IRR: Cash flows in constant- or budget-year dollars?

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IRR: Cash flows in constant- or budget-year dollars?

Post by ringyFinance »

Wikipedia defines Internal Rate of Return as the discount rate that makes the value of all cash flows sum to zero when brought to any particular year (e.g., the present). That makes intuitive sense to me. Given a set of cash flows, one should be able to write an algorithm that can search for the rate of return that makes the net present value of all cash flows sum to zero.

However, it also says that inflation is ignored. This seems weird because of you have an annuity, it is paid in budget-year dollars. If IRR truly doesn't account for inflation, does that mean that I have to convert all cash flows into constant-year dollars before searching for a rate of return that yields zero net present value? Or does it mean that I should blithely treat the cash flow quantities as constant-year dollars (even though they arent't)?

I'm not actually going to write an IRR-finding algorithm. I'm just trying to understand the underlying definition of IRR.

Thanks.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by ghariton »

The approach you take depends on the question you are trying to answer.

If you use current-value cash flows, i.e. cash flows that increase each year with inflation, you get back a nominal rate of return (that includes inflation). If you use constant-value cash flows, i.e. cash flows where inflation from year to year is stripped out. you get back a real rate of return (a rate of return that is in addition to what you need to cover inflation).

We have the approximate relationship that the nominal rate of return equals the real rate of return plus the rate of inflation.

Most of us live with inflation-adjusted prices, and so our standard of living depends on the real rate of return that we receive on our investments. This is true for consumer durables and non-durables alike. So the real rate of return is of interest.

However, some multi-year spending commitments are in current dollars. Perhaps the most important example for DIY investors is a mortgage. When thinking about paying down your mortgage or investing in an alternative instrument, you might want to look at the nominal rate of return on the alternative investment. As a second example, looking at pensions that are not inflation-indexed is also best done in terms of nominal rates of return, so as to facilitate comparisons with regular bonds.

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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by ringyFinance »

OK, thanks. That makes a lot of sense.

If I fully understand your reply, that means that the definition of IRR leaves unspecified whether the rater of return is real or nominal. If one is given an IRR, one has to further inquire about whether it is real or nominal. But most of the time, it will be real. Hopefully I am paraphrasing you correctly?
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by IdOp »

I look at it this way. The return calculated by the IRR method is a function of the cash flows. Use nominal cash flows, and you get a nominal return; use real cash flows, to get a real return. The question is not whether the IRR method ignores inflation. The question is what kind of cash flows were plugged in (i.e., what do they mean, how do you interpret them).
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by ringyFinance »

I was actually hoping that the response your provided would not be provided. Because it basically says that IRR is a method, and how the result is interpretted depends on the meaning of the cash flows that are fed to it. So any time an IRRs are given for certain financial courses of action, one has to seek clarification as to whether it is nominal or real.

The ideal case would have been if the meaning (nominal vs. real) was embedded in the definition of IRR. But after your clarification, I re-examined the wikipedia definition. IRR isn't really a metric per se -- otherwise, it would be possible to *define* the metric as either a real or nominal rate of return. Instead, it is a calculation procedure, so the resulting return depends on the meaning of cash flows that it is applied to (as you said).

I'm pretty sure that any history returns for various mutual funds, index funds, or ETFs are not specified as *internal* rates. I'm pretty sure that they are nominal rates, and one has to subtract inflation from them. Any return rate that claims to account for inflation would have to deal with what inflation rate to use.

Anyway, it all seems pretty clear now. Thanks.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by IdOp »

ringyFinance wrote:I was actually hoping that the response your provided would not be provided. Because it basically says that IRR is a method, and how the result is interpretted depends on the meaning of the cash flows that are fed to it. So any time an IRRs are given for certain financial courses of action, one has to seek clarification as to whether it is nominal or real.
Yes. I think it's helpful to distinguish both the method, and the return provided by the method. In most practical discussions ("excel said my [X]IRR was such-and-such") people will be talking about the value of the return.
I'm pretty sure that any history returns for various mutual funds, index funds, or ETFs are not specified as *internal* rates.
Well, these are generally given with the assumption that all distributions are fully and immediately reinvested in the fund. So there really aren't any (net) cash flows along the way. That is a special case of IRR, but a trivial one.
I'm pretty sure that they are nominal rates, and one has to subtract inflation from them. Any return rate that claims to account for inflation would have to deal with what inflation rate to use.
Exactly.
Anyway, it all seems pretty clear now. Thanks.
You're welcome, glad we could help.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by steves »

The only problem is that inflation, unlike investment growth, is not compounding. Inflation is the slope of the consumer price index curve..... it is linear, not exponential. Over short time frames, this is not a problem, but for 20/30/40 year spans, it can be quite a departure.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by IdOp »

If inflation is 2% one year and 3% the next year, then overall it is 5.06%, the effects of inflation compound. The slope of the price curve could be called the inflation rate at that point in time, but it gives a linear approximation to the curve. Any such single value doesn't represent actual inflation which changes over time. It is itself a curve -- the derivative of the price -- and integrating it gives the cumulative effect of inflation. Yes, extrapolating a linear approximation can be bad over too large intervals.

[Edited for clarity]
Last edited by IdOp on 05 Sep 2016 13:31, edited 2 times in total.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by ringyFinance »

IdOp said: In most practical discussions ("excel said my [X]IRR was such-and-such") people will be talking about the value of the return.

I assume you mean present value of all cash flows. Even there, I picture a series of cash flows. I assume (again) that for personal finance, if you know the cash flows in advance, they are typically budget year figures. It seems to me then that you would have to account for inflation in addition to the IRR when discounting it back to the present. Probably using some rule-of-thumb inflation figure.

I said: I'm pretty sure that any history returns for various mutual funds, index funds, or ETFs are not specified as *internal* rates.

IdOp said: Well, these are generally given with the assumption that all distributions are fully and immediately reinvested in the fund. So there really aren't any (net) cash flows along the way. That is a special case of IRR, but a trivial one.

True enough. But it's still useful to know whether it refers to real or nominal rates of return. Currently, I've assumed that they are nominal, and blithely subtracted out inflation to get real return. I just have the strong impression that when dealing with banks and investment companies, they generally communicate with the masses using non-inflation-adjusted figures. But if you think about it, that means they must pad the real returns with some inflation figure to obtain nominal returns. When I subtract out inflation, my inflation figure may or may not be the same as the one they use for padding. The exact inflation data they use is probably specified in small print in some obscure document.

Also, if (in another reality) I ever get time to simulate different schedules of regular cash flow resulting different investment decisions, I will probably specify my cash flows in budget year dollars. So it'd be nice to know whether rates of return are nominal or real.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by IdOp »

ringyFinance wrote:IdOp said: In most practical discussions ("excel said my [X]IRR was such-and-such") people will be talking about the value of the return.

I assume you mean present value of all cash flows.
Sorry, I wasn't clear. I meant the numerical value of the return, not present value. In other words "IRR" as a number (the return), rather than as a method (discounting cash flows etc.).
True enough. But it's still useful to know whether it refers to real or nominal rates of return. Currently, I've assumed that they are nominal, and blithely subtracted out inflation to get real return. I just have the strong impression that when dealing with banks and investment companies, they generally communicate with the masses using non-inflation-adjusted figures.
Yes.
But if you think about it, that means they must pad the real returns with some inflation figure to obtain nominal returns. When I subtract out inflation, my inflation figure may or may not be the same as the one they use for padding. The exact inflation data they use is probably specified in small print in some obscure document.


I don't follow why they would start with real returns and pad them? Surely they use nominal all the way through. E.g., assume an investor puts $1000 into the mutual fund and figure out how much he would have 1,2 5, etc, years later. All nominal, i.e., using dollar amounts as he would see in his statements with no adjustments for inflation.

Also, if (in another reality) I ever get time to simulate different schedules of regular cash flow resulting different investment decisions, I will probably specify my cash flows in budget year dollars. So it'd be nice to know whether rates of return are nominal or real.

If I understand this right, I think you're describing a nominal calculation. If you wanted to do it in real terms you'd have to convert all the dollars as they occurred back/forward to a common year, using some form of inflation model.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by ringyFinance »

> IdOp said: In most practical discussions ("excel said my [X]IRR was
> such-and-such") people will be talking about the value of the
> return.
>
> I said: I assume you mean present value of all cash flows.
>
> IdOp said: Sorry, I wasn't clear. I meant the numerical value of the
> return, not present value. In other words "IRR" as a number (the
> return), rather than as a method (discounting cash flows etc.).

Oh, I see. I haven't used such spreadsheets (still a newbie), but if they are typically used to study historical data rather than attempt to project forward (keeping in mind that future performance doesn't necessarily reflect the past), then all dollar figures are known, and are in budget year dollars. So such an IRR is nominal.

> I said: True enough. But it's still useful to know whether it refers
> to real or nominal rates of return. Currently, I've assumed that
> they are nominal, and blithely subtracted out inflation to get real
> return. I just have the strong impression that when dealing with
> banks and investment companies, they generally communicate with the
> masses using non-inflation-adjusted figures.
>
> IdOp said: Yes.
>
> I said: But if you think about it, that means they must pad the real
> returns with some inflation figure to obtain nominal returns. When I
> subtract out inflation, my inflation figure may or may not be the
> same as the one they use for padding. The exact inflation data
> they use is probably specified in small print in some obscure
> document.
>
> IdOp said: I don't follow why they would start with real returns and
> pad them? Surely they use nominal all the way through. E.g., assume
> an investor puts $1000 into the mutual fund and figure out how much
> he would have 1,2 5, etc, years later. All nominal, i.e., using
> dollar amounts as he would see in his statements with no adjustments
> for inflation.

I'm was confused. Sorry. Never having gone through the exercise, I'm confusing analysis of past cash flows and fund balances versus projecting into the future. If you project into the future, there is the option of working with real dollars. But if you're analyzing the past, everything is already known in terms of budget year dollars. I assume, therefore, that analysis of the past would typically yield nominal return.

> I said: Also, if (in another reality) I ever get time to simulate
> different schedules of regular cash flow resulting different
> investment decisions, I will probably specify my cash flows in
> budget year dollars. So it'd be nice to know whether rates of return
> are nominal or real.
>
> IdOp said: If I understand this right, I think you're describing a
> nominal calculation. If you wanted to do it in real terms you'd have
> to convert all the dollars as they occurred back/forward to a common
> year, using some form of inflation model

Yes, that's what I meant. Thanks for articulating it more clearly!
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by IdOp »

ringyFinance wrote:Oh, I see. I haven't used such spreadsheets (still a newbie), but if they are typically used to study historical data rather than attempt to project forward (keeping in mind that future performance doesn't necessarily reflect the past), then all dollar figures are known, and are in budget year dollars. So such an IRR is nominal.
I would think so. Of course, looking into the past, inflation would also be known. So you could also convert to real dollars and do a real calculation. Looking into the future, nothing is known, everything's a model. Spreadsheets are used a lot to "project" the future. Normally people might start with a return (or several returns on different asset classes) -- based on historical values -- and use them to project, rather than trying to solve for returns. And if you have a handy model of future inflation, you could project in real terms too.
I'm was confused. Sorry. Never having gone through the exercise, I'm confusing analysis of past cash flows and fund balances versus projecting into the future.
No worries about confusion, this stuff is that way, I've been confused by it many, many times and will be again I'm sure.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by adrian2 »

steves wrote:The only problem is that inflation, unlike investment growth, is not compounding. Inflation is the slope of the consumer price index curve..... it is linear, not exponential. Over short time frames, this is not a problem, but for 20/30/40 year spans, it can be quite a departure.
You may be examining the actual inflation graph and seeing an optical artifact (or maybe an optical illusion), due to declining inflation in the last decades.

Inflation compounds just as much as investment growth.
A chequing account paying 0.1% interest compounds over time, just not very much during an investing lifetime.
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Re: IRR: Cash flows in constant- or budget-year dollars?

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adrian2 wrote:
steves wrote:The only problem is that inflation, unlike investment growth, is not compounding. Inflation is the slope of the consumer price index curve..... it is linear, not exponential. Over short time frames, this is not a problem, but for 20/30/40 year spans, it can be quite a departure.
You may be examining the actual inflation graph and seeing an optical artifact (or maybe an optical illusion), due to declining inflation in the last decades.

Inflation compounds just as much as investment growth.
A chequing account paying 0.1% interest compounds over time, just not very much during an investing lifetime.
Yeah, I was confused by this statement. Why wouldn't inflation compound just like anything else. Each years CPI is applied to the results of last year's increase. That's compounding.

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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by AltaRed »

I think Steves meant that if CPI as an indicator moves from say 102.3 to 104.1, that is not compounding in itself. It is a 1.76% increase. But yes, if it moves the next year to 105.4, then the 1.25% increase is off the new denominator of 104.1. It is a matter of how it is expressed.
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Re: IRR: Cash flows in constant- or budget-year dollars?

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AltaRed wrote:I think Steves meant that if CPI as an indicator moves from say 102.3 to 104.1, that is not compounding in itself. It is a 1.76% increase. But yes, if it moves the next year to 105.4, then the 1.25% increase is off the new denominator of 104.1. It is a matter of how it is expressed.
In the past, Steve has made a similar statement and referred to the shape of the inflation graph in the last two decades or so.
Yes, it may look more like a line instead of a parabola, but that's just compounding a falling annual rate.

I have objected to his characterization then and I'm repeating my objection now.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by steves »

adrian2 wrote: In the past, Steve has made a similar statement and referred to the shape of the inflation graph in the last two decades or so.
Yes, it may look more like a line instead of a parabola, but that's just compounding a falling annual rate.

I have objected to his characterization then and I'm repeating my objection now.
Last two decades? The CPI has been linear since 1970.
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Re: IRR: Cash flows in constant- or budget-year dollars?

Post by AltaRed »

Not quite as far back as 1970 (more like mid-80s) but close enough for the discussion. Go to http://www.tradingeconomics.com/canada/ ... -index-cpi and click on "max" to get a 1950 to 2016 chart. That line is almost linear.
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Re: IRR: Cash flows in constant- or budget-year dollars?

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steves wrote:The CPI has been linear since 1970.
Which is a consequence of the annual number being quite high in the 70's, somewhat lower in the 80's, even lower in the 90's, and still lower this century.

It does not mean that yearly inflation is not compounding.

There is no reason to believe an inflation graph for future decades will be linear.
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