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Put another way, the earnings yield on stocks is essentially a real yield, while the earnings yield on bonds is a nominal yield.

See Fight the Fed Model by Cliff Asness, which covers theory and empirical evidence on this issue.

A related issue (I hope): Is it likely that the 100% equity firm would never pay dividends? Why bother owning the shares if they never cough-up dividends? In fact, I can't think of a reason why a share that never pays dividends should ever be worth anything other than $0! What good is having a claim in earnings if you never actually get your hands on them? Well, OK it's not completely hopeless, the firm could buy back some shares at some point so then it's like an option, but that doesn't change things that much I don't think.

I think you are correct.

I actually don't think that the type of investment matters that much... Even a retail business (where fixed assets are small compared to revenues) would behave the same way as long as you assume that margins remain constant (e.g. you buy a banana for $1 and sell it for $1.05 and in ten years time you buy it for 2$ and sell is at $2.1).

Thinking about the corporate sector in aggregate, that's all you are saying, that corporate profits will remain a constant percentage of GDP rather than a constant number (as they would in a constant profits vs growing nominal GDP world)...

It's the same for rental yields (unless you assume maintenance offsets inflation exactly which seems unlikely) where the yield is really real, but you need to remove depreciation.

But surely a bigger question is how to adjust earnings for the business cycle? Aren't corporate profits a rather large part of GDP at the moment? You could argue that the mean reversion in that relationship will make bonds more attractive...

foosion: "Put another way, the earnings yield on stocks is essentially a real yield, while the earnings yield on bonds is a nominal yield."

That's the way I thought about it too. But when I was halfway through writing this post, and came to the example with a 60/40 debt/equity ratio, I decided that this way of thinking about it understates the difference. The earnings yield on stocks isn't just real, it's "(60/40) real". It's "realer than real". (There's gotta be a better way of saying that, but do you get what I mean?)

Thanks for the link.

Patrick: I get a bit Modigliani-Miller on that one. OK, there's the tax question, and dividends as a way for the firm's managers to signal their beliefs about future earnings, and dividends as a sort of commitment device to stop those same managers grabbing the earnings for themselves. But otherwise I just look at the earnings yield, and ignore the dividend yield. It *should/could* all come back to the shareholders eventually, one way or another.


Surely the '80 showed us that there are corporate raiders willing to buy a company to break it up... If you own shares in a company with no dividends and are willing to sell them for nothing, I'll be happy to take them off your hands... Plus dividends are not earnings, so I think you are off-topic...

acarraro: "I actually don't think that the type of investment matters that much..."

I agree. Provided it's some sort of "real" business, or investment, and not something like a bank that holds mostly nominal assets. But I would want to say that earnings *per share* of a "real" business should rise with inflation, rather than (nominal) GDP. Because even though total nominal earnings should rise with nominal GDP, so should the total number of shares outstanding.

The business cycle is trickier. Earnings should rise coming out of a recession. But nominal yields on bonds should rise too, so bond prices should fall. Nah. Too hard! Let's just stick to inflation anyway. Plus, Felix Salmon's chart covers 90 years, so the business cycle should wash out over that length of time.

I actually think that even banks make most profits from transactions rather than maturity transformation (at least across the cycle), so I would argue even their own earnings are real (as transactions will again grow with GDP)...

I am not comfortable with the more than real assumption though. Wouldn't that imply that earnings will grow forever as a percentage of GDP?

acarraro: Yep, if we think of banks as transactions services providers, as opposed to leveraged investors in nominal assets, and having real assets of buildings, networks of people, and reputation, then I would treat banks as real investments too.

"I am not comfortable with the more than real assumption though. Wouldn't that imply that earnings will grow forever as a percentage of GDP?"

Take my example of the second corporation. Assume there's no real growth. In real terms, its total earnings will stay constant over time but its shareholders' earnings will rise over time because its real debt is falling over time. So all that's happening is that the mix of shareholders' earnings vs bondholders' earnings is changing. If instead it kept the 60/40 debt/equity mix by issuing new bonds to retire shares, everything would stay constant in real terms, and would rise at the same rate as GDP. That resolves the paradox.

I think you are mistating the earnings. True earinigns would be 30$ rent + 20$ capital gain (from land appreciating) - 30$ interest = $20. Capital gain would be measured only rarely, but over the economy everybody realizes some... So there is no change in earnings at any time...

Off topic:

Nick, here my response on fragility at the limit as promised: http://coffeehouse-economics.blogspot.com/2011/08/response-to-nick-rowe-fragility-at.html

Nick, isn't one of your conclusions that rent increases 2% a year? That means rent has a compounding growth rate.

The bond which pays 5% pays the same 5% of principal regardless of the inflation. Without inflation, the bond is better, but with inflation, the corporation's equity is better. Unless you also assume that your bond proceeds are automatically reinvested in more bonds yielding the same.

Does the corporation earn a capital gain on fixed assets due to inflation? It has to replace depreciated assets at the new, inflated cost. This does not apply to farmland (or perhaps mines), but it does to firms with capital equipment. Farmland and possibly mine owners earn economic rent due to inflation: their profits would continually rise as a percentage of GDP.

If a corporation is 60/40 debt/equity, and its assets are real assets, it is a leveraged investor that is long real and short nominal. That's what makes it "realer than real".

accarraro: getting my head around this accounting business.....

For my first corporation, its nominal earnings are $30 rent + $20 capital gains on land = $50. Divide by $1,000 shares giving those shares a nominal yield of 5%.

For my second corporation, its nominal *shareholder* earnings are $30 rent + $20 capital gains on land - $30 interest = $20. Divide by $400 shares giving those shares a nominal yield of 5%.

But the real yield on shares would be:

$30/$1,000 = 3% for the first corporation.

($30rent - $30interest + (2%x$600 reduction in real value of debt))/$400 = $12/$400 = 3% for the second corporation.

Yep, it all works.

"In fact, I can't think of a reason why a share that never pays dividends should ever be worth anything other than $0!"

It's the legal right to dividends which gives value, not the actual payment or even prospect of future payment.

rogue: Yes, I am assuming that land rents (and everything) rises at 2% compounded. And I suppose I might be implicity assuming that everything can be re-invested at the same interest rates in future.

David: but the accountants are already including depreciation of machines as a cost to subtract from earnings. So the inflation on the existing machines would at least partly offset that. What I can't get my head around (and I'm not sure I want to try, because it will make my head hurt) is the interaction of depreciation and inflation, given the way accountants measure depreciation.

amv: thanks!

Nick, I don't understand your first example. You say the corporation is 100% equity financed but then you ask us to consider if the bonds of this debtless corporation do better or worse than its stock.

Fascinating article.

Is there a good article you could point to as to why we don't want to target 0% inflation, Nick? I know that economists say that a lot, but the WHY is always elusive to me, especially in light of your articles on the lower zero bound targeting thing. Couldn't we change the way central banks talk about what they're doing, and then targeting 0% wouldn't run into trouble?

JP: in my first example, my corporation issues only equity. But some other corporations may issue bonds. I've edited the post to make it clearer what I meant.

Iron troll: Thanks! I confess, that writing this post did give me a couple of second thoughts on whether 2% inflation target is better than 0%.

I can't think of any articles immediately (can anyone else?). But there are 3 main reasons:

1. The Zero Lower Bound on nominal interest rates. If we target 2% inflation rather than 0%, nominal interest rates will be (approximately) 2% higher, other things equal. So we are less likely to hit the ZLB.

2. The Zero Lower Bound on wage inflation. For *some* reason, it *seems* that nominal wages really don't want to fall. There's a discontinuity at 0% wage inflation, and it might cause big trouble, like higher unemployment, if equilibrium nominal wages need to fall but can't. (This is quite different from falling *real* (i.e. inflation-adjusted) wages, which theory says are the things that should really matter for firms and workers). If there's a 2% inflation target, wage inflation should be 2% higher, other things equal, so we would be less likely to hit this second ZLB.

3. (Maybe). We *might* want to tax holding currency, as a way to tax criminals and tax evaders, who tend to hold a lot of currency. (Or to tax foreigners, if you are an American, because foreigners hold about half of all US currency, IIRC.) And inflation is the simplest way to tax currency.

acarraro: all flippancy aside, I think it does relate to earning. I'm asking a philosophical question, not opining on investment strategies.

If a stock holder can't get his hands on the earnings (assume mere mortals here), why would a stock be worth anything other than $0 to him? All I can come-up with is that there is a sort of option value (maybe one day they will pay dividends and/or buy back shares), and because he can speculate with it because lots of other people want to speculate with it.

I'll confess that I just re-read one of Jeremy Siegel's books so maybe I'm suffering a sort of brain fever ... ;)

Iron_Troll: I can think of several common reasons.
1) Measurement Bias: substitution effects imply that an individual with fixed nominal wealth and income will be made no worse by slightly positive rates of inflation. This assumes that some prices fall at those rates (i.e. inflation dispersion.)
2) Sacrifice Ratios: If there are costs associated with getting to low inflation, you probably shouldn't bother going all the way to zero (or the zero-cost point.)
3) Stability: Economists are taught that monetary policy "stops working" when interest rates reach zero. Recent events mean these textbook chapters are being revised, but we still think that it is much less effective beyond this point. Since modern economies increasingly rely on monetary policy to stabilize the economy, we think getting close to zero inflation implies a less-stable economy.

On your closing point - if all contracts were indexed to inflation, the macroarguments for a nonzero inflation would no longer apply, right?

More generally, we model inflation as a uniform rise in the price of all non-money goods in terms of money. But aren't many (most? all?) of the economic effects of inflation that make it important, the result of the fact that some prices systematically rise faster than others?

Sorry about the flippancy.

It's hard to imagine how you couldn't get hold of the earnings/assets. Companies where control is divorced from shareholding (e.g. two class of shares with different voting rights) tend to trade at discount, so there are examples of what you say. In general they are private companies as I think there are regulations on those things at the time of listing... Some kind of investment companies always trade at discount for a similar reason (as it can be very difficult to change management). At some point some very weak form of EMH must hold and the price of the company must be losely related to the value of the underlying assets...

In general companies that are expanding shouldn't pay dividends (and tend not to). It's an implicit admission that they cannot find good investment opportunites.

I think current emerging market indexes pay only about 1% dividend yield vs 3-4% in developed markets, which makes sense... I doubt it means you want to sell EM and buy 1st world...

JW: "On your closing point - if all contracts were indexed to inflation, the macroarguments for a nonzero inflation would no longer apply, right?"

Sort of, yes. But, it's very difficult in practice to index currency for inflation. (Right now, we would want to tax US currency, so we could push US nominal interest rtaes below 0%). And, IIRC, when someone (Irving Fisher or one of his followers???) did index wages to inflation, the workers still got really upset when deflation meant their nominal wages should fall.

Most of the effects of monetary policy (the "non-neutrality" of money) come about because the *levels* of all prices don't respond immediately to *unexpected* changes in the *level* of the money supply in the short run. Those short-run unexpected level effects are different from the non-*super*-neutralities from changes in the *long-run* *fully-expected* *growth rate* of the money supply and prices.

The effects of changing the target inflation rate are long-run non-super-neutralities, rather than the short-run non-neutralities.

This post is more about the long run possible non-super-neutralities.

Simon: assume there's (say) a 0.5% upward bias in the CPI inflation rate due to the substitution effect. And assume CPI inflation is 2%, so the "true" inflation rate is 1.5%.

Does that mean we should add 1.5% to stock yields before comparing them to bond yields (assuming 100% equity finance)? Or do we stick to adding 2% to stocks, and then subtract 1.5% from both stocks and bonds to get the real yield?

My head hurts.

So basically, in an inflationary environment, a corporation's reported earnings tell us little about its actual value (even if we restrict ourselves to nonfinancial corporations). At one extreme, there is an unlevered corporation whose earnings come from realizing nominal gains on assets (e.g. one that buys and sells FIFO inventory with low turnover). In that case you have to subtract the inflation rate from the reported earnings yield to get the real earnings yield. At the other extreme is your levered corporation that never realizes gains on assets. (A more clear cut example, maybe, would be one that uses machines until they wear out and therefore couldn't take such gains in the normal course of business, unlike a landowning corporation, which could goose its reported earnings by selling old land and purchasing new land.) In that case, you have to add something to the reported earnings yield, to account for the declining real value of liabilities, in order to get the real earnings yield. I guess, for the market as a whole, it's a good rule of thumb to assume that the real earnings yield equals the reported earnings yield, on the theory that the average corporation is somewhere in the middle between these two extremes.

Surely you should use the "true" inflation number...

The difference should only be added to those istruments that are linked to the "false" inflation index (e.g. TIPS and various benefits). Nothing else has an exposure to it so they should ignore it...

"So its real earnings after real interest are $30-$18 = $12 per year."

I think you have to think in terms of Return on Asset (ROA) in this case. ROA of this company is 30/1000=3%, so the real earning of this company is 3%-2%=1%, which is $10(=$1000*1%) in dollar-value. So real earnings after real interest is $10-$18=-$8 per year, which corresponds to -stock($400)*inflation rate(2%). That is, stockholder earns 0% in nominal terms, which means -2% in real terms. However, he earns additional 2% in the form of capital gain, so his total return is 2% in nominal terms and 0% in real terms.

"I can't get my head around how depreciation and inflation interact given standard accounting practices in measuring earnings."

Well that's the rub. Yes, stockholders benefit in an inflation because the debt takes less of earnings, as you point out. So you can probably add something like 2% to the earnings yield as a rough rule of thumb.

But the interaction of the accounting for depreciation AND inventories has the exact opposite effect on owner earnings in an inflation. It basically has to do with taxes.

Do you take back 2%, 2.5%, 1.5% due to these tax effects? To really determine the effects of inflation on stocks you have to do it on a case by case basis - every business is different and some will rise faster in value than inflation, some slower, depending on the net effects of debt, depreciation and taxes, inventory policy and taxes etc. (Which is why, incidentally, you need an investment adviser who understands the long run non super neutralities of inflation on your portfolio badda boom).


For tax purposes, nominal gains are taxed, so a corporation could realize a capital gain solely as a result of inflation (this is at least part of the rationale for the lower tax rate on capital gains, although that is an imperfect adjustment).

Accaro, Patrick, accrued (but unrealized) gains on capital assets do not generally appear in earnings, or on the balance sheet (since assets are typically entered at book value). You would expect that the value of those assets would be reflected in the price of any reasonably liquid public company (witness the hefty valuation of tech companies with little or no earnings but purportedly valuable assets), but it's a real problem for valuing the shares of private companies.


While you are obviuosly correct that capital gain are not promptly entered in the the balance sheet for all companies, at least some of them will realize the multi-year gains they have hidden in their books, so that across the entire economy it will average out. Plus capital gains are only a part of the total income which mostly comes from buying and selling stuff at a fixed margin.

On the tax side, it complicates matters substantially. Many countries give personal tax credits for taxes paid by corporations (to avoid double taxation), so you should actually add that source of income to the picture (to the real yield). I think standard earning yield is post tax. I am not sure what happens in the USA to be honest...

I don't really see what is the problem here? In 60/40 corporation it is true that we have $0 profit after interest and rent, however those shareholders (not bondholders) would happen to be entitled to hold all increases in equity of the company realized by capital gains. So if the price of the land increased by 2% a year that would mean additional $20 of capital gains spread among $400 of shares - which is 5%.

Let's have an example of corporation which calls it a year and sells everything to pay off its debt to bondholders and satisfy shareholders from what is left. After first year the total worth of the land company owns is $1020. It already paid interest to bondholders from rent, that means all capital gains will be divided only between shareholders, that is 420/400 = 5% nominal yield.

Now let's change the scope to 10 years. After 10 years the company will hold 1000 acres of land worth of $1000 x 1,02^10 = $1219. Let's say that it only paid interest on bonds during the lifetime and only now it has to pay off the principal of $600. That means that original shareholders holding $400 in shares will divide remaining value of $619 among themselves which makes it $1,547 per dollar invested 10 years ago. That leaves them with yield of only 4,46% a year.

What is wrong? We did not take into account increased payments from rents stemming from increased inflation. Total lifetime value of these increases would be worth additional $31.55 in end-of-decade dollars. That would bring shareholders exactly to 5% yield as bondholders have. But maybe I did not understand the article properly. Could you please reiterate what the issue actually is again?

Andy: OK. But at one extreme you would have the corporation that sells all its assets every year, so its accounting earnings would accurately reflect its true earnings. At the other extreme you have a corporation that never sells its assets (like my first example), where you need to add 2% to the earnings yield. If the average corporation is halfway in between those two extremes, we need to add 1%.

But then most corporations are leveraged, something like 60/40? So we need to add (60/40)x1% = 1.5%?

(I'm making the "Canadian" assumption of 2% inflation.)

acarraro: it's not that simple. The substitution bias in the measure of inflation only matters when you want to turn money into consumers' utility. Both the stocks and bonds will yield 5% nominal in my first example, if land and rents are rising at 2%. So that's 3% real on both, or 3.5% real on both if you want to convert them into consumers' utility.

himaginary: that can't be right. It's borrowing at 3% real, and investing in farmland that yields 3% real, so the equity must give 3% real too.

JP: But when they report earnings per share, and the earnings yield on the S&P 500, haven't they already subtracted taxes? Isn't that yield net of corporate profits tax (but before personal income taxes)?

Georgioz: "Could you please reiterate what the issue actually is again?"

In my examples, stocks and bonds give exactly the same yield. But the reported yields on stocks don't fully reflect the true yields. The reported yield on stocks would appear (falsely) to be less than bonds.


You'd be surprised, I once looked at the accounting records of a company which held fairly substantial land tracts with resource exploration potential, which it had acquired the better part of a century ago. As a result, the book value of the land in the accounting records was, by modern standards, nominal, even though the company itself was quite valuable. In that case, the company wasn't publicly traded so it was an open question as to how shareholders should value their shares.

Obviously, most asset classes are problably shorter lived (and depreciate, so gains are less of a problem). On the other hand, the most valuable asset for many companies, namely goodwill, doesn't show up on the balance sheet of the company that generated it and is never sold (at least not until the company itself is taken over, or its business sold off).


On the tax point, you're right that shareholders generally receive preferential tax treatment on dividends relative to interest payments, but then again, companies generally receive preferential tax treatment on interest payments relative to dividends (i.e., interest payments are tax deductible). In theory, the two should cancel out (in fact, they don't, largely because a good chunk of the investor population isn't liable for taxes, i.e. pension plans and similar vehicles, or entitled to preferential tax treament, i.e., non-residents, making equity investment relatively less favourable). In Nick's example above, company 1 would pay more taxes than company 2 (because company 2 would be able to deduct interest payments in computing it's taxable income, but investors (i.e. both shareholders and bondholds) in company 1 would, collectively, pay less tax than investors in company two.

Bob (or anyone, but Bob seems so far best able to answer this): can you gives us a ballpark? If inflation is 2%, how much should we add to the earnings yield of the S&P 500 (or TSX 300) to compare it roughly to bond yields (ignoring risk and personal taxes, but remembering the 60/40 "realer than real" issue)? 1%? 1.5%? 2%? 2.5%?

Nick, this is a good summary. Imagine if the corporation issued preferred shares or convertible bonds. Man it gets interesting for aftermarket trading, but return is return based on the business, not the financing. It's obvious when you put it like that!

Regarding Nick's comment about accountants, the more frequent complaint about accountants is that the use a mix of historical and market values for various assets. Market value should represent the discounted future nominal or real cash flows of the asset. In fact, whether the cash flows are nominal or real shouldn't matter for the valuation of the asset. Basically, if you are valuing an asset using real cash flows, then discount using an inflation-adjusted interest rate. If you are valuing using nominal cash flows, then discount using a nominal interest rate. This is more of an issue for financial analysts than accountants.

Accountants base financial statements on objective information. The notion is that two accountants faced with the same facts underlying a question should basically come up with the same answer. In order for two accountants to agree, they need to have the same interpretation of the information at hand. This is why they try to base their interpretations on information that can be or has been observed, rather than based on expectations or assumptions. To an accountant, future inflation expectations are not objective.

Robillard: but there is a very very simple solution to the problem of inflation when accountants use historical values. If an asset was bought in (say) 1948, if the accountant was going to put it in the books at the historical 1948 price, it would be better instead if the accountant divided it by the 1948 CPI and multiplied it by the 2011 CPI. Perfect? No. But one helluva lot better than what they do now.

But whenever I suggest this to an accountant, they seem to go all accountanty, and wander off in strange directions with a funny look in their eyes. They talk all philosophical about market vs historical values, and how we can't just assume all prices rise at the same rate, and that there's something deeply immoral about doing this, and that before they can stop you you'll be running a Ponzi scheme. Then they talk themselves into a complete circle and end up where they started, back with the 1948 historical value.

"Since we can't make it perfect, we're not even going to try to make it better, and we just don't want to think about it, so a dollar is a dollar" seems to be the underlying philosophy.

Don't get me wrong. They are good people, and highly intelligent. Some of my best friends are accountants. But there's something strange about accountants and inflation.

"But when they report earnings per share, and the earnings yield on the S&P 500, haven't they already subtracted taxes?"

Yes, but in an inflation much of the jump in reported profits is an artifact of historical depreciation and cost-of-goods-sold expenses not keeping up. So firms are reporting unreal operating profits. But real taxes, genuine cash outflows, must be paid on these unreal operating profits. Because the tax authority has taken a greater real quantity of cash from the firm than it would have if the inflation hadn't occurred, or if depreciation and cost-of-goods-sold had been indexed, come the next period the firm has less cash available to fund ongoing operations than it otherwise would.

No one is confused here. Investors take capital gains into account -- which is all you are saying here -- nominal capital gains need to be considered, and they are. That is why one reason why stocks have lower dividend yields than bonds. They are not undervalued.

sp500 dividend yield: //www.multpl.com/s-p-500-dividend-yield/
10 year treasuries: http://www.multpl.com/interest-rate/

In terms of the on-going efforts to change the unit of account away from being money -- of course accountants aren't going to believe you. They shouldn't. CPI, PPI, and all the other deflators are subjective (hedonic) attempts to measure the benefit provided by money assuming a homogenous population. Just because you are comfortable thinking in terms of a representative agent does not really mean that you can divide by a single index to get the "true" value of money for each person or firm.

But the job of the accountant is to measure debits and credits that are extinguished with money. If you change the underlying debts to not be nominal debts, then that is the moment a different unit of measurement will be used. If wheat was lent to firms, and wheat was used to pay debts, then accountants would use wheat as the unit of account, because they would need to track how much wheat was borrowed and how much wheat was repayed.

As I was trying to say above, I think that land is actually a bad example (and tradable securities like TIPS would be even worse). In those case the full earnings would be declared (real + appreciation). I think the reason why corporate yields are real is more from flows.

No accountant will project costs and revenues (and so profit) increasing forever due to inflation as they are not interested in that calculation (they mainly care about the past). But as an investor on the corporate sector in general, I think is reasonable to assume that both inputs and outputs will generally growth at the rate of inflation. If you didn't, you'd have to conclude that corporate profits will dwindle as a share of GDP.

I also think that how you obtain the funding (equity vs credit) is in general a moot point... True you can make or lose money if the current market predition of inflation is wrong, but on average you won't. Plus duration of corporate liabilities is not that high and the corporation will have to refinance at which point it will pay higher borrowing costs.

I think that the most relevant example is a greengrocer, which buys and sells at a fixed margin. His profits will grow with the inflation rate.

rsj: "But the job of the accountant is to measure debits and credits that are extinguished with money."

OK, but suppose the earnings were in one money and the debt was in another (e.g. a foreign currency). And then the exchange rate changed, so the debt was worth less in domestic currency. Would accountants record a profit from the lower value of the debt? It's rather like that when there's inflation.

acarraro: Your greengrocer example is fine. But conceptually I like to think of there being some real asset that creates his ability to earn profits by buying and selling at a fixed margin. His shop, it's location, his own labour and skill, his reputation? It's that asset that is growing in (nominal) value when there's inflation. But a single shop and single greengrocer presumably won't be able to expand trade forever in real terms when real GDP grows. Maybe if technology makes him and his shop more productive it could. But if the real GDP growth comes for more greengrocers and more shops it won't.

Nick@01:18 PM
OK, the last sentence of my previous comment should have been:
"However, he earns additional *5%* in the form of capital gain, so his total return is *5%* in nominal terms and *3%* in real terms."

What I wanted to emphasize there is that nominal return, real return, and capital gain from inflation shouldn't be mixed up. Each return can be summarized as follows:
(Nominal return from earnings)
Total asset : Bondholder : Shareholder = 3% : 5% : 0%
(Real return from earnings)
Total asset : Bondholder : Shareholder = 1% : 3% : -2%
(Capital Gain from inflation)
Total asset : Bondholder : Shareholder = 2% : 0% : 5%

Then, and only then, you can sum up each return and calculate total return:
(Nominal return from earnings + Capital Gain from inflation)
Total asset : Bondholder : Shareholder = 5% : 5% : 5%
(Real return from earnings + Capital Gain from inflation)
Total asset : Bondholder : Shareholder = 3% : 3% : 3%

If you denote nominal interest rate as i and inflation rate as g, the above table becomes like this:
(Nominal return from earnings)
Total asset : Bondholder : Shareholder = ROA : i : (ROA-i*0.6)/0.4
(Real return from earnings)
Total asset : Bondholder : Shareholder = ROA-g : i-g : (ROA-i*0.6)/0.4-g
(Capital Gain from inflation)
Total asset : Bondholder : Shareholder = g : 0 : g/0.4

So the total return can be expressed as:
(Nominal return from earnings + Capital Gain from inflation)
Total asset : Bondholder : Shareholder = ROA+g : i : (ROA+g-i*0.6)/0.4
(Real return from earnings + Capital Gain from inflation)
Total asset : Bondholder : Shareholder = ROA : i-g : (ROA-(i-g)*0.6)/0.4

I also want to emphasize that this form of capital gain cannot be estimated (much less reaped) exactly, and can serve as the seed of bubble. For example, in the 80's the Japanese thought "Hey, those old companies have assets with a lot of fukumi-eki (discrepancy between book value and market value), so their high stock prices can be justified." No need to tell you what happened after that.

But he doesn't need to expand. He just need to keep selling the same amount of stuff every year and his profits will still growth at inflation.

I was mostly trying to separate mark-to-market assets (where yields must be nominal) with non mark-to-market (his goodwill, etc...). A mark-to-market asset will report the nominal yield even if it's a real asset.

I think in general non mark-to-market assets are bigger so the yield is real, but if you had a corporate sector whose only business is investing in index-linked bonds, it would be different.

"OK, but suppose the earnings were in one money and the debt was in another (e.g. a foreign currency). And then the exchange rate changed, so the debt was worth less in domestic currency. Would accountants record a profit from the lower value of the debt? It's rather like that when there's inflation."

No, it isn't. If a firm has foreign suppliers, and purchases from them on credit, it may owe a foreign currency debt. That would be a real contractual debt (no pun intended).

But the fact that inflation is reducing the "value" of firm's payment to its suppliers does not mean that the obligations of the firm are increasing. As long as debts are extinguished with money, as long as the debts are specified with in nominal amounts, then that is what the accountants need to keep track of.

You want to make the debts "real", so that inflation causes the firm's nominal obligations to go up -- but it doesn't. Only a renegotiation/roll-over of those obligations can cause them to change, in an economy in which money is the unit of account. And note that even though "inflation" is a convenient term, it varies significantly from geographic area to area, from type of good (oil/non-oil commodity/etc), and from person to person.

Inflation is only useful as a stylized concept -- as a heuristic to measure how someone's cost of living is changing. But each person has their own inflation -- it's not suited for the precision necessary in accounting.

Note that accountants _do_ deflate income streams all the time. For example, if a customer has a debt that the firm estimates it's not likely to collect on, it will re-value that debt. If the market price of a firm's land holdings change (whether due to "inflation" or other factors), it may re-value that asset. Assets are re-valued all the time -- but they done so in a precise way to measure how much cash-flow the firm can generate and what the book value of the firm is. They are not deflated according to how much some representative agent's utility will change from the cash-flow. Why you should you try to make the world fit the model?

Given that companies normally trade at multiple of book value, maybe accounting doesn't actually capture the entire picture.

Since we are discussing how to compare an investment with alternatives, given the (incomplete) picture accounting provides of earnings, the misgivings you might have on the numbers produced by accounting is relevant I think...

Accounting doesn't value transaction that haven't happened but are very likely to happen. If you want to value a company you need to...

Himaginary and RSJ captured it. Shareholders may realize their profits by capital gains. These may come in form of re-valuation of the company assets. On some ocasions this may be relatively easy (e.g. owning mining rights for well known amount of mineral resources) or as complex as value of brand, intellectual property etc. I believe that these factors should be calculated in the price of a particular stock. So any yield index of S&P 500 yields that takes into account both dividends paid and growth in capitalization should capture this aspect of potential shareholder gain.

Of course you may argue that evaluation of company assets by markets may not be precise - but then why do you think that they have bias towards undervaluation?

Nick, sorry for the delay, I had to think about this.

As a starting point, I'm not sure that the reported earnings yields is neccesarily the meaningful measure of the "return" on equity. After all, that's only income for accounting purposes, which (even apart from accounting shenanigans) can vary wildly (both up and down)from income, understood more generally broadly as the increase in the value of the assorted assets of the company (including cash). I'm not an accountant, but from my limited exposure to accounting, it's a much an art as a science, and depends on all sorts of subjective judgement calls. In contrast, a 5% coupon on a bond, well that is what it is.

But, to answer your question, I'm not sure there is a single right answer. I think the result you get in your initial post is a function of the company having an underlying asset that retains its real value (and, I suppose, inherently is infinitely long-lived). Land is, generally, such an asset (was it Ray Charles who said that he invested in land because "the good Lord ain't making any more of it"?), goodwill might be a similar asset (being more of a concept than a thing). But I can't think of any other classes of assets for which that would generally be true. So it's sort of an odd case.

If you had an asset that is short lived (and so, inherently, decline in real value), then I think (although I'm too lazy to do the math) you wouldn't get the same result. Think of a company whose "asset" is people on 1-year contracts (say, a consulting company which uses working capital to pay its people over the course of the year until it finishes its consulting contract ie., it has revenue of $1030, and operating expenses of $1000, to get to your result above), in that case, given your assumptions, the company's costs (salaries) are increasing with inflation, so in the case of company 2, the real return on investment for shareholders would always be zero (and 3% for shareholders of company 1). You could probably tell a similar, more generic story for a company with any short-lived assets (say computer equipment and software).

Now, I'm having trouble figuring out is how to treat the more realistic intermediate category of companies with depreciating (but otherwise long lived) assets, such as machinery or buildings. My instinct says that inflation is good for them, since there is a lag between the time when their prices increase (i.e., immediately) and when their costs increase (i.e., when the underlying asset is replaced in a few years), but I'm too lazy to do the math to show that.

In any event, the practical analysis will be complicated by the fact that most companies will hold a variety of the three types of assets described above, long term non-depreciation assets like land and goodwill, long-term depreciation assets like buildings and machinery and short-term depreciation assets (computers, software, and, conceptually at least, employment or supply contracts). It's not clear how you'd pick those various effects apart.

I would expect that the underlying value of the assets of a company would be reflected (more or less) in the stock price of a particular company (at least if its publicly traded on a more or less liquid market. On a company by company basis, you might get some sense of the effect by comparing the coupon on a newly issued unsecured bonds with 1/the P/E ratio of its common shares. Setting aside the risk premium associated with shares (and we've kind of assumed it away for this though exercise), the difference between those two results would be the unobserved "income" of the company - or at least the market's best guess of what it is.

"OK, but suppose the earnings were in one money and the debt was in another (e.g. a foreign currency). And then the exchange rate changed, so the debt was worth less in domestic currency. Would accountants record a profit from the lower value of the debt? It's rather like that when there's inflation."

Under Canadian GAAP I think they would record an F/X gain at year end (although, for tax purposes, no gain is generally realized, at least on capital account debt, until it is repaid). And while I agree that the economic effect is identical to inflation, the accounting treatment wouldn't be the same, because there's be no adjustment for the declining real value of your liabilities caused by inflation (conversely, for tax purposes, you also wouldn't report a gain, even though economically you've realized one - inflation isn't always a bad thing for tax purposes).

RSJ: You want to make the debts "real", so that inflation causes the firm's nominal obligations to go up -- but it doesn't. Only a renegotiation/roll-over of those obligations can cause them to change, in an economy in which money is the unit of account. And note that even though "inflation" is a convenient term, it varies significantly from geographic area to area, from type of good (oil/non-oil commodity/etc), and from person to person.

Nick is making the debts "real", and I confess, I had the same problem with that. But I don't think he's out of line in doing so, provided that he's assuming that interest isn't paid annually, but rather compounds over time and is only paid at maturity. Under that assumption, in an environment with 2% inflation, a $1000 bond with a 5% annual interest rate, would be equivalent to a bond with "real" principal amount of $1000 paying a 3% annual interest.

You're point about the variability of what constitutes inflation is a good one though, which is probably why accountants don't try to adjust accounting records for it in the same way they do foreign exchange gains or losses.

I think Nick is asking the following question:

When building a cashflow valuation model for a company, is it reasonable to assume that earnings will remain constant or should they be increased with inflation?

Current accounting earnings give us (imperfect) information on what current earnings are but we don't know what future earnings will be. Market tells use the value of those future earnings, but not the yield (we need to know the actual future flows to calculate that). We need to guess... Once we guess and calculate the yield, we can compare it with yields for other investments and decide what to buy.

Repeating my arguement, I think that guessing constant dollar earnings is a bad guess since it will imply ever decreasing corporate profits as a percentage of GDP.

There are many equity relative value models.

A common approach is to calculate a market-wide earning growth rate by inferring it from some ratio of historical earnings and current market cap. That market earning growth rate is used to forecast future flows company by company and to calculate a valuation metric. This makes sense when scoring different equities but doesn't really help when pricing equity vs credit vs govies.

Personally I look at four numbers: earning yield, cds yield, nominal gov yields, real gov yields.
I think of the following:

earning yield = real gov yield + cds yield + equity premium

I compare each number vs its historical average and pick the exposures I like... For euro I pick germany as the gov (and view other govies as corporates really)...

acarraro: this is what Nick originally asked: "Put it another way. if a corporation has real assets, and uses a mix of debt and equity finance, the value of the shareholders' assets, net of the debt, should be rising even faster than inflation in nominal terms. We shouldn't just add the inflation rate to the earnings yield on stocks, if we want to compare it to bonds. We should add some multiple of the inflation rate. Like (60/40) x inflation."

My point is, that this nominal increase should already be calculated into the price of stocks. So if for example analysts predict that asset value of a company will steadily rise during next 10 years (let's say the company owns a forrest that in 10 years will be ready to be harvested) and that during that time shareholders may expect 0 dividend, then such increase should be reflected in the price of stocks. So for example if you predict the forrest will have value of $1629 in 10 years and that company is fully financed by shares of current worth $1000 (no bonds) then you expect nominal yield of 5% a year.

Or in other way, in order for a company to induce shareholders to buy its shares, it has to offer them such current price of shares as to be competitive with bonds.

I agree that the value of earnings growth (and not just nominal but real as well) is built in the stock price. We are not discussing the value, but the yield. You need more information to calculate the yield (as I said above).

If you believe in efficient markets, the yield is useless since it will be the best forecast you can make (and it doesn't matter what you invest your money in anyway, you just need to leverage to get your target risk).

If you don't, the yield will give you a (I think better) statistic to decide how to invest.

In your example you forecast a value for the forest. In the same way you need to forecst the value of future earnings (and observe current price) to get the yield.

I think a reasonable forecast is that earnings will increase in line with inflation.

Georgioz: "My point is, that this nominal increase should already be calculated into the price of stocks."

Indeed it should be. Agreed. But I am coming at this from a slightly different direction. Suppose you just had data on the earnings yield of stacks compared to bonds. (Ignore risk for simplicity). If bonds had a higher earnings yield than stocks, would that mean that stocks were overvalued? (I.e. would it mean that the price of stocks was higher than it should be?) Or could inflation make this a biased comparison?

Bob: thanks for that. I'm playing it through in my mind, trying to come up with a simple example for my intuition to work on.

Hi Nick,

"Put it another way. if a corporation has real assets, and uses a mix of debt and equity finance, the value of the shareholders' assets, net of the debt, should be rising even faster than inflation in nominal terms."

I would take this further. If you think of a firm's stock as a call option on the value of its assets, then for a firm with real assets that is not in liquidation, there is always option value greater than zero. Therefore, simply looking at the earnings yield will lead you to understate the value of the stock, regardless of the capital structure of the company.

So in your 100% equity farm example, it's not true that you would be indifferent. Or rather, you shouldn't be; you should buy the stock if it is priced the same as the bond.

Sorry, I did not mean "real assets" in my previous post, I meant assets whose prices go up with inflation, like your farm.

"If there's 2% inflation, a 2011 dollar is worth 98 cents in 2010 dollars"

The financials should adjust the other way (convert 2010 dollars to 2011 dollars) since an investor would want the current year's statement to be in terms of current money. Also, IFRS already asks the accountants to adjust for inflation in some cases of hyperinflation. Usually when a firm operates in multiple countries. I don't think U.S. GAAP does, though.

I've enjoyed this conversation. While I understand that the point is to understand minutia of corporate accounting, I think it has gotten to a point of missing the big picture.

As I see it, inflation does two things: it determines the cost of borrowing, and it determines revenue growth over the corporate sector as a whole. While inflation may have little influence over the future growth of revenue for a single firm, it will impact the corparate sector as a whole.

As a simple model, consider an economy with two agents, households and corporations. Households can either buy equity or debt of the corporation. The debt cost should be something like inflation plus a term premium. Equity cost would be a little trickier but you could think of revenue increasing at real gdp + inflation or something similar. Or you could adjust to business cycle. Or adjust to historical ROE.

In the end though, I don't see why you would expect the risk premium on the bonds to be strictly comparable to the risk premium on the equity. The major risk on the bonds is that your estimation of inflation is wrong. On stocks, there are other problems. One can't compel dividends. There are problems of agency. And so on. I remember reading that the banks in 09 lost the combined earnings of a phenomenal time period, like a century, or forever, or something like that. Earnings are subject to later revision through writeoff. So you can look at the two risk premia but it is apples and oranges, and adjudging it to be misestimation of inflation seems like a daunting problem.

These articles may interest you:

Theoretically, expected return of equity can be expressed as
k = i + risk premium
It can also expressed as (from DDM; see http://en.wikipedia.org/wiki/Cost_of_capital#Expected_return)
k = dividend yield + growth rate
i - dividend yield = growth rate - risk premium
Note that this "growth rate" includes inflation rate.

Hello. This problem is addressed in a famous paper: Modigliani, F. and R.A.Cohn, 1979, “Inflation, Rational Valuation and the Market”, Financial Analysts Journal, March/April 1979, 35, 24-44

You'll be pleased to know that you are following in Modigliani's footsteps!

There is a more concise discussion of the issues in the introduction to Ritter, J.R. and R.S. Warr, 2002, “The Decline of Inflation and the Bull Market of 1982-1999”, Journal of Financial and Quantitative Analysis, March 2002, 37 (1), 29-61. They call the two phenomena that you refer to the Capitalization Rate Error and the Debt Capital Gain Error.

Earnings yield is relative to the market price of the shares, not the market price of the physical assets.

Inflation causes companies which will need to replace inventory or depreciable equipment or buildings to overstate earnings because they understate the cost of continuing in business.

Inflation causes companies with debt to understate earnings because their interest expense is overstated by the inflation rate times their outstanding debt.

Trying to use "real dollar" accounting is the road to financial hell (I think Argentina tried it.)

IMHO the charts published by Felix Salmon are the result of two factors: there is a bubble in the bond market driving the nominal yield to historic lows and the earnings being reported by many S&P 500 companies are either not real or not sustainable. For example, companies operating offshore aren't reserving for taxes payable on repatriation of profits and banks are taking reserves into income. Corporate profits are at historic highs as a share of GDP. In a world awash with capital, that is not sustainable.

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