Xirr Vs Irr Continued - This One Is A Tough Question |
Xirr Vs Irr Continued - This One Is A Tough Question - Excel |
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Hello,
I have read several threads on the difference between IRR and XIRR however I can not figure out why XIRR and IRR return (slightly) different results. For example: Assume I buy a 1 year, $100 bond with an 8% coupon. The payments would be as follows:
Dates Cash Flows 1/1/10 12:00 AM $ (100.00) 4/2/10 6:00 AM $ 2.00 7/2/10 12:00 PM $ 2.00 10/1/10 6:00 PM $ 2.00 1/1/11 12:00 AM $ 102.00 Return calculations IRR 2.000000000% IRR adjusted to equivalent annual rate 8.243216000% XIRR 8.243909359% XIRR adjusted to equivalent quarterly rate 2.000163342%
Notice that I adjusted the payments to fall exactly one quarter of a year apart to eliminate any possible error generated by having some quarters longer than others by a few hours.
Since IRR returns an annual rate and XIRR a quarterly rate I adjusted them so I could make an apples to apples comparison. I used these equations:
Quarterly Rate = ((1+Annual Rate)^(1/4))-1
Annual Rate = ((Quarterly Rate+1)^4)-1
I have tried to think of a way to check which one is correct and came up with this:
Dates Cash Flows IRR XIRR 1/1/10 12:00 AM $ (100.00) 4/2/10 6:00 AM $ 2.00 $ 2.1224160 $ 2.1224262 7/2/10 12:00 PM $ 2.00 $ 2.0808000 $ 2.0808067 10/1/10 6:00 PM $ 2.00 $ 2.0400000 $ 2.0400033 1/1/11 12:00 AM $ 102.00 $ 102.0000000 $ 102.0000000 Sum of cash flows $ 108.2432160 $ 108.2432361
Since the IRR and XIRR calculation concept assume that all cash payments are reinvested and earn the same return as the computed IRR, each $2.00 dollar payment should be compounded at the quarterly rate until the bond is repaid on 1/1/11. Doing this with the quarterly rate produced by the IRR and XIRR will produce the respective cash flows in the two right hand columns. Summing the cash flows in the IRR column produces $108.2432160 just as one would expect given the IRR equivalent annual rate of 8.243216%. However, XIRR produces $108.2432361 when, given its annual rate, it should produce $108.2439094, a difference of $.0006732.
Does anyone know what the issue is? Why won't XIRR reproduce the correct cash flows?
I have my number of iterations set at the max and the maximum change is .00000000001 so neither of those are the culprit.
Although the actual monetary difference in this case is small, this is a simplification of a real world financing situation I am working on and in that deal the error represents real money.
Any help would be MUCH appreciated.
-Brad
I have read several threads on the difference between IRR and XIRR however I can not figure out why XIRR and IRR return (slightly) different results. For example: Assume I buy a 1 year, $100 bond with an 8% coupon. The payments would be as follows:
Dates Cash Flows 1/1/10 12:00 AM $ (100.00) 4/2/10 6:00 AM $ 2.00 7/2/10 12:00 PM $ 2.00 10/1/10 6:00 PM $ 2.00 1/1/11 12:00 AM $ 102.00 Return calculations IRR 2.000000000% IRR adjusted to equivalent annual rate 8.243216000% XIRR 8.243909359% XIRR adjusted to equivalent quarterly rate 2.000163342%
Notice that I adjusted the payments to fall exactly one quarter of a year apart to eliminate any possible error generated by having some quarters longer than others by a few hours.
Since IRR returns an annual rate and XIRR a quarterly rate I adjusted them so I could make an apples to apples comparison. I used these equations:
Quarterly Rate = ((1+Annual Rate)^(1/4))-1
Annual Rate = ((Quarterly Rate+1)^4)-1
I have tried to think of a way to check which one is correct and came up with this:
Dates Cash Flows IRR XIRR 1/1/10 12:00 AM $ (100.00) 4/2/10 6:00 AM $ 2.00 $ 2.1224160 $ 2.1224262 7/2/10 12:00 PM $ 2.00 $ 2.0808000 $ 2.0808067 10/1/10 6:00 PM $ 2.00 $ 2.0400000 $ 2.0400033 1/1/11 12:00 AM $ 102.00 $ 102.0000000 $ 102.0000000 Sum of cash flows $ 108.2432160 $ 108.2432361
Since the IRR and XIRR calculation concept assume that all cash payments are reinvested and earn the same return as the computed IRR, each $2.00 dollar payment should be compounded at the quarterly rate until the bond is repaid on 1/1/11. Doing this with the quarterly rate produced by the IRR and XIRR will produce the respective cash flows in the two right hand columns. Summing the cash flows in the IRR column produces $108.2432160 just as one would expect given the IRR equivalent annual rate of 8.243216%. However, XIRR produces $108.2432361 when, given its annual rate, it should produce $108.2439094, a difference of $.0006732.
Does anyone know what the issue is? Why won't XIRR reproduce the correct cash flows?
I have my number of iterations set at the max and the maximum change is .00000000001 so neither of those are the culprit.
Although the actual monetary difference in this case is small, this is a simplification of a real world financing situation I am working on and in that deal the error represents real money.
Any help would be MUCH appreciated.
-Brad
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E.g.
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Something like =IF(A3:D3) are equal, 4,0
Below are a few examples of what I mean:
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Apologies in advance if I haven't explained this clearly enough.
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