So question! I actually got this in a PE interview and I answered it correctly, but more from a “the answer can only be x given the available information” vs. having the innate intuition. would love someone to walk me through the mathematical intuition
You buy box for 100. it gives you 10 every year until you sell it for the same price. what’s the IRR
what’s the intuition here for why the IRR is 10%?
Because it never goes up or down in value?
Equation wise, you could do gordon growth formula and say:
price = dividend in period 1 / ( r - g)
g = 0 price = 100 dividend = 10 r = unknown, solve for 10%.
PV = -100
PMT = 10
n = 10
FV = 100
Solve for i = 10%.
Yea I guess I would actually think its less than 10% due to inflation eroding the value of $100. But IRR ignores those impacts on return
IRR neither ignores it nor includes it; whether it appears in the IRR calculation depends on the input data. If you input nominal dollars, the IRR will include an inflation premium. If you input real dollars, the IRR wil not include an inflation premium.
Your choice.
^ a true OG
That’s a fair point. We seem to always quote IRR in nominal terms, never real. At least, that’s been my experience.
But you’d also have to inflation adjust each payment as well, correct? Although the result will be most senstive to the FV inflation adjustment. Seems like this couldn’t be done in a normal business calculator, unless you know some tricks I don’t.
If you’re putting in real dollars, yes.
Did you really just write that?
To a magician?
^ha ha ha
I thought since my post that you probably could use the unlevel pay NPV calculation. But you’d have to inflation adjust the inputs in a seperate calculation and then put them in as the payments.
I can’t explain the intuitive way, I am sure something to do with re-investing at the discount rate.
Mathematically,
if PV = FV, pmt = x, IRR = i, for n years, then
PV = x/(1+i) + x/(1+i)^2 + … + x/(1+i)^n + PV/(1+i)^n
Let 1+i = y and multiply all by y^n
PV y^n = x(y^[n-1] + y^[n-2] + … + 1) + PV
PV (y^n - 1) = x * (y^n - 1) / (y - 1)
PV = x /(y - 1) = x/(i) or i = x/PV.
The IRR is the average rate of growth of the investment each year.
Here, each year you’re skimming off the growth of $10 each year and returning the corpus to $100 to grow next year. So:
Every year it grows 10%, so the average yearly growth – the IRR – is 10%.
now you’re throwing an assumption into your solution that doesn’t exist in the problem…
I think he is just trying to make the calculator happy.
Some non-zero n is sufficient. Hopefully positive, though I don’t have my TI BA-II handy to see what happens if n is negative.
I get that, but if we assume that the value of n doesn’t matter without a proof or some argument, we might as well pick n=1 and do it in our head: 100=(100+10)/(1+IRR).
Actually . . . I have no idea where I came up with n = 10.
Reading too many threads, apparently.
It’s quite simple. You’re getting 10% of the principal’s value each period indefinitely, so the rate of return is return/investment.
You’ve probably had the number 10 in your working memory from the IRR answer.
Objection: assumes facts not in evidence.
Objection: assumes facts not in evidence.
The technical definition of IRR is “the discount rate that results in an NPV of Zero”. So, it’s the interest rate that makes the PV of the cash flows equal to $100.
The intuition behind PV is that it’s the amount that you’d need to deposit in an account at a set interest rate in order to EXACTLY fund the future cash flows. In this case the $100 in the future represents the principal, and since it’s the same as the initial investment (i.e. the PV at the given discount rate (or IRR)), the $100 must be equal to the amount of annual interest. So, that must be 10/100 or 10%.