by summing the discounted cash flows.
In short, WACC is an input variable in the NPV calculation.
With IRR, the sequence is different.
You start off quantifying the nominal cash flows over the years for your project.
You set the Net Present Value in the formula at zero.
You can then calculate IRR, which is the output variable or dependent variable.
Here’s the Net Present Value formula.
NPV is the sum (over the years of the project) for returns of a project that are adjusted
for discount rate and time.
Both WACC and IRR show up in the same place: right here where the “i” is.
Here are the steps to use in the NPV formula when you use Weighted Average Cost of Capital.
Step 1: start with the nominal cash flows.
Step 2: apply the WACC as an input variable.
Step 3: Calculate NPV.
Here are the steps to use in the NPV formula when you use Internal Rate of Return.
Step 1: start with the nominal cash flows.
Step 2: set NPV to zero.
Step 3: Calculate IRR as the output variable.
Let’s illustrate NPV, WACC and IRR with numbers.
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.
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).
And so on (to the power 3, to the power 4) through year 4.
We have now translated all cash flows into today’s equivalent.
To get to NPV, you now simply sum across, add up the five numbers (minus 1000, plus
333, plus 278, plus 231, plus 193) 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 your company.
WACC and IRR.
They are in the same place in the NPV formula, but WACC is an input variable and IRR is an
output variable.
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