Welcome to Alanis Business Academy.
In this lesson we're going to walk through how to calculate the Internal Rate of Return.
Now there are several methods of calculating the Internal Rate of Return of IRR for short.
You can use a financial calculator, Microsoft Excel, and even a trial and error approach
that we reviewed in episode 127.
All of these methods can help you determine IRR, however the process and effort needed
differs a bit.
Now a couple of months ago, one of our subscribers Daniel Young, let me in on an even better
trial and error approach to solving for IRR.
So we're going to walk through that process here, and of course thanks to Daniel for sharing.
If you're familiar with the trial and error approach the process is very similar, but
with a change at the very end.
Now IRR represents the interest rate that reduces the Net Present Value or NPV to zero.
Lets assume that we want to determine the IRR of a project that requires an initial
investment of $10,000, and generates future cash flows of $3,000, $5,000, and $6,000 in
years 1, 2, and 3 respectively.
We of course need to solve for IRR, which is unknown.
Using the Present Value equation, we need to discount our future cash flows to the present
time and then subtract the total value of them from our initial investment to determine
the net present value.
Before we solve for the present value for each of these cash flows, we need to select
an interest rate to discount them by.
This is just a guess, and I'm going to use 5 percent.
We've learned about solving for the present value in past lessons, so I'm going to quickly
calculate those figures.
Discounting each future cash flow by its corresponding number of years, we should receive $2,857.14,
$4,535.15, and $5183.03 for years 1 through 3 respectively.
Just quick FYI is I rounded these numbers to the neared hundredth for simplicity, but
you can keep them in their original form for improved accuracy.
The next step is add these three cash flows together, which will result in $12,575.32.
Then subtracting that figure from our initial investment of $10,000 we get $2,575.32.
Clearly I was a ways off off from determining the correct IRR, but that's okay because we
need to complete the process one more time.
Since our NPV is so far away from zero lets select a higher interest rate, say 15 percent.
Discounting each future cash flow by 15 percent should give us $2,600.70, $3,780.72, and $3,945.10
after rounding as we did before.
Next, we'll add these three number together to get $10,334.52 and then subtract our initial
investment of $10,000.00 to get $334.52.
We're definitely getting close, but we haven't quite reached the IRR Since an interest rate
of 15 percent produced an NPV of 334.52, we know that the IRR is probably just a little
higher than 15 percent.
Now in our past lesson, we would select another interest rate, say 16 percent and go through
the calculations again until we reached an NPV of zero.
Depending upon how good we are at guessing, we could potentially go through the process
another 2 to 5 times before we arrive at a correct answer.
I don't know about you, but this sounds incredibly inefficient.
So lets walk through a second approach that'll save us some time.
We have already determined the NPV twice using 5 percent and 15 percent, giving us NPV's
of 334.52 and 2,575.32 respectively.
In our first step, we going to subtract our lower NPV from our higher NPV.
This will give us 2,240.80.
Second, we're going to divide by the difference of our two interest rates.
Since we're using 5 percent and 15 percent, we'll divide by 10 as 15 minus 5 equals 10.
This will give us 224.08.
If you're curious this represents how much our NPV rises and falls with a one percentage
increase or decrease in our interest rate.
Our third step is to determine how many percentage points are between the two interest rates
we selected.
To do this, we divide our higher NPV, which is 2,475.32 by the result of step 2, which
is 224.08, giving us 11.49.
In our fourth and final step, we add the 11.49 percent to our lowest interest rate of 5 percent,
which gives us 16.49 percent.
This is our IRR, or at least close to it.
If you were to use a financial calculator you would probably get something like 16.79,
with the difference of course being that the calculator doesn't round and I of course did.
So I hope that helps to clarify how to solve for the IRR.
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Thanks for watching.