Why IRR > WACC & not TWR > WACC

Hey all,

Was solving some problems related to annualizing returns and I had the following scenario:

I borrow $100 and invest it, and I get the following results:

Year 1: 15% Return --> Ending CF: 115 Year 2: -10% Return --> Ending CF: 103.5 Year 3: 5% Return --> Ending CF: 108.7

Solving for the Geometric Mean, I get 2.81%. Now, assuming I borrowed that $100 at a 1% cost of capital, I would make profit as follows (correct me if I’m wrong, as I usually am).

Year 1 Total Debt owed: 100*(1+1%) => $101 Year 2 Total Debt owed 101(1+1%) =>$102 Year 3 Total Debt owed 102(1+1%) =>$103

So, why cant the rule by TWR > WACC => Good investment.

Am I missing anything? Moreover, when I attempt to do IRR with these figures, I get a huge percentage!

Thank you.

TWR does not take into consideration the addition or withdrawal of funds. TWR would stay the same if you added 1000 in start of y2 and withdrew before y3. You would have lost a bundle, but TWR would exceed WACC…and try that IRR thing again. Tell me what you got and I’ll try to figure out where you went wrong.

Hello Sir,

Sorry I do not quite follow, where is the issue in the removal and addition of funds if the returns realized are staying the same?

Thank you.

The issue is, they are not. Imagine the yield in year 1 is -5% and in year 2 it is 30%. If you remove a significant amount of money at the end of year 1, you would have “earned” a loss with your entire principal in year 1 and will earn 30% over the next year just with the remainder. And vice versa.

IRR would show you the return with all cash flows taken into consideration, but it would not show you the true return earned, as it has no way to deal with the removal or addition of funds, nor for dealing with changing yields within the period.

The first part of your answer is correct. However, this statment doesn;t make sense to me. First off, I’m not sure what you mean by the “true” return earned.

The MWR IS the IRR. Further, for single lump sum investments (i.e. money invested at the beginning and withdrawn at the end, the TWR=MWR=IRR.

However, when there are intermediate cash flows, the investor’s MWR (i.e. the IRR) does NOT equal the TWR.

I mean “earned” return. With intermediate cash flows you will end up with a positive MWR even if rate of return is 0 in both sub-periods.

I am not sure what you used to calculate your IRR but I calculated it and i got 2.82% IRR and GeoMean of 2.8120%. With below assumption. IRR > GeoMean > WACC (1%) and hence good investment.

CF0 = -100 (Your investment)

CF1= 0


CF3= 108.7 (Sell of your investment)