## Friday, November 30, 2012

### Buffett Math

Warren Buffett, New York Times on November 25th 2012:
Suppose that an investor you admire and trust comes to you with an investment idea. “This is a good one,” he says enthusiastically. “I’m in it, and I think you should be, too.”

Would your reply possibly be this? “Well, it all depends on what my tax rate will be on the gain you’re saying we’re going to make. If the taxes are too high, I would rather leave the money in my savings account, earning a quarter of 1 percent.” Only in Grover Norquist’s imagination does such a response exist.
MBA final exam question: Explain the mistake in this paragraph.

How do we decide whether to invest in a project?  Discounted cash flow.

For example, suppose you’re thinking of building a factory (or starting a business). Once built, your best guess is that the factory will produce \$10 profit every year. Discounting at a 5% required return, typical of stock market investments, the value of that profit stream is 1/.05=20 times the yearly profit, or \$200. If the factory costs \$150 to build, it’s a good deal and will return more than its costs. You build it. If the factory costs \$250 to build, you walk away.

Did you forget to put in after-tax cash flows? Whoops, that's a B- now at best. For example, if the tax rate is 50%, then your after-tax profits are only \$5 each year. Now the value of the profit stream is only \$100. The factory still costs \$150 to build however, so now you’d be a fool to do it. It truly is better to leave your money in the bank earning a quarter of a percent.

Mr. Buffett made an elementary accounting mistake. How did he get it wrong? Implicitly, he is thinking that he pays \$100, then gets back \$100 for sure, and only the profit is taxed. He's thinking that a 5% rate of return gets cut to 2.5%, which is still better than 0.025%. But when you build a factory or start a business, you are not guaranteed return of principal. You only get the profits, if any. If the government taxes half the profits, that’s like taking half the initial investment away.

This is perhaps an understandable mistake for a financial investor such as Mr. Buffett. In my example, the market value of the factory was \$200, and falls to \$100 when the tax is imposed. Mr. Buffett doesn't build factories or start businesses, he buys them.  Now, Mr. Buffett -- ever the "value" investor -- can swoop in, buy the factory for \$100, and a \$5 per year after-tax cashflow generates the same 5% rate of return. But nobody will build new factories, and that’s the economic damage.

Ok, now you get an A. Let's go for the A+.

Mr Buffett ignored risk. If somebody offers you a 5% rate of return, risk free, when Treasury bills offer you a quarter of 1 percent, his name is Madoff, not Buffett-Buddy.

Mr. Buffett wants you to think his investments are arbitrage opportunities, and a 2.5% arbitrage is as attractive as a 5% arbitrage. That's false. Investments involve bearing risk, and taxes make those investments directly worse.

Now, the effect of taxes here is subtle. Yes, a 50% tax rate cuts a 5% expected return down to 2.5%. But it also cuts volatility too. Isn't this just like deleveraging? Answer: no, because unless you're investing in green energy boodoggles only available to Administration cronies, the government takes your profits, but does not reimburse your losses.

If the investment makes 10%, you get 5%. If it makes 5%, you get 2.5%. But if it loses 10%, you lose 10%. It's a strictly worse investment when taxed. (Yes, you might be able to sell the losses if the IRS doesn't notice what you're up to... but now you know why Buffett is a "master of tax avoidance.")

And there is always another margin: If rates of return on investment look lousy, just stop investing at all and go on a consumption binge. The estate tax is a big subsidy to the round-the-world cruise and private jet industries.

I am really amazed by how this argument has evolved. Only a few months ago, supporters of the Administration's plans for higher tax rates admitted the plain fact that higher tax rates on investment are bad for growth. But, they argued that higher taxes would be good for other goals, like "fairness," redistribution, or winning elections important for other policies they like such as ACA. (These taxes are not going to put a dent in the deficit.)  And we had a sensible argument about how bad the growth effects would be, and how long it would take for them to kick in.

Now they're trying to argue that taxes aren't bad for the economy at all.  Some are suggesting higher investment tax rates are actually good for the economy.  All in the face of the natural experiment playing out in front of us across the Atlantic. The contortions needed to make this argument are just embarrassing. As above.

It seems clear to me that the Administration wants to raise the tax rate on high income people for political reasons, whether or not they raise tax revenues from such people; witness the deafening silence about reforming the chaotic tax code. The Buffetts of the world who can exploit the loopholes in the tax code and lobby for more will do fine in the new world. But they shouldn't stoop to such obvious silliness to try to fool the rest of us that pain don't hurt.

(Thanks to Cliff Asness who brought this to my attention and suggested some of the arguments.)

1. John,

"For example, suppose you’re thinking of building a factory. Once built, your best guess is that the factory will produce \$10 profit every year. Discounting at a 5% required return, typical of stock market investments, the value of that profit stream is 1/.05=20 times the yearly profit, or \$200. If the factory costs \$150 to build, it’s a good deal and will return more than its costs. You build it. If the factory costs \$250 to build, you walk away."

Your example is a bit misleading. Most of the time large capital intensive construction (like building a factory) is funded with debt not equity. Equity holders typically do not want the burden of funding the upfront construction costs for no return. Bankruptcy laws are written to favor bondholders over equity holders, and so if a company gets their new plant up and running but can't turn a profit, equity holders get nothing. Bond holders get liquidation value of the factory.

Here is your doctoral entrance exam - How does tax policy affect the cost of money including principle repayment?

1. Point taken, but the assignment is to illustrate the mistake with the simplest example, not to write a CBO report on investment distortions in the Federal tax system.

2. This is what I was talking about earlier with regard to Miller Modigliani. The equity buyer looks at the firm's margins - how much profit will the factory bring in. The bond buyer looks at the firm's assets - what is the present value of the factory in terms of cash flow and liquidation value.

And so bond buyer values firm one way, equity buyer values firm another way.

3. True, but the point still stands. Lenders can also choose between lending to "No campaing contributor Inc." and face potential bankruptcy and buying tax free, risk free t-notes. If the company goes broke, they get the factory which they will have to sell at a big discount.
What I´m saying is that tax hikes also make lending money more risky because companies are less likely to succeed.

4. Anonymous,

But here again, bond buyers (lenders) and equity buyers (stock holders) look at tax policy differently.

Equity buyers look at marginal tax rates. Bond buyers look at after tax cost of money.

5. Everyone, bond investors and equity investors, look at after tax money. Equity holders pay corporate income tax and dividend tax (if the business is organization as a regular corporation), bond investors pay income tax on the interest payments they receive. No matter how you slice it, investors look at after tax money and then decide whether the returns justify the risk. Bond investors need to be compensated for the risk they bear in order to entice them to invest, just like equity investors. Nit-picking semantics about debt vs equity is off point. The point is that anything, taxes or anything else, that reduces returns will impact investment decisions.

6. Anonymous,

I wasn't very clear so let me try to explain.

Tax Rate = Government Revenue / Private Sector Income
Tax Burden = Government Revenue / (Private Sector Assets - Private Sector Liabilities)

Can you conceive of a tax policy regime where tax rates are high but the tax burden is low?

7. I'm really not sure what the relevance is to the point that taxes dis-incentivize investment, but...

The equations you offered don't work out. Recall that one man's liability is another man's asset. For example: I loan you money, you've got a liability, I've got an asset. If what you want to do is capture the "value" of the private sector as a whole, you would simply add up the value of every privately held asset, whether that asset is a debt obligation or a piece of real estate, or whatever. In other words, take every private entity's "market value" balance sheet and add up the ASSET side only (the liability / equity side of the balance sheet just has to do with HOW those assets are financed or owned).

2. Great piece, I've shared it. But just a heads up, his name is spelled Buffett, not Buffet.

3. Your example is very misleading. If you invest \$100 to build a factory, you get to depreciate that as cost. Say you choose straight-line depreciation over 20 years, you get to deduct \$5 per year. If the operating profit is \$10 as you said, your net income is only \$5 per year. You will be taxed on those \$5 instead of the \$10.

Of course, you may say that the \$100 is the NPV of your initial investment outlay (i.e. you invest \$200 upfront, and deduct \$10 every year for 20 years which works out to NPV of \$100 with 5% discount) But please do clarify this. I'm all for simple examples but not when they are misleading.

1. The example is simple but not misleading. In the example, the factory seems to exist in perpetuity. Liye is correct that the owner can take tax depreciation, but also must note that factories in the real world actually do depreciate. The asset of the factory declines in value each year (ever driven through Detroit?). The simple example is very reasonable to illustrate the point.

Separately, perhaps Mr. Norquist values liquidity highly because of various current uncertainties. In the past, Mr. Buffett has extolled the virtues of keeping some "dry powder." Factories are generally highly illiquid (again, ever driven through Detroit?). Waiting patiently for an excellent opportunity rather than settling now for a sufficient opportunity is a reasonable strategy most of the time to maximize long-term profit.

2. "The example is simple but not misleading. In the example, the factory seems to exist in perpetuity..."

I disagree. The key is you get to depreciate your investment against tax, so it is your actual profit that is taxed, not your entire future cash flow. This is completely ignored in Prof. Cochrane's example, which makes it misleading.

The difference between finite horizon and perpetuity is minor -- I could assume profit to be 0 after 20 years and the point still remains. In real world, you use the asset and depreciate it against tax over finite horizon anyway.

3. Sorry, no. Liye explicitly added the assumption of "operating" profit. Professor Cochrane did not. As a business owner I understand the declining value of my real asset is a real expense regardless of accounting and tax. This is a relatively trivial simplification within the overall discussion.

4. Liye - I think you made a critical point. Taxes cut both ways: they reduce profits but also make investment "cheaper" because of the tax shield on depreciation. In absolute terms, these typically offset for a break-even project, but there are of course nuances around differences in tax treatment between components of cash flow and timing of tax benefit vs. expenditures that impact NPV.

The fact that depreciation is a "real expense" has no bearing on this observation. Your profits and taxes are also "real".

This tax shield on depreciation is a first order effect, much more important than these second order (if that) risk adjustments.

4. MBA final exam question: Explain the mistake in this paragraph?

Tricky, but the correct answer is crediting Grover Norquist with an imagination.

Beyond that, Buffet has wisdom and knows that as for discounted cash flow---who's that smart?

Buffet has written for years how he values investments. Why not look at matters through the lens of his letters.

1. Because (1) Buffett is not an entrepreneur, he is merely a stock investor. and (2) Buffett is mendacious and self serving.

2. Alexander Hamilton... your comment reveals a lack of understanding of finance and economics.

5. Today's NYT reports:

But in fact, most Americans in 2010 paid far less in total taxes — federal, state and local — than they would have paid 30 years ago. According to an analysis by The New York Times, the combination of all income taxes, sales taxes and property taxes took a smaller share of their income than it took from households with the same inflation-adjusted income in 1980.

Households earning more than \$200,000 benefited from the largest percentage declines in total taxation as a share of income. Middle-income households benefited, too. More than 85 percent of households with earnings above \$25,000 paid less in total taxes than comparable households in 1980.

Lower-income households, however, saved little or nothing. Many pay no federal income taxes, but they do pay a range of other levies, like federal payroll taxes, state sales taxes and local property taxes. Only about half of taxpaying households with incomes below \$25,000 paid less in 2010.

Inquiring minds want to know, why 97% of our population is worse off after cutting taxes for the last 30 years?

1. It is interesting how the NYT graphs change dramatically if you don't start them in 1980 but rather in 1982 or 1983 (the first two years where Reagan really could have had any impact on the tax code - notice that the title of the article says "Tax Burden for Most Americans Is Lower Than in the 1980s" but it really is about a comparison with only 1980 and 1981, not the remaining years in 1980s (the title was even worse in the printed edition where it said "Reagan's 1980s", although tax rates 1980 or 1981 could not possibly have been related to Reagan's administration)).

If you for instance start in 1983, it is no longer true that "household earning more than 200k benefited from the largest percentage declines in total taxation". On the contrary, they saw an increase since then. In fact, if you start in 1983, every income bracket in the NYT graphs below 100k income saw a decline, all the brackets between 100k and 200k saw no change, and both brackets above 200k saw an increase (from 35% and 40% to 38% and 42%, respectively).

The same is true for the graph that shows the ratio of each group’s share of taxes paid to its share of the nation’s income. The caption to the graph says that over the last three decades, the taxation in the U.S. became less progressive. But this is only true if you take 1980 as your starting point. Take 1983, and the answer completely reverses - for all income groups this ratio declined, except the two highest income groups for which this ratio increased.

If NYT wanted to report honestly, they wouldn't have chosen a particular initial year when they must have seen how sensitive the answers are to this choice. They could have plotted regression lines through the time series to average out the initial outliers. But then most of their argument would simply disappear.

The graphs also show that it is simply nowhere close to the truth that the rich as a group pay lower tax rates than the middle income or the poor, as it is sometimes indicated with the different "Warren Buffett" or "Mitt Romney" examples.

As a side issue, it would also be nice if the graphs indicated how the monetary and non-monetary transfers linked to different welfare subsidies evolved over time.

2. Because government never learned to live within it's means?

3. Greg Mankiw points out that since 1988, tax rates are lower for households earning 150k or less, unchanged for those between 150K and 200k, and have RISEN for those earning over 200k.

Other inquiring minds want to know: Why (as you claim) 97% of our population is 'worse off' after making our tax system more progressive?

4. If you accept the premise that you are indeed entitled to SS and Medicare, then the payroll taxes are little more than a means to partially defray the cost of these programs. That is more true the lower you go on the income scale. Sure, those earning less than \$25k pay a higher percentage of their income in payroll taxes, but they will receive far more in benefits than they paid in, although likely less than if the money had been honestly invested instead of consumed in a Ponzi scheme. State and local taxes are the province of state and local governments, but keep in mind that while those earning less paid a higher proportion of their income in local taxes, they also received a higher proportion of the benefit relative to their income, i.e. they got what they paid for (or they lived in CA).

Now let's look at the distribution of income in the Times' charts. The percentage of people earning less than \$25k has stayed in a range of 26-30% hitting that 30% high from 1993-1995, i.e. during and immediately after Clinton raised marginal rates. Let's look at a table of all income groups:

Income: 1980(%)/2010(%)
<\$25k: 26%/29% (max of 30% from 93-95)
\$25-50k: 28%/26%
\$50-75k: 22%/16%
\$75-100k: 13%/11%
\$100-125k: 5.4%/6.1%
\$125k-150k: 1.4%/3.5%
\$150k-200k: 2.1%/3.7%
\$200k-350k: 1.5%/2.8%
\$350k+: 0.2%/1.1%

Do you notice anything happening there? There is a pivot point at \$100k. More people continued to move up the economic ladder in spite of all of the claims otherwise. Sure, those making less than \$25k seem range bound to between 25-30%, but the middle class has done reasonably well. Again, the \$50-75k group in particular has.

Do you notice anything else about the income distribution? When those making more than \$350k made up 0.2% of the distribution they accounted for 2.6% of the total income. Now that they account for 1.1% of the population they account for 15% of the total income. 1.1/0.2=5.5; 5.5*2.6%=14.3%. Wow, so the Times is seriously whining about that extra 0.7% for high income earners. And during the boom times of 2007? Well then they accounted for 25% of income and represented 1.9% of the population. 1.9/.2=9.5; 9.5*2.6%=24.7%.

6. Think there's any chance we'll get the deductions cap? After all, it was Obama's idea, before it was Romney's.

7. You are ignoring the demand part of the economy. Sure, taxes influence investment decisions. But no business will survive if its customers don't have money (or credit) to buy its products/servlces. If Romney gets an extra \$100, he might invest it or he might hide it offshore. If a blue collar worker gets \$100, he/she will almost certainly spend it and quickly. Buying an iPad is better for Apple than buying their stock or shares. Redistributing wealth when demand is weak is an excellent idea because it stimulates demand. Increased demand will almost always result in higher supply and investment. But if the demand is weak investment will stall (this is why we have high unemploymemt now, not enough demand, but investors are sitting on a lot of money). Supply side economics failed. But we know from history that high taxes do not imply less investment, quite the opposite: WWI, WWII, big government, high taxes -> economic boom. The idea is to tax people who are not likely to invest or spend and give it to those who are likely to spend. Warren Buffet is right (of course).

If Apple sells you an iPad, they get \$600. Let's assume that this is pure profit. If Apple issues a new share and sells it to you, they get \$600. Why should Apple care which way they got the \$600? Either way, they have \$600 more in cash, and the valuation of the company increased by \$600.

"The idea is to tax people who are not likely to invest or spend and give it to those who are likely to spend."

Yes, let's remember the word INVEST from this sentence, and let's return to the beginning of your claim, where you said:

"If Romney gets an extra \$100, he might invest it or he might hide it offshore."

Indeed, Romney may INVEST it. That's what you want! Of course, he may hide it offshore. But the more investment friendly the environment will be (clear, transparent tax code with low broad rates and no loopholes or ridiculous deductions), the more likely it is that he won't hide it offshore.

"Redistributing wealth when demand is weak is an excellent idea because it stimulates demand."

I wonder whether we will ever see the opposite argument when demand becomes strong. I actually DO believe that the variation in the marginal propensity to consume as a function of wealth is an important mechanism. But still, using this (presumably temporary) weakness in aggregate demand as a justification for redistribution somehow seems to imply that when these conditions are gone, we should do the reverse, or?

2. Demand is always there. What sometimes is lacking is consumer confidence. That can be effected positively with more building, and more hiring. Or negatively by more actions from governments and central banks which prove that they don't know what they are doing.
.
You make the mistake of thinking that the economy is spurred by consumer demand. This is basically the same mistake of the Keynesians. But growth is caused by business investment,not demand.

3. > if the demand is weak investment will stall (this is why we have high unemploymemt now, not enough demand, but investors are sitting on a lot of money)

rafal, your logic does pass the test of numbers. Here's why.

There are about 18 million unemployed people, perhaps 10M above the normal rate. To employ these people you need about \$1 trillion of revenues generated by you capital investment. Now the total amount of capital that investors are keeping as cash is about \$1.7 trillion, 50% above the 2007 level. There is no way \$850B in investment can generate \$1 trillion in revenues to employ 10M people. No?

4. Of course: transfer capital from the productive to the non-productive and we'll get, ah, more productivity. Might as well make that transfer complete to maximize productivity then.

5. WWI, WWII - Big government, hight taxes ->

World War I - 15 million people dead world wide
World War II - 40 million people dead world wide

So that is what the Keynesians are believing today, bring back Hitler and Stalin and all will be well.

6. Here's a simple example: I have a bushel of corn. You want to eat the corn. There's the clear demand. Now if I give you all of the corn and hold none back (invest) and you consume it, then tomorrow there will be no corn when you are hungry again. However, if I plant half of the corn (invest) and you eat the other half, then tomorrow I have lots of bushels of corn and we both eat (some of the much more available corn). Consumption is never the problem.

7. Your argument is very easy to defeat. Giving me all the corn is equivalent to taxing at 100% (nothing left to invest). But if you invest your profits before the end of the year, say you buy a new corn harvest machine, you don't pay a tax on that amount. Revenues are not taxed, just profits. But your corn business will only suvive if people have money to buy your corn. If Social Security benefits are slashed, fewer people will buy your corn. Also slashing SS benefits is equivalent to leaving them the same and increasing taxes on them. If consumption is not a problem, find the poorest county in the U.S. and open a Rolls-Royce dealership there. Let's see if you make money.

8. Prof. Chochrane,

I'm just a lowly JD, but here's what my answer would have been:

1) Taxes will distort marginal investment decisions. If I'm on the fence between investing/not investing, then taxes will push me to the non-investment side. If we're talking about what effect these taxes will have on the growth of the economy, the effect is obviously negative, because all of the obvious investments have been made already. We want to encourage the marginal ones, so we want to lower taxes on investment as much as possible.

2) When discussing whether to invest or not, Mr. Buffet ignored the most obvious alternative use to which I can put my money. I can spend it rather than save it. If I'm a wealthy investor, and each dollar of savings only brings me (or my children, more realistically) 25-35 cents of future consumption, I think I'd prefer to spend more lavishly now, so as to not waste my purchasing power.

Oversimplified?

9. Where are the two Presidents with the last name of Bush?

It seems we have a chicken or egg thing going between the ideas here and on the editorial pages of the WSJ.

What keeps being left out?

Why the two Bush presidencies as noted by Chait of the NYTimes

Prof Cochrane: Where is the prosperity promised by all those Bush II tax cuts for the rich? What lessons were not learned from Clinton/Rubin?

1. First of all Bush senior actually broke his promise of no new taxes by increasing them. Leading to his loss in election. And Bush did cut taxes. As a result, we saw labor-productivity gains that averaged 2.5 percent annually — a rate that exceeds the averages of the 1970s, 1980s, and 1990s. Real after-tax income per capita increased by more than 11 percent. And from 2000 to 2007, real GDP grew by more than 17 percent, a gain of nearly \$2.1 trillion. Reality is a bitch. Especially to liberals and the retarded. Which can be often conflated correctly.

2. Clinton/Rubin benefited from so many tail wainds during the Admin that lessons other than "pick the time frame of your presidency" would explain nothing but rounding errors. (Even then, the so-called Clinton years ebince two dinstinct growth periods: the first -- moderate growth after the 92 tax hikes, even though we were coming out of the 91-92 recession; followed by much faster growth after the Congressional elections (and the policy changes it required) and the cut in cap gain taxes in the later 90's.

10. Prof Cochrane - what about depreciation in your first example? If you get to write off the cost of the factory via depreciation, then it seems like you are only getting taxed only on the profit and not the principal. Or am I making a mistake there?

1. The depreciation must be spread out over a long period of time (27 years or so) with non-inflation-adjusted dollars and then the owner is subject to full capital gains (I.e. zero cost basis). He'll have lower capital gains if he doesn't depreciate, but the government doesn't adjust that gain for inflation.

11. Someone else already hit on the debt-funding point, which is important.

The other thing missing from your equations is the value of the factory itself as a ratcheting-up engine placed into the economy at large. With the addition of this factory, all the economy is better off, and that means all players in the economy are better off too, including the investor, because that "smaller return" also becomes more highly valuable because it can now buy, for example, widgets produced by this factory at a better price, or requiring less shipping, etc. Meanwhile the town in which the factory is built will experience an economic boon, which increases the standard of living of everyone there. Stores and restaurants do better, etc. And, if this investor is local to that town, he can probably get a better steak and a better beer served by better staff for his less profit.

I think your post is myopic, economics without perspective. It's not factually incorrect, but rather lacking scope. It's just missing the point that VALUE is more than the MONEY you can count on your own little balance sheet. The investor who builds the factory gets the intangible benefit of owning a factory! Through the factory, an investor with character will have a means of personal expression unreachable to most, something to manage better than other factories have been managed, something in which to invest his intelligence and skills to make it more efficient, etc. In other words, the investor gains something which far outweighs the impact of marginal taxes: PURPOSE, a place to "Do something that matters in this world".

But sadly, most people with money don't have that view. They just want to throw their money out there and leave, and expect their math to ensure that the dollars will more than pay for themselves. Why should they pay for themselves if you're not also going to invest your attention and your effort? Why should such a capitalist deserve any return for no effort? His only effort is a defensive and completely selfish exercise of crunching the numbers such that, given the state of the economic system MAINTAINED ON HIS BEHALF BY THE GOVERNMENT AND THE LABOR FORCE, his money will be multiplied with no work on his part. Worthy of NO APPLAUSE is this weasel-logic!

Profit should come from effort well applied. Not a self-defensive and selfish (one-sided) dependence on a system which you rail against at every chance.

1. Well said. What you are basically arguing is value is built on productivity not on money. There have been efforts to do economics to mitigate the influence of money. But unless we go to a barter system, money will still play a part. Even still here is what I consider a good macro-economic measure of productivity:

And based on this measure (contrary to what economists will tell you) productivity in the United States has been falling for at least the last 50 years.

2. Well I'm glad that you can objectively define purpose. Aside from the fact that money captures the value that the market, which includes you and your intangibles, places on an item or activity, what you describe is some silly art history approach to economics. You can have your intangible unicorns. I will continue to evaluate returns based on numbers.

The economic system is maintained on his behalf by the government and the labor force? You do understand that free market capitalism is responsible for the greatest improvement in poverty in the history of the human race, don't you? Are you stuck in some German tea shop in 1917? I think your dialectic is showing, Herr Marx.

3. Skippy,

Here are some numbers to think about:

Federal Reserve Flow of Funds Z1 Report (Household Balance Sheets)

http://www.federalreserve.gov/releases/z1/Current/z1.pdf

Page 119 - 2012 2nd Quarter
Household assets - \$76.13 trillion
Household liabilities - \$13.46 trillion
Asset / Liability ratio: 5.66

http://www.federalreserve.gov/releases/z1/Current/annuals/a1945-1954.pdf
Page 104 - 1950
Household assets - \$1,125 billion
Household liabilities - \$76.8 billion
Asset / Liability ratio: 14.65

How do you go from an asset to liability ratio of 14.65:1 to 5.66:1 and think that you are wealthier as a nation? I don't decry capitalism itself, I just recognize its inherent weaknesses.

12. "Answer: no, because unless you're investing in green energy boodoggles only available to Administration cronies, the government takes your profits, but does not reimburse your losses."

The government actually does reimburse some losses. This is why banks are sitting on piles of "Deferred Tax Assets" (reimbursable losses from the past) at the moment, particularly in Europe, where accounting standards make this worse.

This selective reimbursement of losses creates its own distortions. For example, a firm may carry forward a net operating loss to reduce future taxation for seven years. Consider then two projects, with a risk free interest rate of 1% and a 50% tax rate.

Project 1 ("Cyclical Retail, Inc."):
For 10 years, every year either a profit (75% chance) of \$100 or a loss (25% chance) of \$100.
NPV (no loss carry forward) = about \$12
NPV (10-year loss carry forward) = about \$47

Project 2 ("Hightech Science, Inc.")
Every year in perpetuity, either (p=.90) a profit of \$83 or (p=.1) a loss of \$250.
NPV (no loss carry forward) = about \$12
NPV (10-year loss carry forward) = about \$40

13. Asymptotically FreeDecember 1, 2012 at 11:06 AM

Hello Professor Cochrane,

I really enjoyed your post. The problem might be even worse than you suggest.

Building a factory represents an irreversible investment decision and thus the investor holds an American style call option on the opportunity. The true value of the investment adjusts to include the value of the investor's option. So, even if we keep Modigliani-Miller intact, the government's tax policies can create even greater distortions than those simply arising from the reduced discounted cash flow. If the government's tax policy also serves to increase the importance of the option to the investment decision, we will find an even larger wedge. Waiting for more information on the margin gets more valuable and more investment decisions get delayed.

Do you think that option effects in investment decisions will be distorted by the Administration's suggested tax policies?

14. I'm presuming this is an individual investor. Otherwise the discussion is not particularly relevant to what is currently on the table. Suppose the person takes the investor up on the offer and invests \$100. The investment turns out to be a good one and the \$100 is doubled to \$200. If the tax rate is 40 percent, the investor has earned, net of tax, \$60. The next time around the investor will have \$160 to invest. Had the tax rate been say, 15 percent, he would have had \$185 to invest.

Irrespective of one's propensity to invest, higher effective tax rates inevitably result in a smaller pool of private investible savings. If Warren is assuming that no investor will ever realize and recognize investment gains (although raising rates will certainly diminish one's propensity to do so), there's no reason to raise tax rates at all. Warren not only made a mistake with his example---in making his argument he also committed a significant error of omission.

15. But Professor Cochrane, it's not fair! : )

16. Guy, your response is myopic. You are imprinting your value system on mine. Maybe I don't care if I own a factory and am only interested in positive cash flows of investment. You cannot quantify the satisfaction of actually owning the factory.

Alexander Hamilton says higher taxes lead to higher prosperity because of the Clinton years. If you look at govt spending as a percentage of GDP post 1994, and combine that with a once in a generation productivity gain because of the internet begin applied, you have your answer as to why taxes were less of an influence then than they would be today.

Again, I think Obama's fiscal plan has been very stupid, and going forward it's Dumb and Dumber. But, he won by around 400k votes. Let's go over the fiscal cliff, raise taxes and NOT fix AMT. I bet \$1000 bucks we go into a recession. Who wants that action?

1. If you look at govt spending as a percentage of GDP post 1994 . . .

and where, pray tell, are your studies showing this is meaningful?

again, try angrybear, learn!!!!

There are no "per se" tax or spending caps: lame duck negotiations no place for Medicare/Medicaid cuts

2. Obama DOES want to go over the cliff, let taxes increase, and of course blame it on the Republicans. Then, just as a recession looms, he proposes a tax cut for the middle class. As the cries of "Hosannah! Obama in the highest!" ring out from his "angelic" choir (the main stream media), the Republicans (Satan) are demonized yet again, setting up for a 2014 democrat sweep. You saw part I of this movie, didn't you?

17. Well, in practice, if the business is viaable, except for taxes, you can always sell it to an endowment, pension fund or a foreign investor, who pays taxes differently and doesn't face the same constraints. So, in practice most likely Warren Buffett is right that you won't see this much

18. I gave this post to my students to help them on their final projects...

1. Noah - your students should be able to do better than the good professor. They should start by making the reality check observation that Buffett is fabulously wealthy and Professor Cochrane is a man of comparatively (compared to Buffett that is) modest means. They should ponder who might better know how to value an investment.

The first rule of exam taking is to READ THE QUESTION. Buffett was responding to a standard right wing talking point which claims that investors are holding excess cash because of fear of taxes. In his example Buffett refers to an INVESTMENT opportunity, which his friend has invested in and which he may choose to invest in (that is - this is something divisible and tradable). Cochrane goes running off and starts talking about PROJECTS and FACTORIES.

Buffett's real point is that investors are holding cash not out of a fear of taxes but for lack of apparent profitable business opportunities.

In considering Professor Cochrane's example your students should turn their mind to what the \$10.00 per year return is - for example is it the risk adjusted expected profit after all expenses including amortization?

Cochrane basically says that Buffett's approach is an over simplification but then introduces his own misleading simplifications. If an existing company with existing profitable businesses builds a new factory for a new product line which is not successful then the losses from that new factory can be deducted from the profits earned by the rest of the business.

As other commenters have noted, investment capital flows to projects through various means (including debt and equity) and from investors facing different tax consequences. Returns on project financing by debt from a pension fund is effectively tax free. Nominal interest is deductible even though it contains a component for inflation.

Professor Cochrane really uses one very narrow example of a fully taxable investment in a stand alone project to implicitly argue that taxes on all business should be reduced. Any new businesses that were created as a result of reduced tax rates would be marginal in the economic sense and it is doubtful that the increased economic activity from those few marginal projects would make up for the loss of tax revenue from all of the more robust projects currently existing.

2. Cochrane basically says that Buffett's approach is an over simplification but then introduces his own misleading simplifications.

Wonder how this truth got past the censor?

3. I find this actually rather comical. Most of the above addendum's to Professor Cochrane's fake exam question were along the lines of "your general premise is correct, but we wanted to add a few other wrinkles because we know investment decisions and tax effects are more nuanced than you suggest." This is rather different from saying, "Professor Cochrane, you dishonest hack...we all know you're using Buffett's statement as an obvious strawman and your whole crackpot theories are obviously junk."

In all seriousness, is there really a debate about how the tax system distorts investment decisions at all? Whether the effects are large, small, non-equally distributed, or skewed by varying other dynamics, the overwhelming evidence suggests its negative any way you slice it.

The real sad thing is, the naively simplistic arguments that the mass public is eating up are being made by Buffett and Krugman. They are the one's that keep peddling the notion of more government spending, tax the rich and problem solved. Its as simple as rinse and repeat, while its been the other side that has had to make the more nuanced argument stick. Ask yourself, has Cochrane ever blithely just said: "Cut Taxes, Cut spending, Give money to rich, profit?"

4. Ajit

There is no dispute THAT the tax system distorts investment decisions but there is a great deal of disagreement about HOW and HOW MUCH the tax system distorts investment decisions.

You attribute to the left less sophistication than they have and to the right rather more sophistication than they display. A large segment of the right never get beyond the infantile "all taxes are theft" stage.

You may disagree about the fairness or efficacy of individual government spending decisions but if you believe in democracy then you cannot deny the right of democratically elected governments to set spending priorities. Assuming that the desired tax revenues can be raised, the question then becomes how to raise the tax revenue with the least dead weight loss to the broader society (always bearing in mind that government spending generates some off setting benefits which may be large or small).

In a sense ALL income is derived from investment (education, job training, tools, machines, buildings etc.) Given that Western societies have decided that it is in the collective interest that the state take a large slice of total GDP, it makes sense to spread the burden across many different types of investment and economic activity rather than to focus it on a few types of activity and that spreading the burden will tend to reduce the dead weight loss.

19. I wonder if Cochrane is confusing corporate taxes with capital gains taxes. No one is talking about raising the corporate tax rate. In fact, if anything, it is much more likely that the corporate tax rate gets cut.

Buffett is referring to the capital gains tax rate which he thinks should be raised directly or indirectly (through some minimum tax rate on individuals). Capital gains taxes are not paid on corporate profits (or the profits of businesses in the form of partnerships, LLC's, etc.). Therefore, I'm not sure if Cochrane's example addressed Buffett's point.

As far as I see it, raising capital gains rates might steer people away from riskier investments towards less risky investments and might steer people away from investments and towards consumption. It is unclear how big these shifts would be. I tend to think that the shift towards consumption would be small, but the shift towards lower-risk investments could be significant.

20. A couple of things I would consider. First, if my money is already invested (very likely) changing investments hits you with the tax 2 times - once selling your current investment and once selling the new investment. Meaning unless it is a fantastic opportunity with a high rate of return, you should not do it. Second, what about risk? If you factor risk and taxes into your investment decisions, a higher tax rate virtually guarantees one won't take a risk. Both of these would push one towards the no decision, and therefore higher capital gains tax leads to investing stagnation.

21. Your excellent point was converted to a full-fledged nice article at Patria.cz, a leading Czech server for investors. Automatic translation back from English. The title is Schoolboy's mistake of Buffett. I hope you won't sue them for violating the copyrights, I guess that they don't earn too much money from your article even though it's very good. ;-)

22. Sorry for being late to the party... I find it interesting that Buffett contiually argues that everyone else pay higher taxes but continually avoids them himself:

One of Bershire Hathaway's holdings, Netjets was sued earlier this year for underpaying taxes. http://articles.businessinsider.com/2012-03-10/wall_street/31142467_1_ticket-tax-unpaid-taxes-penalties

A year ago it was pointed out that the IRS claims Berkshire owes \$1 Billion in unpaid taxes going back to 2002. http://www.huffingtonpost.com/2011/08/29/warren-buffett-taxes-berkshire-hathaway_n_941099.html

Buffett only receives a salary of \$100,000 as CEO of Berkshire, a rate very low compared to other CEOs (I believe Buffett has said that others are paid too much) -- so as Mankiw points out in the linked blog post, he is avoiding paying taxes himself.

Some of the operations of the insurance units are to reinsure life insurance policies. Aren't some (whole life) policies tax shelters? So by arguing for increased taxes, Buffett is rent seeking.

23. I haven't studied every reply, but I don't think anyone has reminded Prof. Cochran that the hurdle rate also represents taxable income. Therefore, tax policy tends to cancel out. Next year (presumably) taxes on investments will be treated more like other income, so they cancel more perfectly.

1. not sure what you mean...maybe give an example of tax policy cancelling out?

Currently you can (under fairly straightforward circumstances) get taxed lower on things like dividends, etc, than you would on regular income...

2. Probably too late, but ....
The argument posed included an NPV using a hurdle rate of 5%, which represented a relatively "sure-thing" alternative investment. The NPV calculation is meant to return a number representing excess profits compared to that other investment. So, if we are going to apply tax policy to the factory, we have to apply tax police to the "sure thing" investment. Tax policy will eat away at the profits of each.

Bob Haugen taught us, way back when I was in business school, to largely ignore the effect of taxes because taxes would apply to the investment under consideration as well as to the alternative (the "discount rate"). If tax policy for equity investments becomes more in line with how corporate profits are taxed next year, then taxes will tend to cancel each other out.

24. Warren Buffett’s op-ed supports the Obama administration’s proposal to raise tax rates on capital gains, dividends and the top two income tax brackets. The stated purposes are “fairness” and deficit reduction. I suspect that taxpayers with high incomes or substantial capital gains and dividends are more able (and more likely) to invest than others. Who would argue that higher tax rates would make them more likely to invest or increase the pool of investable funds? I also suspect that high income taxpayers have more control over the amount, character and timing of their income. Doesn’t the historical record show that a lot of the income these rates are designed to tax will simply disappear before it can be taxed?

So, if the President’s proposals (which Buffett supports) are unlikely to raise much revenue and likely to reduce investment, is there an unstated purpose? Every deduction or credit in the tax code is meant to shape behavior. Higher rates increase the value of tax credits and deductions. The principal effect of these higher rates will be to steer private investment into tax favored projects.

Given the trillions in losses from unwise investment in housing (encouraged by the mortgage interest deduction) and given the immense human cost of the “Great Recession” we’re now struggling to overcome, will we really benefit from more direction of private investment by the tax code?

1. "The principal effect of these higher rates will be to steer private investment into tax favored projects".

That's a very good point. The higher the marginal income tax rate on investment, the more incentive there is to take advantage of subsidies designed to mitigate the effect of those high rates. Raising investment tax rates makes it even more possible for government to steer investment to wind and solar energy, public housing or whatever it decides is the flavor of the day. It increases the government control over the economy and results in even more private market distortion. It also is a huge incentive for private lobby efforts designed to carve out special benefits for a particular constituency. Higher tax rates are a real boon to politicians of every persuasion because it gives them more ability to hand out specific favors.

25. I'd say a third element is missing from Buffet's analysis: many investments take effort beyond putting in a buy/sell order to your broker. An auto repair-shop owner who is a friend of mine faced the question of whether to expand his shop. He could have got a loan, purchased the property next door, hired an architect, hired a construction crew, managed the build-out, hired new employees to work in the expanded shop. He was confident it had a positive NPV (even after taxes), but it would have required him to put in 10 more hours per week beyond the 60 he already worked. The move would have come completely inside the top marginal tax bracket and he said "no thanks, I'd rather spend time with my grandkids than earn a fraction of my dollars."

26. I wonder what Buffett thinks would happen Berkshire Hathaway's stock price if Congress passed an unrealized-gains tax. Nothing?

27. John:
Why do you not apply the tax rate to the interest income from savings? You assume that income is only taxed if it is from the investment, but that is not Buffett's example. If the marginal tax rate on my income over 250,000 is raised, why does that cause me to be less willing to invest in a project than keep it in a savings account, corporate tax unchanged? That is what Buffett's example was about.

28. I highly doubt that Warren Buffett doesn't understand that investments are risky and that higher taxes lowers the expected value of an investment.

I think Buffett's argument rests on the implicit assumption that, unlike in academia, where humans are modelled as homo economicus, real-world investors don't make decisions at the margin. A private equity manager contemplating buying a firm either feels pretty good about the investment, in which case he'll go forward with it, or he doesn't like the company, in which case he'll pass. Whether he gets taxed on future possible profits at a 35pct. or 38pct. rate won't impact his general opinion on the investment.

29. So my cousin Phil (and I assume every family has such a cousin) says he will not bother looking for a job until wages and working conditions improve.

Is the first priority of our nation to cut taxes and improve working conditions for employees?

Or (more likely) is there both a glut of capital and labor, meaning if that some pull back, others rush into the vacuum?

That said, I would cut federal outlays to 15 percent of GDP. That would require large cuts in agency spending, such as eliminating HUD, USDA, and huge cuts in defense, VA and Homeland Security.

You can't lower income taxes without cutting agency spending. Entitlements are largely paid for through payroll taxes.

Of the type my cousin Phil says prevents him from working.

30. Discounted cash flows are based on compounding. It is not simply year 1 roi and inverted into a PE

31. Buffett's statement has nothing to do with valuation. Buffett is simply saying higher taxes would not necessarily kill capitalism in the economy, people will continue to transact and make profit.

Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.