WACC-A-MoleDale WettlauferCharlotte Lane CapitalNovember 30, 2015

I often say discussions about weighted average cost of capital (WACC) are among the most boring because they become religious: You get orthodoxy, fervent Messianism, and the truly fringe. Understanding I may well fall somewhere near the fringe, I will add to the cacophony.

Conclusions

(1) The beta component of CAPM is a plug that came about in an era of expensive computing power. It might backtest well, but it’s not explanatory.

(2) The mysterious equity risk premium is really not that mysterious. I believe credit spreads account for the majority of the ERP.

(3) In this paper, I therefore propose an alternate theory of calculating the cost of equity as well as WACC. I have employed this approach in modeling since 2009-2010, having been informed in my thinking by the incredible values available in distressed debt at that time. Major influences also include Rob Arnott and the inestimable Peter Bernstein, Michael Mauboussin, and in working on private equity investments at that time.

(4) Using expected return data extracted from the credit market, one can discount cash flows with more sensitivity toward risk-adjusted returns than the brittle CAPM calculation can hope to address.

(5) Quantitative Easing1 has distorted the risk free rate (I prefer “base rate”) component of CAPM; I propose and alternate solution based on 60 years of real yields for the 10-year treasury note.

Let’s start with a perhaps divisive target: The “risk free rate.” The Capital Asset Pricing Model (CAPM) posits this is the yield above which all other instruments must be priced. The idea that sovereign debt is risk free is nearly absurd on its face and history also demonstrates sovereign yields weren’t always the base rate above which everything else must offer a superior yield.

Sidney’s Homer’s A History of Interest Rates2 contains a fascinating passage that has informed my view of the topic:

Princes, on the other hand, could not bind their subjects to pay their debts. Usually they could not even pledge the credit of their successors. Their credit was thus ephemeral, depending often on youth, good

1 I don’t have a problem with QE. I believe it’s preferable to a deflationary de-leveraging of the US economy, though I believe it does cause distortions in the economy.2 4th edition. This is a reading as important as Graham and Dodd’s Security Analysis and The Intelligent Investor, in my opinion. Homer was a contemporary of Graham, was the founder of Solomon Brothers’ credit research group, and was a fascinating individual: https://www.fiasi.org/1997-hall-of-fame/66-sidney-homer

health, and military success. With the death, disaster, or bad faith of the prince, his creditors often lost everything. Furthermore, deliberate default often could be punished only by the sanction of a future denial of credit. Thus it was princely loans, when not amply secured by enforceable pledges of assets or revenues, usually were made at much higher interest rates than prime commercial loans or loans to sound free cities. Lenders might have been even better advised to heed the words of Ecclesiastes: “Lend not to him who is mightier than thou.” (VIII: 13)3

Perhaps a minor point in this discussion and this is probably one most Americans today can’t deal with, but the ramifications are important across the history of sovereign monetary regimes. When you hold currency, you are a creditor to a government; throughout the postwar period, this claim has been debased nearly continually. As for sovereign rates, the US has never defaulted, which was one of the geniuses of Hamilton in The Federalist and the Constitution, but that has been an exception in the history of sovereigns. They default all the time. Even though I keep this in mind, this is one of the orthodoxies in CAPM I do maintain in my model4.

As for base rates (a term I use instead of “risk free” rates), quantitative easing has rendered the current curve useless for discounting long-term cash flows. I have historically used the yield on the ten-year treasury note as my base rate, but with QE in place, I substitute where I think the real yield on the 10-year would be without any Fed intervention. From 1954 through 2014, the real yield on 10-year notes averaged 2.62% with a median of 2.9%:

Exhibit 1: Real 10-Year YieldSource: Bloomberg, Charlotte Lane Capital (CLC)

(4.00%)

(2.00%)

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

I use the implicit GDP price deflator for the inflation term – there are many data series for this, so one can pick one’s one poison here. If we take 1.6% expected inflation (based on TIPS breakevens) and add the 2.9% median real long-term yield on 10-year notes, we get a base rate of 4.5% today. I personally use expected inflation of 2.0% given the shape of the TIPS breakeven curve as well as the problems with hedonic adjustments in the calculation of inflation, so my base rate is around 4.8% today, but opinions will vary.

3 Homer, pp. 91-924 At times, I have observed credit spreads on AAA and AA issues at 10-20 bps.

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Equity Risk Premium. The CFA Institute and various business schools have convened multi-day conferences with august practitioners and academics to hash out the equity risk premium. It’s incredible this central factor in CAPM is subject to such a lack of agreement. Part of this revolves around the fact there is no sure agreement on whether the equity risk premium (ERP) should be examined on an ex ante or ex post basis. It’s intuitive to look ex post at the average periodic return of the S&P 500 less the yield on the 10-year note and call that excess return “ERP.” On that basis, the S&P 500’s YoY total return, measured quarterly, less the 10-year yield, from Q2 1953 through Q3 2015, has averaged 6.2% with a median of 7.2%:

Exhibit 2: S&P 500 Total Return, YoY vs. 10-Year Treasury YieldFour Quarter Average

Source: Bloomberg, CLC

(40%)

(30%)

(20%)

(10%)

0%

10%

20%

30%

40%

50%

In their tour de force paper, What Risk Premium is “Normal”?5, Rob Arnott and the late Peter Bernstein examined the subject and worked from an ex ante approach. Their findings, to boil down a few points from a fascinating paper I recommend highly, are as follows:

The historical average equity risk premium, measured relative to 10-year government bonds as the risk premium investors might objectively have expected on their equity investments, is about 2.4 percent, half what most investors believe.

The “normal” risk premium might well be a notch lower than 2.4 percent because the 2.4 percent objective expectation preceded actual excess returns for stocks relative to bonds that were nearly 100 bps higher, at 3.3 percent a year.

Between 1926 and 2001, stocks rose from a valuation level of 18 times dividends to nearly 70 times dividends. This fourfold increase in the value assigned to each dollar of dividends contributed 180 bps to annual stock returns over the past 75 years, even though the entire increase occurred in the last 17 years of the period (we last saw 5.1 percent yields in 1984). This accident explains fully one-third of the 75-year excess return.6

5 https://www.researchaffiliates.com/Production%20content%20library/FAJ_Mar_Apr_2002_What_Risk_Premium_is_Normal.pdf6 Arnott, Bernstein, pdf pp. 4, 18

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Looking at the issue from an ex ante perspective, we see the equity risk premium in expected returns is much smaller than ex post. First, we need to establish the role of base rates as a component of expected returns in equity markets. Again, Arnott and Bernstein decompose this beautifully, showing treasury yields are a function of expected real economic growth and expected inflation. Below, we can see the yield on the 10-year treasury compared with the subsequent 10-year IRR on the S&P 500. For example, as of Q4 1954, the 10-year treasury was yielding 2.61%. Over the period 1954-1964, the S&P 500 returned an annual 8.8%, for an equity risk premium of 6.2%. As soon after as 1959, the 10-year treasury was yielding 4.72% and the subsequent 10-year IRR on the SPX was 1.15%, for an ERP of (3.57%).

From 1954 through 2004, the relationship is as follows:

Exhibit 3: 10-Year Treasury Yield vs. Subsequent SPX 10-Year IRRSource: Bloomberg, CLC

0.00%

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6.00%

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(20.00%)

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(5.00%)

0.00%

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SPX IRR, Subsequent 10 Years10-Yr Yield (RHS)

Cutting off the chart at 1965, prior to which contains the only period in the above chart in which directionality of the two asset classes was out of sync (low treasury yields that subsequently rose did presage a coming dark period for the market, however), the correlation improves to 70%:

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Exhibit 4: Correlation, 10-Year Treasury Yield vs. Subsequent SPX 10-Year IRRSource: Bloomberg, CLC

y = 0.1988x + 0.0638R² = 0.4925

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

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16.00%

(20.00%) (15.00%) (10.00%) (5.00%) 0.00% 5.00% 10.00% 15.00% 20.00%

A 49% R-squared is perhaps not satisfactory for all, but two major asset classes with one lagged ten years showing this correlation coefficient indicates fairly well the validity of the interplay.

When we look at the ERP realized by buying a 10-year treasury7 and holding to maturity and comparing the 10-year IRR for the market for each year between 1954 and 2004, we find there is no equity risk premium. In fact, there is an equity risk penalty, as the returns for the 10-year note exceeded those of the equity market by an average of 1.2% and a median 2.3%:

Exhibit 5: Equity Risk “Penalty,” 1954-2004Source: Bloomberg, CLC

7 Arnott and Bernstein explain treasury yield expectations are formed by real growth and inflation expectations. Below we see the “predicted” growth, as evidenced by the 10-year treasury yield vs. the subsequent ten years of real GDP per capita plus the implicit price deflator: Predicted growth averaged 6.2% for the period and actual growth, summing GDP per capita plus the implicit price deflator, then averaging the ten year run, was 5.2%. The treasury is certainly not a perfect predictor, but coming within 100 bps over 50 years is fairly decent and a good rule of thumb to use to estimate nominal GDP growth.

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(25%)

(20%)

(15%)

(10%)

(5%)

0%

5%

10%

Perhaps quite by accident, the average equity risk “premium” for the ex ante and ex post approaches is 2.5%, or right around what Arnott and Bernstein suggest.

Why Is Equity Risk Premium Such A Mystery? Let’s Get Rid of Beta, Too. When CAPM and beta were codified in the 1960s and 1970s, computing power wasn’t cheap, so the number of variables that could be back-tested was limited by PhD candidates’ and finance departments’ finite resources. Beta popped out as a plug to explain the variance of assets vs. the benchmark and the model fit, in general. But there are numerous exceptions, which Buffett of course brought up with his point on the beta of Washington Post going up as the stock became cheaper and cheaper (though in an alternate history, it wouldn’t have been fun for WPO if Nixon had succeeded in pulling the company’s broadcast licenses).

For some reason, CAPM and ERP ignore the fact that for many companies, there lies something between the equity return and the base rate (or “risk-free” rate), which is the expected return on corporate debt. Over an extraordinary 60-year run for the market from 1954 through 2014, the ex post ERP for the market was 6.4% while treasurys yielded 6.0% on average and Baa corporates yielded 8.0%. The credit spread

0.0%

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16.0%

Actual growth Predicted growth

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on the lowest rung of investment grade debt therefore averaged 200 bps over this period, explaining one third of the mysterious equity risk premium.

On this subject, Mauboussin wrote in 2006,

Whether you add 200 or 600 basis points* to the current risk-free rate of 4.7 percent (mid-March 2006) will make a significant difference in the model’s output. Exhibit 2 shows a sample of equity risk premiums assumed in recent sell-side analyst reports. Our best advice is to settle on a cost of capital that makes business and economic sense. Some academics suggest the equity risk premium is in the 3 to 4 percentage point range, which strikes us as reasonable.89

If we see ERP of 300 – 400 bps as reasonable, then the credit spread embedded in Baa yields vs. the 10-year note’s yield, over the course of 60 years, explains 50% to 66% of the oh-so-mysterious equity risk premium. Now of course there are tons of companies that have no debt, so let’s just use this observable input on companies that do have debt as a general stand-in for business failure risk. We can estimate the option-adjusted spread (OAS, or credit spread) for companies without debt by looking at similar companies or business models.

I would re-write the cost of equity as Base Rate + credit spread (actual or estimated) + 200 bps equity risk premium. This says in addition to the inflation protection one demands from a treasury, plus the growth participation, one also demands risk premium for the corporate credit, which is a contractual obligation of the firm. Then on top of that, the equity investor demands at least a minimum of return premium in exchange for being the most junior piece of the capital structure net of the option of capturing all the upside.

Let’s look at a current example of how this works. Take Chesapeake Energy’s 5 3/4% of 2023 debt. Its credit spread is 2,000 bps right now with this senior unsecured credit trading at 42¢. With a yield-to-worst (YTW) at maturity, this produces a 22% IRR over 7+ years. In this case, there is no way in the world cash flow to the firm or equity should be discounted over that time horizon at anything less than some premium over the 22% YTW the credit delivers. It’s a contractual obligation of the corporation, after all, so they HAVE to pay you that return. If they can’t, the equity will either be worthless or diluted.

8 Common Errors in DCF Models, Michael Mauboussin. http://www3.nd.edu/~scorwin/fin70610/Common%20DCF%20Errors_LeggMason.pdf

This paper also contains what I believe is the definitive explanation of terminal multiples and what makes the most sense from a theoretical and practical perspective. The bottom line on this as I see it: “perpetual growth” is bunk.9 I would note here Arnott and Bernstein also pinned on valuation expansion 180 bps of the 5% to 5.7% 75-year excess return from 1926 through 2001. Deducting this from the observed long-run ERP gets us to an “adjusted ERP of 3.2% to 3.9%.

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What does CAPM have to say about this situation? With a 5-year beta of 1.3 to 1.5, CAPM would calculate it thus (using my base “risk-free” rate of 4.8%): 4.8% + (1.5 * ERP of 4%), or 10.8%. It makes no sense to discount non-contractual cash flows at less than half the rate as contractual, senior unsecured cash flows. It does make sense, if one believes the entity will be around to take that credit to maturity, to use a terminal value based on a more normalized long-term cost of capital.

In the brief DCF below, you’ll notice I bow the cost of capital components over time. A company emerging from distress, if you see the fundamental cash flow picture flattening and then regaining some health, will very likely see a decline in its cost of capital over time, carrying through that fundamental forecast to how the markets will see its financial picture at some point in the future. I don’t think a cost of capital forecast over an explicit forecast horizon necessarily has to be a straight line. This is why distressed companies can provide excellent returns coming out of their periods of extremis. The multiple expansion that accompanies a decline in cost of capital often delivers a huge portion of these returns.

Exhibit 6: Brief DCF Illustrating WACC ConceptsSource: CLC

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I will point out a few things here. The terminal value is not accorded a punitive discount rate; just the interim cash flows are. Notice also the IRR on equity vs. debt at this point is about 700 bps higher with

equity priced here at fair value. Also note the low earnings and EBITDA multiples implied by this valuation. Investors will often accept a lower rate of return on equity than they should leaning on valuation rules of thumb, but the warranted multiples to produce a high enough risk-adjusted return when the debt is trading at 50¢ are incredibly low. I will post this spreadsheet for people to play with the variables (in blue font).

Now let’s look the values produced by a model using CAPM to calculate cost of equity.

Exhibit 7: Brief DCF Using CAPM for Ke

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2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 TermYears 1 2 3 4 5 6 7 8 9 10 10FCF 100$ 90$ 80$ 80$ 85$ 99$ 104$ 115$ 115$ 115$ 1,309$ YoY grow th (10.0%) (11.0%) 0.0% 6.0% 17.0% 5.0% 10.0% 0.0% 0.0%

Base rate 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80%OAS 18.0% 18.0% 18.0% 18.0% 18.0% 18.0% 18.0% 10.0% 7.0% 5.0% 4.0%ERP 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00% 2.00%WAC, after tax 14.8% 14.8% 14.8% 14.8% 14.8% 14.8% 14.8% 9.6% 7.7% 6.4% 5.7%WAC at issue 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0%Int exp $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 Ke 24.8% 24.8% 24.8% 24.8% 24.8% 24.8% 24.8% 16.8% 13.8% 11.8% 10.8%Debt % 80% 75% 70% 60% 50% 40% 40% 40% 40% 40% 40%Equity % 20% 25% 30% 40% 50% 60% 60% 60% 60% 60% 60%WACC 16.8% 17.3% 17.8% 18.8% 19.8% 20.8% 20.8% 13.9% 11.3% 9.6% 8.8%

NPV, FCFF 86$ 65$ 49$ 40$ 34$ 32$ 28$ 40$ 44$ 46$ 565$ FV, FCFF (250)$ $ 90 $ 80 $ 80 $ 85 $ 99 $ 104 $ 115 $ 115 $ 115 $ 1,309 NPV, FCFE 55$ 37$ 25$ 20$ 18$ 18$ 15$ 24$ 26$ 27$ 458$ FV, FCFE (261)$ 58$ 48$ 48$ 53$ 67$ 72$ 83$ 83$ 83$ 829$ FV, debt (50)$ 7$ 7$ 7$ 7$ 7$ 7$ 107$ Debt 700$ Last px 50$ Firm value $ 1,029 Equity value $ 329 Last px $ 329 FCF yield 30.4%IRR, Equity 28%IRR debt 21.4%FCF conversion 85%Net 68$ P/E 4.8xEBITDA 179$ EV / EBITDA 5.8x

Source: CLC

In this example, the equity value is caclulated at $418, or 27% higher than in the former example. This produces a 10-year IRR on equity of 21.6%, which exceeds the IRR on debt by 20 bps, which is clearly not a good proposition.

CAPM is linear and not every dynamic when debt is trading at a discount. Beta is a back-tested concept, but the correlation doesn’t link very well to causation, in my opinion. When CAPM indicates the value of something such that the unwind of the discount rate gives an equity holder no return advantage over a senior, contractual obligation of the corporation, I think CAPM falls well short.

On Calculating Expected Return. I am often surprised there isn’t wider agreement on calculating expected return for a given stock. People almost uniformly understand discounting to the present a stream of cash flows and then buying at a discount to the NPV of those cash flows, but there is little agreement on what that means for the return on that asset in future periods. There is general agreement that buying something at $80 what one believes is worth $100 will yield a return of 25%, but that assumes an instantaneous return to fair value. What if it takes three years or five years?

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2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 TermYears 1 2 3 4 5 6 7 8 9 10 10FCF 100$ 90$ 80$ 80$ 85$ 99$ 104$ 115$ 115$ 115$ 1,309$ YoY grow th (10.0%) (11.0%) 0.0% 6.0% 17.0% 5.0% 10.0% 0.0% 0.0%

Base rate 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80% 4.80%OAS 18.0% 18.0% 18.0% 18.0% 18.0% 18.0% 18.0% 10.0% 7.0% 5.0% 4.0%ERP 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00%WAC, after tax 14.8% 14.8% 14.8% 14.8% 14.8% 14.8% 14.8% 9.6% 7.7% 6.4% 5.7%WAC at issue 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0% 7.0%Int exp $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 $ 49 Beta 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 Ke 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% 10.8%Debt % 80% 75% 70% 60% 50% 40% 40% 40% 40% 40% 40%Equity % 20% 25% 30% 40% 50% 60% 60% 60% 60% 60% 60%WACC 14.0% 13.8% 13.6% 13.2% 12.8% 12.4% 12.4% 10.3% 9.5% 9.0% 8.8%

NPV, FCFF 88$ 69$ 55$ 49$ 46$ 49$ 46$ 52$ 50$ 48$ 565$ FV, FCFF (250)$ $ 90 $ 80 $ 80 $ 85 $ 99 $ 104 $ 115 $ 115 $ 115 $ 1,309 NPV, FCFE 62$ 47$ 35$ 32$ 32$ 36$ 35$ 36$ 33$ 30$ 458$ FV, FCFE (350)$ 58$ 48$ 48$ 53$ 67$ 72$ 83$ 83$ 83$ 829$ FV, debt (50)$ 7$ 7$ 7$ 7$ 7$ 7$ 107$ Debt 700$ Last px 50$ Firm value $ 1,118 Equity value $ 418 Last px $ 418 FCF yield 23.9%IRR, Equity 21.6%IRR debt 21.4%FCF conversion 85%Net 68$ P/E 6.1xEBITDA 179$ EV / EBITDA 6.3x

Bond math comes into play here as well as some passages from The Intelligent Investor.10 Bonds provide a great illustration of expected return. I referenced above the yield-to-worst on a bond. If something is at 42, it matures at par in seven years, and the current yield is 13.6%, you get the current yield plus the reinvested cash flows and the accretion of the security from 42¢ to par. In equities, there really is no difference.

If I believe something is worth $100 in present value terms, it’s trading at $67, its cost of equity is 8.7% on average over ten years, it pays no dividend, and FCF is reinvested to yield returns on capital that neither exceed nor fall short of the company’s cost of capital11, the $100 value today should accrete to $108.70 at the end of year one, $118 at the end of year two, etc. as it unwinds its cost of equity. The IRR or expected return on that equity, holding it for 1, 3, 5, n…, years is straightforward. It’s the slope from $80 today to those points in the future. In this example, the one-year IRR would be 36%, the 3-year IRR would be 17%, and the five-year IRR would be 13.7%.

One of the tools I use in position sizing it comparing that expected return vs. its cost of equity. In 2008-2009, I had lower cost of equity positions such as Brown-Forman and Estee Lauder sitting next to more distressed positions with debt and operating leverage because the expected return relative to their cost of equity were all uniformly high. There has been no point other than this in my career where the opportunity to construct a portfolio covering the efficient frontier was as lush as this. I rank position sizes in many other ways, which I discuss elsewhere in our documents, but this is very much a part of that process.

Conclusion. I don’t attack orthodoxy for the fun of it and I didn’t start with the goal of trashing CAPM and beta. From what I have experienced in markets, however, and having studied a wide variety of writings from practitioners and academics alike, I have found these formulae pretty fragile. They work OK in linear environments and then they break down in moments of crisis.

Because I price equity from the credit layer down, I retain the option in the Charlotte Lane mandate to go up the capital structure, where I can capture equity-like returns with greater security of contractually-obligated cash flows and I have a preferential position in the order of liquidation (very rare for me) or recapitalization of the firm (far more often in the scenarios I construct). Oftentimes, a class of credit at a deep discount can “create” the entity at 2x, 3x, 4x gross cash flow when nothing in the equity world came come anywhere close to that sort of valuation.

I remain very aware of credit market signals in every step of our process, both in terms of tactical operations and in terms of security analysis and portfolio construction. As always, my process is evolving and as I learn more, the tools at my disposal will sharpen and I will correct the lenses through which I see the world. I invite readers’ comments on these topics.

10 Graham discusses a company with a cost of equity of 10% and a dividend yield. If the dividend yield is 3% and the company unwinds its cost of capital, annual appreciation will be 7% and annual income will be 3% if the payout ratio is maintained and incremental ROE = 10%.

11 Please see my piece, How A “Platform Company” Works: The Shortcomings of DCFs and Why People Miss Lollapaloozas, for more on the circularity of DCFs.

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