What is investment today worth tomorrow?

Once upon a time, canals were the latest thing in infrastructure investment. During the early years of the Industrial Revolution, they made it possible to move heavy goods, like coal, from mines to factories, using a fraction of the energy required by road transport. Delicate goods, like pottery, could be shipped with little breakage. Enterprising engineers and industrialists built canals in all sorts of unlikely places. There is even a canal system that crosses from England into the Welsh mountains, complete with the towering Pontcysyllte Aqueduct, which allows canal boats to traverse the Dee valley.

I visited Pontycysyllte this summer. When I showed Nick Rowe my holiday pictures and told him about the canal, his first reaction was “this is an argument for discounting future returns”

Why? The Pontcysyllte Aqueduct opened in 1805. Within 40 years, it was becoming obsolete, as railways began to supersede canals. Pontcysyllte exemplifies the fact that investment is an uncertain business. Any kind of technological or other kind of shock can cause the returns to infrastructure investment to evaporate.

For example, suppose I build a canal, expecting to generate, if current economic trends continue, a return of $5 million per year indefinitely. What if, every year, there is a one percent chance that a technological revolution will cause the canal's future profits to fall from $5 million per year to zero? The amount that the investor can expect to receive from the canal in year t then becomes 0.99t*$5 million - the compounded effects of there being, in every year, only a 99 percent chance that the canal will continue to be useful. In a picture:

 

The expected returns shown in the picture above are not the result of a traditional net-present-value calculation. Even a person who is indifferent between receiving $1 now and $1 in the future must realize that the future is uncertain, and factor that uncertainty into his or her investment calculations - not by discounting the future, but rather by recognizing uncertainty when estimating the future benefits and costs of their investments.

My reaction to the Pontcysyllte Aqueduct was very different from Nick’s. I thought: “this is an argument against discounting.” Why? Today, the Pontcysyllte Aqueduct is a lynchpin of the local economy. The tourists it attracts are one reason why the nearby town of Llangollen is thriving. The benefits that Pontcysyllte is generating now, more than 200 years after it opened, matter.

Discounting means that far distant costs and benefits are ignored in cost-benefit analyses. For example, using an 8 percent real discount rate – the rate cautiously suggested by the Treasury Board here - a $100 benefit received 200 years in the future is not worth one penny today. Yet when I stood on Pontcysyllte Aqueduct this summer the experience didn’t feel worthless – it meant something to me. What possible justification can there be for ignoring the long-run impacts of our actions? Future lives matter too.

One argument for discounting the happiness of future generations is that they will be so much richer than us that the future costs and benefits of our actions today will not matter to them. Perhaps a real return of $5 million will mean nothing in 200 years’ time. Yet it is also possible that future generations will be poorer than us, and $5 million will mean more to them than it does to us. Indeed, if climate change, resource depletion and population growth have serious negative consequences in the medium to long term, there is a case for using a negative discount rate. That is, if our grandchildren will be significantly worse off than we are now, it's worth sacrificing $100 today to generate benefits of $90 for our grandchildren. 

Another argument in favour of discounting is “pure time preference” – the idea that having jam today is preferable than having jam tomorrow. (Until tomorrow comes and you’re hungry and wish you had some jam.)

For understanding individual decision making, the assumption of time preference makes a certain amount of sense. Empirical evidence suggests most people save little of their income for future consumption. Yet from a moral or ethical stand point, it is not clear why the happiness of future generations is of less worth than the happiness of people alive today.

The Stern Review on the Economics of Climate Change made this point quite forcefully:

Thus, while we do allow, for example, for the possibility that, say, a meteorite might obliterate the world, and for the possibility that future generations might be richer (or poorer), we treat the welfare of future generations on a par with our own. It is, of course, possible that people actually do place less value on the welfare of future generations, simply on the grounds that they are more distant in time. But it is hard to see any ethical justification for this. It raises logical difficulties, too. The discussion of the issue of pure time preference has a long and distinguished history in economics, particularly among those economists with a strong interest and involvement in philosophy. It has produced some powerful assertions. Ramsey (1928, p.543) described pure time discounting as ‘ethically indefensible and [arising] merely from the weakness of the imagination’. Pigou (1932, pp 24-25) referred to it as implying that ‘our telescopic faculty is defective’. Harrod (1948, pp 37-40) described it as a ‘human infirmity’ and ‘a polite expression for rapacity and the conquest of reason by passion’.

The Stern Review’s argument, in a picture:

The final justification for discounting the future returns from investment is the opportunity cost of capital. The funds required to build, say, an aqueduct must come either from foreign or from domestic savings. Any domestic savings used to finance an aqueduct represents money that could have been used for something else, either consumption, or other domestic investment. The opportunity cost of building an aqueduct is the returns the money could have earned elsewhere – and if the aqueduct does not generate returns at least as great as those available elsewhere in the economy, it is not worth building.

Jenkins and Kuo set out the opportunity cost argument for discounting here. Using data on the real returns to Canadian domestic investment from 1966 to 2005, as well as estimates of individuals' rates of time preference and the cost of foreign borrowing, they conclude, “The results suggest that estimates of the economic discount rate can range from 7.78 percent to 8.39 percent real”. Drawing in part from Jenkins and Kuo’s work, the Canadian Treasury Board Secretariat's 2007  Guidelines for Cost Benefit Analysis suggested the use of an 8 percent real discount rate. While this might seem high given current yields, it was actually significantly lower than the ten percent real rate of discount recommended by the Treasury Board in 1998.

The valuation of future benefits and costs is critical in any kind of long-term decision making, especially for deciding how much to invest to prevent or ameliorate the impacts of climate change. Consider, for example, an investment in preventing climate change that is expected to have some kind of payoff in 50 years’ time. With an 8 percent real discount rate, a $10 investment in a 50-year-time-horizon-project must have an expected payoff of at least $469 ($10*1.08^50) to be worthwhile. I would expect few projects to pass that kind of a test.

Recent government reports which have advocated taking action on climate change have done so on the basis of much lower real discount rates than the ones the Treasury Board recommended back in 2007. For example, a March 2016 Technical Update to Environment and Climate Change Canada's Social Cost of Greenhouse Gas Estimates had this to say on the choice of discount rate:

….there is no consensus position in the literature on the “correct” discount rate to use. Some advocate discount rates based on observed market rates of return. Others argue that it is unethical to value costs to future generations less than those to current generations.

The U.S. Group selected three different discount rates to reflect varying views in the economic literature (2.5%, 3% and 5%). The central rate at 3% is recommended by the U.S. Office of Management and Budget when a regulation primarily affects private consumption.

And then:

The Canadian Group considered how best to adapt the U.S. SCC work for Canada over the course of 2011. While alternative parameters, such as declining discount rates, were discussed, it was ultimately determined that it was more practical to adopt the U.S. results (emphasis added).

For some more background on how those US numbers were calculated, and the thinking behind the choice of discount rate, see here.

The most fundamental public policy choices we face involve trade-offs between current and future consumption: the desirability of tax cuts and deficit finance; the value of reducing greenhouse gas emissions; the advisability of investing in infrastructure. If you want to know an economist’s views on things that matter, forget about minimum wages or free trade. The most important question of all is “what is the social discount rate”? The moral argument for discounting the well-being of future generations has always been dubious. The opportunity cost argument might have seemed convincing during the heady days of the tech boom. But now that negative interest rates are a serious possibility, even the opportunity cost of capital argument for discounting seems questionable.

Comments

[Benoit Essiambre]

Exactly! These arguments have bothered me for a long time in that they are usually missing from discussions about discount rate. To me, the conspicuous presence of negative real rates in the markets gives a lot of weight to the idea of using low or even negative discounting in cost/benefit analysis.

[Benoit Essiambre]

Also, for the medium term, the presence of a large cohort of near retirees means a whole lot of people actually prefer to consume later, things they work for now.

[Frances Woolley]

Benoit - thanks. I strongly agree with your second point. It may not always be straightforward to translate production today into consumption tomorrow. There are circumstances (e.g. declining productivity, increased scarcity) where it would make sense to accept a negative rate of return in order to be sure of having something to consume later.

[Oliver]

Although sone engineering feats have retained their original use value over time, many, such as the viaduct you mention, we value for traits that at the time were mere after thoughts for those who commissioned the work. It is the pride and craftsmanship of the designers whose value becomes aparent with time but which, at the time of construction, is often overlooked and hardly ever rewarded. Having said that, hardly anything we build today will last as long as that bridge has. But good design should still aim to transcend petty, utilitarian goals even if the time scope in question has shrunk to a generation or two. Most, of course doesn't.

[Avon Barksdale]

Trying explaining the equity premium puzzle with negative rates. All risks are not perfectly diversifiable. There is a premium required to hold nondiversifiable risk. This premium is reflected in the market's stochastic discount factor - it's not the risk free rate.

It's not clear whether climate change is a hedge or a risk. We don't really even understand the direction of the effect. It's even more complicated than just deciding on the discount rate.

Given these difficulties we should be very reluctant to use government for anything but pure public goods.(And I agree that climate change is a public good problem, but most infrastructure is not.) If the Soviets couldn't even get the price of coffee right, how can anyone believe that our government experts could get something as complicated as the societal discount right?!

[Frances Woolley]

Oliver: "But good design should still aim to transcend petty, utilitarian goals even if the time scope in question has shrunk to a generation or two. Most, of course doesn't."

This is a tricky one. Here's some pictures of Ottawa's water treatment plant: http://fmatiasphotography.blogspot.ca/2010/11/lemieux-island-water-purification-plant.html. It's beautiful. A gorgeous art deco building. But it's a water treatment plant. It's hardly ever open to the public. Was it really sensible to spend so much money making a water purification plant a thing of beauty?

Then again, good design doesn't have to cost money - ugly paint colours aren't any cheaper than more aesthetically appealing ones.

[Oliver]

As an architect, I'd have to say yes, although if I were an investor I'd obviously see things differently. And I wouldn't be so certain that it cost much more than a comparable one of less beauty. Also, as the aqueduct or canals show, there can be beauty without sophisticated details. I guess societies must choose where to stuff their surplus energy. SUVs and McMansions or great(er) (public) buildings? In any case, architects are instilled with a strong sense of responsibility towards society as a whole during their education. And I think that is a good thing. But it obviously does not abrogate the uncertainty faced by the investor.

[Avon Barksdale]

"With an 8 percent real discount rate, a $10 investment in a 50-year-time-horizon-project must have an expected payoff of at least $469 ($10*1.08^50) to be worthwhile. I would expect few projects to pass that kind of a test."

What?! The stock market has produced this real return of return for nearly two centuries. Looks to me like lots of projects get funded.

[Frances Woolley]

Avon: "The stock market has produced this real return of return for nearly two centuries."

Here are some numbers for the 19th century: http://efinance.org.cn/cn/fm/The%20Equity%20Premium%20Stock%20and%20Bond%20Returns%20since%201802.pdf and the 20th century http://www.stockpickssystem.com/historical-rate-of-return/. So, yes, the past 200 years have seen not bad returns, though they haven't been consistently been above 8 percent.

For millennia before 1800, however, per capita GDP really didn't change a great deal - see, e.g. Brad de Long's estimates quoted here: https://ourworldindata.org/Economic-growth-over-the-long-run/.

IMHO anyone who figures the kinds of rates of return we've experienced over the past 200 years are going to continue is dreaming in technicolour. But I could be wrong. I hope I am.

[Frances Woolley]

Oliver: "As an architect, I'd have to say yes, although if I were an investor I'd obviously see things differently"

Economists have this idea of a Pareto improvement - something that can make at least one person better off and no one worse off. Good design is like that - it just makes life better.

Economists tend to assume that there are no $20 bills on the sidewalk, that competitive markets produce things efficiently. I'm sure if we thought long enough we could think of a reason why badly designed buildings exist e.g. ones that set cars on fire or . Probably transaction costs or signalling or something.

[Frank Restly]

Avon,

"What?! The stock market has produced this real return of return for nearly two centuries. Looks to me like lots of projects get funded."

I don't think you are factoring in survivor bias. Yes, equity market indices have delivered returns averaging about 8%. The only problem is that the makeup of those indices changes over time.

The failure rate using a 50 year time horizon is pretty remarkable. Here are the DOW Jones Industrial Average members from 50 years ago (1967):

https://en.wikipedia.org/wiki/Historical_components_of_the_Dow_Jones_Industrial_Average

Allied Chemical - Merged to become Allied Signal in 1985
Aluminum Company of America - Still around today
American Can Company - Renamed Primerica in 1991 and eventually became part of Citigroup
American Telephone and Telegraph - Still around today
American Tobacco Company - Dissolved under anti-trust
Anaconda Copper Mining Company - Sold to Atlantic Ritchfield in 1977
Bethlehem Steel - Dissolved in 2003
Chrysler Corporation - Filed for bankruptcy in 2009, bailed out by U. S. government
DuPont - Still around today
Eastman Kodak - Filed for bankruptcy in 2012
General Electric Company - Still around today
General Foods Corporation - Purchased by Altria in 1985
General Motors Corporation - Filed for bankruptcy in 2009, bailed out by U. S. government
Goodyear Tire and Rubber - Still around today
International Harvester - Dissolved in 1984
International Nickel Company - Purchased by Vale Canada in 2006
Johns Manville Corporation - Purchased by Berkshire Hathaway in 2001
International Paper Company - Still around today
Owens Illinois Inc. - Still around today
Procter and Gamble Company - Still around today
Sears Roebuck Company - Purchased by K-Mart in 2004
Standard Oil of California - Renamed Chevron, still around
Standard Oil of New Jersey - Renamed Exxon Mobile, still around
Swift and Company - Purchased by JBS in 2007
Texaco Inc. - Merged with Chevron
Union Carbide - Purchased by Dow Chemical in 1999
United Aircraft - Renamed United Technologies in 1974, still around
U. S. Steel - Still around
Westinghouse Electric - Renamed CBS corporation in 1997, still around
F. W. Woolworth - Renamed Foot Locker in 1999, still around

6 of the 30 (20%) companies from 1967 in the DOW were dissolved or went through bankruptcy (International Harvester, General Motors, Eastman Kodak, Chrysler, Bethlehem Steel, and American Tobacco). American Tobacco was actually split into several companies though I have no idea how shareholders in the overall company were treated during the dissolution.

Using a 20% failure rate over a fifty year horizon, lost equity (from failures / bankruptcies) amounts to about a 0.37% annual loss assuming equal sized companies. The failure rate for smaller companies is much higher.

[Avon Barksdale]

Frank,

"The failure rate using a 50 year time horizon is pretty remarkable. Here are the DOW Jones Industrial Average members from 50 years ago (1967)"

That's called economic growth. I'm talking about the premium required to hold equity.

[Avon Barksdale]

Frances,

“So, yes, the past 200 years have seen not bad returns, though they haven't been consistently been above 8 percent.”

Careful with difference between ex-post sample path results vs ex-ante expected return. The equity premium puzzle is a robust and persistent issue – good luck does not seem to solve the problem.

“IMHO anyone who figures the kinds of rates of return we've experienced over the past 200 years are going to continue is dreaming in technicolour. But I could be wrong. I hope I am.”

No Frances, think Finance 101 – the expected return on equity is a statement of risk aversion encoded in the stochastic discount factor. The return is for holding risk, not for expected high economic growth. The stochastic discount factor is time varying and by just the right amount to explain the variance in returns (and the high volatility of the stock market). If the equity premium puzzle is real and not just luck, there is little reason to think that this generation or future generations will require less expected return for holding nondiversifiable equity risk. Time variation of the stochastic discount tells us to expect low returns on equity during good economic times. It’s during the bad times that we get an extra kick on the premium for holding risk. (Few people could hold equity risk in 2009 so the premium had to be high – a period of high expected returns. Boy, it sure was!)

Economic growth is another matter. You might be right that the economic growth we saw over the last 200 years will not be repeated. OK, but why? Is it that we’ve run out of ideas? I doubt it. Is it some new economic phenomenon of secular stagnation? Maybe, but there really is no theory there, it’s pretty hand-wavy. Or is it the regulatory-turn-crony-capitalist state? When it takes longer to get an oil pipeline approved, let alone built, than it took to build the transcontinental railway by hand a century and a half ago, when it takes our government longer to simply buy fighter aircraft than it took to win both World War I and War War II combined, it’s pretty clear where the problems are.

[JKH]

“Discounting means that far distant costs and benefits are ignored in cost-benefit analyses. For example, using an 8 percent real discount rate – the rate cautiously suggested by the Treasury Board here - a $100 benefit received 200 years in the future is not worth one penny today. Yet when I stood on Pontcysyllte Aqueduct this summer the experience didn’t feel worthless – it meant something to me. What possible justification can there be for ignoring the long-run impacts of our actions? Future lives matter too.”

Those impacts are not ignored.

The fact that today’s returns were not reflected materially in the original value of the original investment is not an argument against discounting.

Today’s returns, if correctly foreseen, would have been discounted correctly when the investment was old enough, or at any older point (i.e. sufficient time had passed)) to make today’s returns economically (and mathematically) relevant. And that value would have been reflected materially in the capital value of the investment at that time – and increasingly at subsequent times - not in its value at the time of the original investment.

In other words, updating of a successful long term investment’s value over time reflects today’s returns in a very relevant, rational, and quite sufficient way.

[Oliver]

Economists have this idea of a Pareto improvement - something that can make at least one person better off and no one worse off. Good design is like that - it just makes life better.

Economists tend to assume that there are no $20 bills on the sidewalk, that competitive markets produce things efficiently. I'm sure if we thought long enough we could think of a reason why badly designed buildings exist e.g. ones that set cars on fire or . Probably transaction costs or signalling or something.

Thanks for your replies. I realise I'm way off topic.

I think my point is that good design cannot be mathematically calculated and thus not discounted in any meaningful way. Clients may wish for it but chances are, they won't know whether or not they've got it even if it hits them straight in the face. And your question, as I understood it, is not whether it makes current generations better off, but whether it will make future generations better off as well. You can make a survey to figure out the prior but it takes an art, a bunch of experience and a bit of faith to deal with the latter.

The reason badly designed buildings exist, imo, is because those who commissioned and / or designed them aren't good at what they do, probably because they're busy filling out an excel sheet in search of THE discount rate.

That's not an argument against one or the other, though. Just a reminder that investment requires looking beyond excel sheets.

[Frances Woolley]

Oliver: "I think my point is that good design cannot be mathematically calculated and thus not discounted in any meaningful way."

There is an amount that people are willing to pay for good design. That suffices to put a value on it. IKEA could probably tell you down to the last penny the value of good design, because that's what makes people pay good money for collections of laminated particleboard.

The problem is that it's really hard to know when you're buying something, especially a big piece of infrastructure, whether or not you've getting good design. For example, I was staying at a apartment in a new condominium building in Waterloo a few months ago. The apartment had a sliding door - the kind of door that should open onto a balcony - but it opened out onto thin air - there door had been installed where a window should have been. Now it didn't open all that far, and there was some kind of bar across the doorway, but a child could easily have slipped through it. Mindbogglingly, spectacularly bad design. But bad design that could be priced (risk of death from child falling out of window*value of child's life).

Moreover, the fact that something is difficult to price is not an excuse to value it at nothing (or infinity). "We don't know the long-run health impacts of oil spills on local communities, so we'll just ignore that risk and those potential consequences." Cost benefit analysis is all about trying to put prices on things that are extraordinarily difficult to price.

for example, here in Ottawa, with our long, cold winters, we get a lot of ice building up on the sidewalks. It's dangerous. People fall and seriously injure themselves. The cheapest way to get rid of ice is by dumping salt on it. (Grit, a grit/salt mix, and expensive non-toxic stuff also work). Salt makes walking in winter much safer, but it's also seriously damaging to the environment. People's health versus the environment versus the cost of switching to a less toxic method of ice removal? Even everyday, relatively uncomplicated cost/benefit analysis questions involve putting values on things that are hard to price.

[Oliver]

Thanks again! I think I agree with all of that. Ikea is a good example! The sliding door sounds more like criminal neglect though. It certainly wouldn't pass any building inspection here in Switzerland. And btw., bad design can be quite expensive: http://www.housebeautiful.com/design-inspiration/house-tours/g3501/donald-trump-penthouse/?zoomable

[Oliver]

Architecture and engineering works are a bit more difficult than furniture, though. They tend to be around for a lot longer.

[John Hulls]

The most difficult economic task is to determine the actual long-term benefits of infrastructure. For instance, if one takes the Hoover Dam, the overall impact and societal benefit far exceeded the initial planning. Thanks to a 1933 'Fortune' article, we can see the contemporaneous understanding of the massive project. At the height of the depression, it provided thousands of jobs, and only cost the equivalent of $1 per head of the U.S population and still makes millions of dollars a year from power sales. For more details and links, see my blog,which I have long ignored, at: somewhat logically.com/?p=523 'Dam the Economists!. Far too many economists re-enact the fable of the wise blind men's wildly incorrect descriptions of an elephant by failure to look beyond their own highly constrained focus.

John Hulls

[Civilitas]

While I am generally a huge supporter of infrastructure spending, not all infrastructure spending is good or will be useful for a long time to come. Bridges to nowhere come to mind, as do airports built too far from cities... Looking at very successful long-term projects like the Hoover Dam or the Ponty canal is just a form of selection bias, bearing no necessary relationship to the overall average useful of infrastructure over long periods of time.

I completely agree that "time value of money" should not apply to social discount rate discussions. Governments, by definition, should not have "time value", because citizens tomorrow are equally citizens compared to today.

It strikes me, however, that the "technology uncertainty" argument described at the top of the post is really just a special case of the "opportunity cost" discussion at the bottom: should you spend your resources on project X today, which is based on technology T, or should you wait until tomorrow for project Y, which will be much better/more efficient/etc. because it is based on new technology U, which is not currently available. You have to make a choice today, despite uncertainty. Using a "social discount rate" is just a stand-in for that uncertainty, and picking a specific rate is an exercise in guessing what the real rate of change in the efficiency of technology actually is on average. Similarly, should you build a road today that will have a 10-year life, or a wind turbine today that will have a 25-year life? Will the benefits of the road to the economy over the next 10 years outweigh the benefits of the wind turbine over 25 years? There is uncertainty because the realization of the benefits depend on a host of factors that the decision-makers don't control, not least of which is changing technology that will affect either/both.

As an aside, I would argue that using stock market returns to equity as the long-term real rate of return on risk is a biased answer at best. The stock market represents a small fraction of economic activity, and in fact only a privileged and highly de-risked part of it. Private business investments (think small business and venture funded start-ups) have much higher risks and costs of capital, and government investments (think R&D grants) have risks so high that no business will take them, so what is the cost of capital on those? On the other hand, debt capital is cheaper than equity, and why should those even lower-risk (but NOT zero risk) investments be ignored? If you want to use the average, economy-wide long-term return to capital as a benchmark for the social discount rate, then you don't get there by looking at the stock market.

[Avon Barksdale]

Civilitas

"The stock market represents a small fraction of economic activity, and in fact only a privileged and highly de-risked part of it."

What? De-risked? Privileged?

"Debt cheaper than equity"

No. See Modigliani-Miller. There's no free lunch in financing decisions.

[Frank Restly]

Avon,

Modigliani-Miller

https://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem

"This means that there are advantages for firms to be levered, since corporations can deduct interest payments. Therefore leverage lowers tax payments. Dividend payments are non-deductible."

[Avon Barksdale]

Frank

Read the ifs that make MM hold. Understand how MM is the background theorem to understanding financing decisions. When people say debt is cheaper than equity, they usually have no idea what they're talking about.

More to the point, MM is more generally about the irrelevance of total return to how you split the risk. Government distorts risk taking all the time - see CMHC. But in the end, the total return is determined by the firm's opportunities and the management of those opportunities, not on how the firm packages insurance contracts.

[Frank Restly]

Avon,

With no government at all, what is the distinction between debt and equity?

That has always bothered me about most definitions of the Miller-Modigliani theorem.

https://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem

"The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed (debt or equity)."

Well if we eliminate bankruptcy costs, how are debt and equity distinguishable from each other?

[Frank Restly]

Are there any distinguishable characteristics of debt and equity that identify each in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information? If not, then the theorem is meaningless.

[Frances Woolley]

Frank - I'm with you on debt v. equity. I feel the equity premium is one of those "all swans are white" type theorems.

[Avon Barksdale]

Frank

No. The theorem is not meaningless. It provides the background to understand why and when financing decisions matter.

Debt and equity are distinguishable even in the limit of no taxes and bankruptcy costs. They are composed of different Arrow securities. Imagine a firm that goes bankrupt with a combination of debt and equity. If there is enough recoverable value for the debt holders, they will be made whole. Equity gets nothing. But this is just splitting the risk. It makes no difference to the value of the firm. In fact you can think of equity as simply a call option on the value of the firm.

Modigliani-Miller sharpens your thinking so that you don't fall into fallacy traps. Yes, in the real world financing decisions matter, but if you don't use the logic of Modigliani-Miller you won't understand why, or the particular circumstances of the firm's opportunities.

Statements like "debt is cheaper than equity" in an economic context is meaningless. In equilibrium all risk is held at its marginal rate. The question to answer is: Who is holding the risk? In government, it's the taxpayer by force so you need to be careful when you say that the equity premium doesn't matter for government project discount rates. That premium is what voluntary investors would have required to hold nondiversifiable risk.

[Avon Barksdale]

Frances

Seriously, you think that the premium for holding equity is some silly misspecified statement?

Trying reading the paper Discount Rates by John Cochrane (2011), or basically anything by Lars Hansen. Come on this is serious economics. Understanding the nature of the market's stochastic discount factor represents some of the best research in economics in the last 40 years. And we've learned a great deal in the last 20 years. Some of the best minds in economics work in this area.

[Frances Woolley]

Avon - "Seriously, you think that the premium for holding equity is some silly misspecified statement?"

No I do not think that.

For hundreds, perhaps thousands, of years people in the northern hemisphere confidently believed "All swans are white", because they'd only ever seen white swans. Then people from the northern hemisphere went to Australia and encountered black swans and realized that they'd been wrong all along. My gut feeling is that the equity premium is something like that: it's a phenomenon that probably holds over the past couple of hundred years of stock market and and bond returns (though there are people who would debate that). Doesn't mean it will always hold.

[Avon Barksdale]

Frances,

Economics is a science - so yes, theories are falsifiable. The size of the premium for equity (nondiversifiable risk) is time varying - we already know that there are periods of low expected returns and high expected returns - there is time series predictability in asset returns. I am not sure what "theorem" you are referring to. It is an empirical fact that equity commands a premium, so lets' try to explain it. Maybe society will change so much in the future that people will not require much compensation to hold that type of risk, or maybe intergalactic trading will diversify all risk, but there is no theorem that is violated here. Modigliani-Miller still holds.

But take a look at the financial crisis and the aftermath. These ideas say that starting in 2009 that the expected return would be high. Risk on. Lot's of people could see that 2009 was the buying opportunity of a lifetime, but when you are losing your job, house - and if an American - your healthcare, then you don't lever up to buy stocks. That's rational - and that behaviour generates the high return environment. Economists who really understood asset pricing and could afford to take risk in 2009 levered up. So while your gut says that people are going to change their appetite for risk and universally lever up in periods like 2009 and thereby reduce the premium for equity, my gut says: I doubt it.

[Frank Restly]

Avon,

"Debt and equity are distinguishable even in the limit of no taxes and bankruptcy costs. They are composed of different Arrow securities. Imagine a firm that goes bankrupt with a combination of debt and equity. If there is enough recoverable value for the debt holders, they will be made whole. Equity gets nothing."

Now wait a minute. In the first sentence you have accepted that there are no bankruptcy costs to the firm. In the third sentence you acknowledge that debt holders in a bankruptcy will be made hole by the firm with recoverable value. Which is it?

"It is an empirical fact that equity commands a premium, so lets' try to explain it."

Based upon what? There are no examples that I can think of where debt and equity coexist, but there are no bankruptcy laws or taxes (We live in a world of white swans). Where is the real world example where all the extraneous stuff (taxes, bankruptcy, agency costs, etc.) does not exist?

[Avon Barksdale]

Frank,

“Now wait a minute. In the first sentence you have accepted that there are no bankruptcy costs to the firm. In the third sentence you acknowledge that debt holders in a bankruptcy will be made hole by the firm with recoverable value. Which is it?”

You misunderstand bankruptcy and bankruptcy costs. MM doesn’t require the absence of bankruptcy, it requires the absence of bankruptcy costs. Bankruptcy costs are all the lawyers I have to pay, the court time to sort out claims, the delay in receiving what I’m owed, etc. In the real world, bankruptcy tends to be a costly process, which decreases the value of debt financing. Yes you will have a claim on the residual value of the firm, but you might not see it for 5 years and only after paying a legion of lawyers.

Equity does command a premium. Holding the stock market has generated significant out performance from holding (near) riskless government bonds or inflation protected treasuries. Equity generates a massive premium over the risk-free rate. For the last 50 years, it’s been about 9% and it’s been in that ballpark for the last 200 years. Why does equity command such a high premium over the risk free rate? Don’t get confused, a risky firm can’t avoid it’s true cost of capital by becoming debt financed. In the limit of 100% debt financing the firm’s interest rate will reflect it’s risk. Only the banks can do this sleight-of-hand because they have explicit and implicit government guarantees on debt, but not equity. CMHC is a great example of the government distorting the capital structure of our banks to get votes. There is a reason why Canadian bank stocks generate about 7% per year, but its debt pays peanuts – an nice big fat insurance contract that will always pay off because the government has the power to tax. Have you ever wondered why banks are almost 100% debt financed? In banking, financing really does matter a lot! The logic of Modigliani-Miller says look for where the body is buried (psst... the grabbing hand of government).

The problem is to understand the magnitude of the premium for equity? Is it just good luck? Apparently not, this premium is persistent. To quantify the level of risk aversion implied by the equity premium puzzle, apparently investors would prefer a certain payoff of $51,300 to a 50/50 bet that pays either $50,000 or $100,000. Talk about a high discount rate! The most confusing thing about the stock market is that on the face of it, it is not risky enough to command the premium in receives. On a risk-reward basis, the stock market appears as the absolutely best deal going. Why on earth don’t people give up homeownership and lever up to buy the stock market instead?! However, when you start thinking about the macroeconomic foundations of the stochastic discount rate, allowing for habit formation, the use non-time separable utility, and the time variability of the stochastic discount rate, we can account for why the premium will be much higher than one might naively expect. Crashes might be rare, but they are scary, and people need to be paid to hold that earthquake risk.

[Civilitas]

Avon, Modigliani-Miller says that capital structure is irrelevant to the valuation of a firm, absent tax effects, bankruptcy, etc. It does NOT say that the nature of a security (i.e., debt, equity, pref equity, mezz, etc.) is irrelevant to its price. Each security has a different price precisely because of the specific bundle of characteristics and risks it represents.

You argued in your (much) earlier post that social discount rate should be related to the equity risk premium. My point was and is that the equity risk premium is bundled up closely with the nature of the security itself (i.e., being a publicly traded, relatively liquid investment asset called an equity, that has a very specific bundle of rights and risks attached to it), which has very different characteristics than the many other financial assets available in the economy (many of which have bundles of risk that are perceived as "riskier", and many of which are perceived as "less risky"). The public equity market is factually and demonstrably a small fraction of the financial assets available and traded in the economy, and it still is not clear to me why that particular slice of the asset world should be used as a price guide for the social discount rate.

In addition, I would point out that equities are purchased and traded by private individuals, who inherently have time value of money and liquidity preferences that are also priced into equities, given their specific limitations and characteristics (e.g., in the event of a stock market crash, liquidity may disappear at the exact moment it is most desired, and therefore the risk of that lack of liquidity is priced into the equity). As was discussed by Frances and other commenters, it is arguable that social discount rate should not include a time value of money, and should not include a liquidity premium.

[Avon Barksdale]

I never said the the equity premium should be the discount rate for government investment. I said that it's hard to determine, that the Soviets couldn't get the price of coffee right and that we should be cautious about using government power.

I said that it's not true that at 8% little would get funded. The stock market is case in point.

I don't know what the societal discount rate should be - hence the monstrously difficulty in determining the right price for carbon. I think that the stock market offers a guide for nondiversifiable risk that pays off in good times and does horrible in bad times.

[Avon Barksdale]

"it is arguable that social discount rate should not include a time value of money, and should not include a liquidity premium."

It's so much easy when it's other people's money and you don't have to ask for it. Isn't it?

[Frank Restly]

Avon,

"MM doesn’t require the absence of bankruptcy, it requires the absence of bankruptcy costs. Bankruptcy costs are all the lawyers I have to pay, the court time to sort out claims, the delay in receiving what I’m owed, etc."

And paying back creditors isn't a bankruptcy cost incurred by the firm?

"Equity does command a premium. Holding the stock market has generated significant out performance from holding (near) riskless government bonds or inflation protected treasuries."

Miller Modigliani isn't about the difference between equity and riskless government bonds. I agree that corporate equity AND bonds trade at a discount to government bonds as they should - both involve taking risk. I thought that you were treating the equity premium as the premium (if it exists) between equity shares sold by a firm and bonds sold by the same firm.

In my opinion, without taxes, bankruptcy costs (including the legally mandated pay back of creditors), agency costs, etc., there is no difference between corporate equity and bonds hence there is no corporate equity / bond premium.

[Avon Barksdale]

No Frank, different Arrow securities come at different prices. The firm is free to package its payoff anyway it likes. The firm could finance itself by only using derivatives. MM is much broader than equity vs debt. It is the irrelevance off ANY financing strategy including the irrelevance of dividends.

The expected return on each instrument will be different, depending on how the instrument absorbs the firm's risk, but the collective payoff from buying all the instrument is the same regardless of how complicated the instruments are. The firm's value is not altered by the repackaging of its cash flows.

[Henry]

MM wasn't much use to the "masters of the universe" at Long Term Capital.

[Henry]

The discount rate is not all that is relevant (if it's relevant at all given the radical uncertainty of the real world). The time horizon is also of some relevance if you are going to play the discounting the future game. (And of course, the higher the discount rate, the less relevant are the far out years.)

Who, 200 years ago, would have thought about (or be concerned about) possible changes to technology or that a transport system would become a tourist attraction?

The capitalists of the day looked at their then present transport needs, saw that canals were down on the cost curve, and went for it. They were probably more concerned with whether the water would keeping filling the canals than the discount rate.

And who would these days build a new canal system to establish a tourist industry?

The glorious thing about capital is once it's in it's cost is sunk - and there's no going back.

[Frank Restly]

Avon,

It's a simple question - in the absence of bankruptcy, taxes, agency costs, etc., (basically everything that MM excludes) do equity shares of a firm command a premium over bonds issued by the same firm? If so, what is the source of that premium?

[Frank Restly]

Avon,

One possible source of the equity premium (meaning shares are more expensive to issue than bonds) is a central bank as lender of last resort - even in the absence of taxes, bankruptcy, etc. Obviously most central banks stay away from lending directly to non-banking enterprises - they lend to commercial banks who in turn lend to private firms. But with a fixed intermediation cost charged by commercial banks competing against each other, this can put an upper limit on the returns granted to corporate bond holders. There is no share holder buyer of last resort, and so equity buyers can demand a higher return than bond holders.

I was kind of hoping you would come to this realization on your own.

[Avon Barksdale]

"It's a simple question - in the absence of bankruptcy, taxes, agency costs, etc., (basically everything that MM excludes) do equity shares of a firm command a premium over bonds issued by the same firm? If so, what is the source of that premium?"

In a mixed capital structure, equity stands last in line in bankruptcy, but first in line for unexpected positive shocks. The risk in the firm is split differently between the equity holders and the debt holders (decomposition in terms of their Arrow securities are different) in such a way that the equity holders absorb most of the risk in the firm. That does NOT change the value of the firm. The firm can split the risk anyway it likes, but the firm's value comes from the TOTAL risk in the opportunities that the firm has acquired and manages. This has nothing to do with the lender of last resort or central banks.

For crying out loud, work through the proof of MM!

My background is theoretical physics. As the financial crisis got going in late 2007 and early 2008, I started to get interested in economics. Unlike the bullshitters in these comments (and I mean this term in the Harry Frankfurt sense, not in any excessively pejorative sense), I decided to read because I knew that I knew nothing. So I read graduate level micro, graduate level macro, graduate level econometrics, graduate level corporate finance, and the coalface literature of asset pricing and mathematical finance.

As I've grown older, I have come the the realization that Harry Frankfurt is spot on when it comes to the public who comments on stuff they haven't bothered to understand beyond the Wikipedia page:

"Bullshit is unavoidable whenever circumstances require someone to talk without knowing what he is talking about. Thus the production of bullshit is stimulated whenever a person’s obligations or opportunities to speak about some topic are more excessive than his knowledge of the facts that are relevant to that topic. This discrepancy is common in public life, where people are frequently impelled - whether by their own propensities or by the demands of others - to speak extensively about matters of which they are to some degree ignorant. Closely related instances arise from the widespread conviction that it is the responsibility of a citizen in a democracy to have opinions about everything, or at least everything that pertains to the conduct of his country’s affairs. The lack of any significant connection between a person’s opinions and his apprehension of reality will be even more severe, needless to say, for someone who believes it his responsibility, as a conscientious moral agent, to evaluate events and conditions in all parts of the world."

And this is why you don't see the public bullshit about the Higgs boson or SO(10) grand unification, but they love to do so about discount rates.

[Frank Restly]

Avon,

"In a mixed capital structure, equity stands last in line in bankruptcy, but first in line for unexpected positive shocks."

MM specifically excludes bankruptcy costs. Those bankruptcy costs include legal fees as well as transfer of assets from the firm to the bondholder in the event of a bankruptcy. As such, without bankruptcy, both debt and equity stand side by side / hand in hand.

"As I've grown older, I have come the the realization that Harry Frankfurt is spot on when it comes to the public who comments on stuff they haven't bothered to understand beyond the Wikipedia page"

Fine, provide a link to a source that describes the bankruptcy costs identified in MM are limited to legal fees only as you seem to think.

[Avon Barksdale]

Frank,

Bankruptcy costs are paid by the debt holders. In the real world, the benefit of the tax deductibility of debt is partially offset by the bankruptcy costs that debt holders have to pay.

MM is a risk SPLITTING theorem, not all-forms-of-risk pay-the-same theorem. MM doesn't assume no uncertainty and it doesn't assume the absence of bankruptcy.

All payoffs from the firm can decomposed into Arrow securities - you get paid $1 contingent on some event. All claims on the firm can be decomposed this way. All forms of funding are just packages of Arrow securities. For a long time people thought that the firm's value would depend on the packaging. Using arbitrage arguments, Modigliani and Miller showed that repackaging Arrow securities cannot affect the firm's value. The capital structure of the firms is simply how the firm packages its cash flows. Repackaging the Arrow securities into bonds, commons stock, swaptions, callable bonds, preferred shares - none of it matters to the value of the firm. Of course the expected return on each weird instrument will be different because they hold different components of the firm's risk. MM is about the irrelevance of splitting risk to total firm's value, it does not say that all forms risk get paid the same.

If you really care to understand how this stuff works, try Financial Theory and Corporate Policy, by Copeland, Weston, and Shastri.

[Henry]

"So I read graduate level micro, graduate level macro, graduate level econometrics, graduate level corporate finance, and the coalface literature of asset pricing and mathematical finance. "

AB,

Which are all based on a set of narrow assumptions and axioms designed to met the needs of tractability rather than reality.

[Henry]

And if anything satisfies Frankfurt's definition of "bullshit", I would say it's the literature of modern economics.

[Avon Barksdale]

Henry,

So, you've decided that economics is garbage. What do you think of black hole thermodynamics? How do you feel about cosmic inflation? What do you think about E8xE8 heterotic string constructions?

Because economics touches all of our lives, as a citizen of the world, you think that you can understand economic truth through introspection and "common sense" alone. No you can't - that's what Frankfurt is calling bullshit on. While it appears to you that you can pass judgment on economics without actually working through it, that makes as much sense as trying to pass judgment on topics in theoretical physics by your gut feel.

"It takes considerable knowledge just to realize the extent of your own ignorance." - Thomas Sowell

[Henry]

AB,

I don't have a degree in physics, so I can't answer the questions you ask, rhetorical as they are. I do however have a degree in economics, not that makes me an expert in the subject, very far from it. I have some knowledge, so I guess following Sowell's epigram, I have only a limited knowledge of the extent of my ignorance. Be assured, I have every intention of surveying the extent of my ignorance. Having returned to the study of economics I find that the space is populated by physicists and mathematicians who have attempted to apply the "scientific way" of thinking to economics, leaving the field of economics bereft of any economic sensibility. Economics is not about the construction of elegant and sophisticated abstract mathematical models which by and large bear little resemblance to reality.

Frankfurt says of the "Bullshitter":

"He does not care whether the things he says describe reality correctly. He just picks them out, or makes them up, to suit his purpose."

I would assert that, on several levels, this applies to modern economics.

[Henry]

And AB, if you really want to learn something about economics, I suggest you read Thomas Sowell's "Says Law - An Historical analysis."

[Avon Barksdale]

Henry,

Economics is a beautiful and subtle subject. All models are wrong, some are useful. Don't let that distract you from the beauty and insight that modern economics teaches us.

[Henry]

Things of beauty and which inspire us belong in museums and galleries.

A painter of houses does not need to be able to reproduce the Mona Lisa.

A capitalist of the 19th century did not need the calculus of modern financial theory to decide whether to build a system of aqueducts and canals. As I suggested above, he was probably more interested in whether the water would continue to fill his waterways.

[Avon Barksdale]

Henry,

“Things of beauty and which inspire us belong in museums and galleries.” That’s ignorant anti-intellectual nonsense.

Modern economics helps us understand optimal decision making. The 19th century decision makers didn’t require modern models to decided what to do. Our modern models explain why they made the decisions they did.

Think Poker. Poker is an economics problem masquerading as a game. Solving this problem is an incredibly complicated dynamic program – the same methods used in economics. Now, most good Poker players know little about dynamic programming or the approximate dynamic programming methods used to solve the game out to finite horizons. But, good Poker players BEHAVE as though they do know how to solve these complicated math problem. Through hard-won experience and a good memory good Poker players build mental heuristics that come close to the actual mathematical solution. The same thing happens with investing. Of course few investors, 19th century or otherwise, solving dynamic programming problems, computing Gittins indices, or solving shortest path problems to optimality, but their collective behaviour is like the Poker player – they largely behave as though they are solving these hard math problems. That insight allows us to ask deeper questions and understand the underlying structure of the problem that investors are solving.

A great practical example of this type of thinking involves discounting. In the 1980s, the US government introduced rebates for high grade residential insulation to help reduce energy costs for homeowners. Based on a simple discount model, the US government set a rebate policy. To their surprise, the program was really unpopular – few people/builders used the program. Later, proper economic analysis showed that there is a large option value in the decision because the decision is irreversible and energy prices are highly volatile. When you include the value sitting in the option, you can see that people were making optimal decisions in not participating in the rebate - the rebate was peanuts compared to the value of the option. Even though people didn’t solve complicated dynamic programs at the kitchen table, they largely behaved as if they did.

[Frank Restly]

Frank,

"Bankruptcy costs are paid by the debt holders. In the real world, the benefit of the tax deductibility of debt is partially offset by the bankruptcy costs that debt holders have to pay."

The tax deductibility of debt is a benefit to the debt seller (firm). It stands to reason that the bankruptcy costs (referenced in MM) are those that are seen by the debt seller (firm) as well. Benefit for the firm (tax deductibility of interest) is partially offset by cost to the firm (transfer of assets during bankruptcy).

[Avon Barksdale]

Frank

The tax deductible interest payments lowers the cost of capital to the firm by lowering the effective interest rate. But the anticipated bankruptcy costs in the event of bankruptcy means that the lenders will demand a higher interest rate as compensation, which raises the firm's cost of capital. That's the partial offset.

[Henry]

"Our modern models explain why they made the decisions they did. "

AB,

There is good deal of assertion making and circularity in your argument in this post.

[Avon Barksdale]

Henry

Glad to see you're one of the smartest people on the planet. Make sure to publish your insights on economics somewhere - it'd be a shame if humanity doesn't get to learn from it.

[Frank Restly]

Avon,

http://www.investopedia.com/walkthrough/corporate-finance/5/capital-structure/bankruptcy-optimal-structure.aspx

"For each company there is an optimal capital structure, including a percentage of debt and equity, and a balance between the tax benefits of the debt and the equity. As a company continues to increase its debt over the amount stated by the optimal capital structure, the cost to finance the debt becomes higher as the debt is now riskier to the lender."

The risk of bankruptcy increases with the increased debt load. Since the cost (to the firm) of debt becomes higher, the WACC (Weighted Average Cost of Capital) is thus affected. With the addition of debt, the WACC will at first fall as the benefits are realized, but once the optimal capital structure is reached and then surpassed, the increased debt load will then cause the WACC to increase significantly."

Notice that the bankruptcy costs (discussed in this article) are those realized BY THE FIRM (higher interest costs once the debt load exceeds what is considered it's optimal debt load).

Or if you prefer:

http://albertbanalestanol.com/wp-content/uploads/cfmsc-chapter-1.pdf
Page 26 of 34:

Bankruptcy costs

Debt might have an important disadvantage:
1. High debt levels increase the chance of financial distress
This is only important if bankruptcy a§ects revenues or costs Direct costs:

2. Legal process of restructuring (court costs, advisory fees) on average 2-3% of the assets (these are legal fees paid by the firm, not bondholders)

Examples:
Enron $30 million per month, $750 million in total
Worldcom (reorganisation to become MCI) $657 million
United Airlines, 8.6 million per month for legal and professional services related to chapter 11 reorganization

Indirect costs:
1. Loss of customers
Bankruptcy may enable firms to walk away from future commitments (support, future upgrades,. . . )

2. Loss of suppliers:
Bankruptcy may enable firms not to pay for inventory Swissair forced to shut because suppliers refuse to fuel planes

3. Loss of employees:
Fear of job security

4. Loss of receivables:
Debtors might have an opportunity to avoid obligations

5. Fire sales of assets:
Companies need to sell assets quickly to raise cash

Again, all costs realized by the firm (not bondholders).

Finally,

http://www.csef.it/WP/wp139.pdf
Page 8 of 14

To elucidate this point, consider the MM theorem about the irrelevance of capital structure. It states that the amount and structure of debt taken up by a company do not affect its value if: 1) There are no taxes
2) Bankruptcy does not entail any real liquidation costs FOR THE COMPANY nor any reputation costs for its directors
3) Financial markets are perfect, that is, are competitive, frictionless and free of any informational asymmetry

Do you need more sources?

[Avon Barksdale]

Frank,

Creditors seek compensation for the extra costs that they will bear in the event of bankruptcy. This compensation comes in the form of higher interest rates which increases the firm's cost of capital. If I lend to a corporation, I know I could lose in case of bankruptcy, that's why I demand more than the riskless rate. But if I also know that at bankruptcy part of the residual of the firm will be disapated, I need extra compensation in the form of a higher interest rate. The firm's cost of capital increases.

MM supposes that these costs are absent and that the interest rate only reflects the real risks in the opportunities, i.e., the price of every Arrow security in the firm is the price of risk to hold that component of the risk to which the Arrow security is exposed and nothing else. The firm is free to repackage the risk anyway it likes but it doesn't affect the firm's value.

That every corporation has an optimal financing structure is a statement of how MM fails to hold in the real world. In the real world the value of the firm does depend on how it splits the risk. It's different for every corporation and industry. By tracing through how MM is violated in each circumstance leads to insight into how the firm will make financing decisions.

Now one of us works with these ideas as a professional. Can you guess who?

[Frank Restly]

https://en.wikipedia.org/wiki/Avon_Barksdale

Definitely not you.

[Henry]

"Glad to see you're one of the smartest people on the planet. Make sure to publish your insights on economics somewhere - it'd be a shame if humanity doesn't get to learn from it."

AB,

Nothing less than a Nobel Prize in Economics ( or whatever they call it) will satisfy.

Might even put in a word for you.

[Frank Restly]

Avon,

I went back and looked at the source:
Miller Modigliani, 1958
"The Cost of Capital, Corporation Finance, and the Theory of Investment"

https://assets.aeaweb.org/assets/production/journals/aer/top20/48.3.261-297.pdf

Footnote 17 (page 273)

"We conjecture that the curve of bond yields as a function of leverage will turn out to be a non-linear one in contrast to the linear function of leverage developed for common shares. However, we would also expect that the rate of increase in the yield on new issues would not be substantial in practice. This relatively slow rise would reflect the fact that interest rate increases by themselves can never be completely satisfactory to creditors as compensation for their increased risk. Such increases may simply serve to raise r so high relative to p that they become self-defeating by giving rise to a situation in which even normal fluctuations in earnings may force the company into bankruptcy. The difficulty of borrowing more, therefore, tends to show up in the usual case not so much in higher interest rates as in the form of increasingly stringent restrictions imposed on the company's management and finances by the creditors, and ultimately in a complete inability to obtain new borrowed funds, at least from the institutional investors who normally set the standards in the market for bonds."

And so your statement:
"Creditors seek compensation for the extra costs that they will bear in the event of bankruptcy."

This is true to a point. However, MM acknowledges that interest alone may not fully compensate a lender when the interest rate (r) is too high relative to the firms capitalization rate (p). In this case the cost is fully born by the firm - lost access to credit markets.