Myth 4.5: DCFs break down with near-zero risk free rates!

In any version of a risk and return model for discount rates, where you start with a riskfree rate as a base and build up to costs of equity, debt and capital, it seems blindingly obvious that as interest rates go lower, discount rates will follow and that value will increase. It is this logic that has led to the hand wringing about how central banks have both created pricing bubbles and made discounted cash flow valuations implode by “lowering’ rates. In a recent article, Sanford Bernstein proclaimed DCF all but dead in a world with near-zero risk free rates, because as they see it, the resulting low discount rates were pushing up the value of future cash flows, and since these cash flows are inherently more difficult to estimate, DCFs were less reliable. I have no problem with Bernstein's equity research analysts abandoning DCF and switching to pricing stocks instead, but I believe that they need to do it for the right reasons, not the ones outlined in that thought piece.

Risk free Rates in a Static World

A few months ago, I posted on the hubris of central bankers who (a) believe that they control the level of interest rates and (b) that by changing the level of rates, they can affect stock/bond prices as well as real investments at companies. It is this misguided view of the world that, in my view, has given us years of ever-lower central banking rates, without the promised for results (of more capital investment and higher real growth). It is instructive that almost a decade into quantitative easing, the global economy still seems to be struggling to find its footing. 

Unfortunately, this delusion that you can change the risk free rate and leave all else in the process unaffected is not restricted to central bankers and seems to have spread like a virus among valuation analysts, leading to many following the Bernstein script and abandoning DCF. The mathematics are impeccable. If you leave risk premiums (equity risk premiums and default spreads) unchanged, hold on to old growth rates and lower just the risk free rate, you will see value increase as the risk free rate decreases and perhaps approach infinity at really low or negative risk free rates.

To see why, let's assume that you had valued a company in 2007, when the risk free rate was close to 4% and the equity risk premium was also 4% and that you had assumed that this company's cash flow to equity, $100 million in the most recent year, would grow at 10% a year for the following five years and 4% thereafter. The value that you would obtain in a DCF would be $3.378 billion. Now assume that you have been revaluing the company every year in the years since, keeping the rest of your parameters fixed and changing just the risk free rate. As the risk free rate has dropped to levels not seen in recent history, your valuations will have zoomed:

Download spreadsheet

Your value of this company increase from $3.4 billion to $9.1 billion , as the risk free rate dropped to 1.5%, and lowering the risk free rate further will only increase value. In fact, at a 0% risk free rate (which is where the Euro and the Swiss Franc are at in November 2016), your valuation would approach infinity. As an added feature, as your risk free rate decreases, a greater proportion of your value comes from the terminal value, accounting for almost 94% of your value at a 1.5% risk free rate compared to 84% of value at a 4% risk free rate. That is the crux of the Bernstein argument against DCF, with the twist that estimating future cash flows is always difficult and that lower risk free rates have tilted valuation towards cash flows even further into the future. 

Risk free Rates in a Dynamic World

Let's get real. When risk free rates change substantially, it is not because central banks will them  to be lower or higher, but because of shifts in the fundamentals, and those shifts will affect your other inputs into valuation. In this section, I aim to start by showing how changing risk free rates affect growth rates and risk premiums and then argue that the value effect of a change in the risk free rate can be complicated (as market watchers have found out over the decades).

Risk free Rates and Growth (Real and Nominal)

If you have read my prior posts on interest rates and central banks, one of my favorite tools for understanding interest rates is the Fisher equation, which breaks down a riskless rate into two components: an expected inflation rate and an expected real interest rate. Using a proxy of real GDP growth for the real interest rate, I derive an "intrinsic" risk free rate as the sum of the inflation rate and real GDP growth. I may be stretching but it works surprisingly well at explaining why interest rates move over time, as evidenced in the graph below, where I compare the T.Bond rate to the sum of inflation and GDP growth each year from 1954 to 2015.

So, what's the point of this graph? In addition to emphasizing the fact that central banks can affect rates only at the margin, it brings home the reality that low interest rates are indicative of a market that expects both inflation and real growth to remain low. It is entirely possible that the market is wrong but if you are doing valuation, you cannot selectively override the market on one variable (growth in the static example) while holding on to it on the other (risk free rate). 

Dynamic Implication: As the risk free rate changes, your estimates of nominal growth will have to be stepped down, not because you have changed your beliefs about a specific company, but because you should be lowering the base growth rate for the economy (global or domestic).

Risk free Rates and ERP

The second variable that goes into play when risk free rates change is the equity risk premium. Again, you have to let go of the notion that equity risk premiums are static numbers that come out of historical data but are reflections of market worries about the future and investor risk aversion. Not surprisingly, the same forces that cause interest rates to move also affect the market's perception of risk and will cause equity risk premiums to shift. This can be seen when you look at implied equity risk premiums, where you back out what the market is demanding as an expected return on stocks from cash flows and subtract the risk free rate. In the graph below, I outline this effect since 2008.

The most striking finding, at least for me, is how little the expected return on stocks has changed since 2008, staying around 8%, while risk free rates have more than halved. The net effect is that the equity risk premium, close to 4% prior to 2008, has now moved to 6% and above. 

Dynamic Implication: As the risk free rate changes, the equity risk premiums you use will also have to change to reflect the market's updated expectations. A crisis that causes rates to plummet will also make risk premiums rise. If you stick with historical risk premiums, while using current risk free rates, you will misvalue companies.

Risk free Rates and Default Spreads

The same forces that cause equity risk premiums to rise as risk free rates drop also come into play in the bond market in the form of default spreads on bonds. In the graph below, I estimate the default spread on a Baa rated bond by comparing the Baa bond rate to the T.Bond rate each year from 1960 to 2015.

As with the equity risk premium, default spreads have widened since 2008, from 2.02% in 2007 to 3.23% in 2015. 

Dynamic Implication: As the risk free rate changes, the default spread used to estimate the cost of debt should also change, thus ensuring that the cost of debt will not move in lock step with the risk free rate.

Risk free Rates and Debt Ratios

To complete the story, the final ingredient that you need for the cost of capital estimation is a debt to capital ratio in market value terms. If as risk free rates change, both the equity risk premium and default spread also change, it should come as no surprise that the relative benefits of using one (debt) over the other (equity) will also shift. To chronicle these change, I looked at the aggregate debt to capital ratios, in market and book value terms, for all US stocks, each year from 2000 to 2015.

If you divide the time period into pre-2008 higher risk free rate and post-2008 lower risk free rate sub periods, it seems quite clear that US companies are borrowing more money than they used to. The facile explanation is that this is exactly what you would expect with lower interest rates but remember that those lower rates feed into both the cost of equity and debt. This effect is a more subtle one and reflects the relative risk premiums for equity and debt, perhaps suggesting that the price of equity risk has risen more than debt risk. 

Dynamic Implication: As the risk free rate changes, the debt ratios for companies will also change as they reevaluate the trade off of using debt as opposed to equity. That change, in conjunction with tax and default risk assessments, will lead to a change in the cost of capital.

Risk free Rates and Value: The Full Picture

Now that we have a fuller picture of how risk free rates are interconnected to risk premiums and growth rates, let me revisit the example that I initiated in the static world of valuing equity in a company with a base year cash flow to equity of $100 million. Rather than let the growth rates and the risk premiums stay unchanged, here is what I assumed:

• The nominal growth rate in the economy will be equal to the risk free rate, reflecting how closely the T.Bond rate has tracked the nominal GDP growth rate.
• The company will grow at a rate 6% higher than the nominal growth rate of the economy for the next five years. Thus, with a 4% riskfree rate, the growth rate is 10%, matching the original assumption, but at a 2% riskfree rate, the nominal growth in cash flows will be 8%. In perpetuity, the company will now grow at the riskfree rate = nominal growth rate of  the economy,
• The equity risk premium is the trickiest component, but if the market's behavior over the last decade is any indication, the expected return on stocks will stay at 8%, with the equity risk premium adjusting to the new risk free rate. Thus, if the riskfree rate drops to 2%, the equity risk premium will be 6%.

The effect on value of changing the growth rate is captured in the picture below:

Download spreadsheet

Note that the neither the value nor the percentage of the value from terminal value change much as the risk free rate drops; in fact, they both decline marginally. Furthermore, I can now explore the effect on value of having a zero or negative riskfree rate and it is benign.

I can only give you my personal perspective on how lower interest rates have affected my valuations. With lower rates, contrary to the Bernstein thesis, I find myself less worried about terminal values and the assumptions that I might have made incorrectly. When my nominal growth rate in perpetuity is capped at 2%, 1% or even 0%, I can do far less damage with my assumptions about what a firm can do in perpetuity, than I did in 2007. If anything, low risk free rates makes my intrinsic valuations less volatile, not more so. It is true that these are dangerous times for auto-pilot DCFs where a combination of inertia, trust in historical data (on risk premiums and growth rates) and failure to check for internal consistency can lead to explosively bad DCFs. If Bernstein's point is that a good pricing (based upon multiples and comparable firms) is better than an auto-pilot DCF, I am in agreement!

Playing Devil's Advocate
If you are skeptical about my arguments, I don't blame you! In fact, I will preempt you and bring up some counter arguments that you can make against my thesis.

1. Mean Reversion: The essence of mean reversion is that when something looks unusually low or high, it will be revert back to historic norms. Using this argument on risk free rates, there are some who use "normalized" risk free rates (with the extent of normalization varying across users) in valuation. There are two problems with this argument. The first, and I referenced it in a different context in my post on CAPE, is that assuming things will revert back to the way they used to be can be dangerous, if there has been a structural shift in the process. The second, and perhaps even stronger, argument is that you cannot selectively mean revert some numbers and not mean revert others. Thus, if you decide to replace today's risk free rate with a normalized risk free rate of 4%, reflecting 2007 levels, you have to also adjust your growth rates and risk premiums to reflect 2007 levels. In effect, you will be valuing your company in 2016, as if your were back in 2007. Good luck with that!
2. Central Bank as Master Manipulators: The conventional wisdom is that the Fed (and central banks) are all-powerful and that the low rates of today have little to do with fundamentals and more to do with central banking policy. If you believe that and you also believe that markets are being led by the nose, you do have the basis for a "bubble" argument, where "artificially" low interest rates are leading all financial assets into bubble territory. The problem, though, is that if this were the case, the cost of equity should be tracking down, in step with the risk free rate, and as the figure on equity risk premiums (in the section above) notes, that does not seem to be the case. 

That is not to say that I am sanguine about low interest rates. The low growth and low inflation that these numbers signal are having their effect on companies. Real investment has declined, cash flows to investors (in dividends and buybacks) have increased and cash balances have surged. The increase in debt at companies will not only increase default risk but make these companies more sensitive to macro economic shifts, with more distress and default coming in the next downturn. Finally, to the extent that central banks send signals about the future, the desperation that is being signaled by their policies does not evoke much confidence in them. 

Conclusion

The risk free rate is an input into a discounted cash flow valuation but it is not an input that can be changed in isolation. When risk free rates change, they reflect shifts in fundamentals that should also show up in risk premiums and growth rates, making any resulting change in value difficult to forecast. As the hysteria mounts ahead of the next FOMC meeting, my suggestion is that you step back and take a big-picture perspective. This too shall pass!

YouTube Video


Attachments

1. Risk free rates, Inflation and GDP Growth
2. Risk free rates and ERP
3. Risk free rates and the Baa Default Spread
4. Risk free rates and Debt Ratios over time
5. Static and Dynamic Valuation Spreadsheet

DCF Myth Posts

Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. It's all about D in the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant in the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.

Negative Interest Rates: Impossible, Unnatural or Just Unusual?

In the years since the 2008 crisis, there is no question in finance that has caused more angst among investors, analysts and even onlookers than what to do about "abnormally low" interest rates. In 2009 and 2010, the response was that rates would revert back quickly to normal levels, once the crisis had passed. In 2011 and 2012, the conviction was that it was central banking policy that was keeping rates low, and that once banks stopped or slowed down quantitative easing, rates would rise quickly. In 2013 and 2014, it was easy to blame one crisis or the other (Greece, Ukraine) for depressed rates. In 2015, there was talk of commodity price driven deflation and China being responsible for rates being low. With each passing year, though, the conviction that rates will rise back to what people perceive as normal recedes and the floor below which analysts thought rates would never go has become lower. Last year, we saw short term interest rates in at least two currencies (Danish Krone, Swiss Franc) become negative and this year, the Japanese Yen joined the group, with rumors that the Euro may be the next currency to breach zero. While it has been difficult to explain the low interest rates of the last few years, it becomes doubly so, when they turn negative. I would be lying if I said that negative interest rates don't make me uncomfortable, but I have had to learn to not only make sense of them but also to live with them, in valuation and corporate finance. This post is a step in that direction.

Setting the table
There are a handful of currencies that have made the negative interest rate newswire, but it is worth noting that the rates that are being referenced in many of these stories are rates controlled by central banks, usually overnight rates for banks borrowing from the central bank. In March 2016, there were two central banks that had set their controlled rates below zero (Switzerland and Sweden) and two more (ECB and Bank of Japan) that had set the rate at zero. (Update: The ECB announced that it would lower its rates below zero on March 10.)

February 2016

Note that these are central bank set rates and that short and long term market interest rates in these currencies can take their own path. To provide a contrast, consider the Japanese Yen and Euro, two currencies where the central banks have pushed the rates they control to zero. In both currencies, short term market interest rates have in fact turned negative but only the Yen has negative long term interest rates:

In a post from earlier this year, I looked at long term (ten-year) risk free rates in different currencies, starting with government bond rates in each currency and then netting out sovereign default spreads for governments with default risk. Updating that picture, the government bond rates across currencies on March 9, 2016, are shown below:

Ten-year Government Bond Rates - March 9, 2016

Joining the Japanese Yen is the Swiss Franc in the negative long term interest rate column. Why make this distinction between central bank set rates, short term market interest rates and long term interest rates? It is easier to explain away negative central bank set rates than it is to explain negative short term interest rates and far simpler to provide a rationale for negative rates in the short term than negative rates in the long term. Thus, there have been episodes, usually during crises, where short term interest rates have turned negative, but this is the first instance that I can remember where we have faced negative long term rates on two currencies, the Swiss Franc and the Japanese yen, with the very real possibility that they will be joined by the Euro, the Danish Krone, the Swedish Krona and even the Czech Koruna in the near future.

Interest Rates 101

I am not a macroeconomist, have very little training in monetary economics and I don't spent much time examining central banking policies. Keep that in mind as you read my perspective on interest rates, and if you are an expert and find my views to be juvenile, I am sorry. That said, I have to process negative interest rates, using my limited knowledge  of what determines interest rates.

Intrinsic and Market-set Interest Rates
When I lend money to another individual (or buy bonds issued by an entity), there are three components that go into the interest rate that I should demand  on that bond. The first is my preference for current consumption over future consumption, with rates rising as I value current consumption more. The second is expected inflation in the currency that I am lending out, with higher inflation resulting in higher rates. The third is an added premium for any uncertainty that I feel about not getting paid, coming from the default risk that I see in the borrower. When the borrower is a default-free entity, there are only two components that go into a nominal interest rate: a real interest rate capturing the current versus future consumption trade off and an expected inflation rate.

Nominal Interest Rate = Real Interest Rate + Expected Inflation Rate

This is, of course, the vaunted Fisher equation.  There is an alternate view of interest rates, where the interest rate on long term bonds is determined by the demand and supply of bonds, and it is shifts in the demand and supply that drive interest rates:

How do you reconcile these two worlds? To the extent that those demanding bonds are motivated by the need to earn interest that covers the expected inflation and generate a real interest rate, you could argue that in the long term, the intrinsic rate should converge on the market set rate.

In the short term, though, as with any financial asset, there is a real chance that the market-set rate can be lower or higher than the intrinsic rate. What can cause this divergence? It could be investor irrationality, where bond buyers overlook their need to cover inflation and earn a real rate of return. It could be a temporary shock to the supply or demand side of bonds that can cause the market-set rate to deviate; this is perhaps the best way to think about the "flight to safety" that occurs during every crisis, resulting in lower market interest rates. There is one more reason and one that many investors seem to view as the dominant one and I will address it next.

The Central Bank and Interest Rates
In all of this discussion, notice that I have studiously avoided bringing the central bank into the process, which may surprise you, given the conventional wisdom that central banks set interest rates. That said, a central bank can affect interest rates in one of two ways:

• The first and more conventional path is for the central bank to signal, through its actions on the rates that it controls what it thinks about inflation and real growth in the future, and with that signal, it may alter long term rates. Thus, the Fed lowering the Fed funds rate (a central bank set rate that banks can borrow from the Fed Window) will be viewed as a signal that the Fed sees the economy as weaken and expects inflation to stay subdued or even non-existent, and this signal will then push expected inflation and real interest rates down. This will work only if central banks are credible in their actions, i.e., they are viewed as acting in good faith and with good information and are not gaming the market. 
• The second channel is for the central bank to actively enter the bond market and buy or sell bonds, thus affecting the demand for bonds, and interest rates. This is unusual but it is what central banks in the United States and the EU have done since 2008 under the rubric of quantitive easing. For this to have a material effect on interest rates, the central bank has to be a big enough buyer of bonds to make a difference. 

Thus, as you read the news stories about the Japanese central bank and the ECB considering negative interest rates, recognize that they cannot impose these rates by edict and that all they can do is change the rates that they control and let the signaling impact carry the message into bond markets.

Measuring the Fed Effect
Just ahead of the Federal Open Market Committee meetings last year, as debate about whether the Fed would ease up on quantitative easing, I argued that we were over estimating the effect that the Fed had on market set rates and that while it has contributed to keeping rates low for the last six years, an anemic economy was the real reason for low interest rates. To compute the Fed effect, I chose to track two numbers:

• An intrinsic interest rate, computed by adding together the actual inflation each year and the real growth rate each year, two imperfect proxies for expected inflation and the real interest rate.
• The ten-year US treasury bond rate at the start of each year, set by the bond market, but affected by expectation setting and bond buying by the Fed.

The graph below captures both numbers, updated through 2015:

Note how closely the US treasury bond has tracked my imperfect estimate of the intrinsic interest rate, and how low the intrinsic rate has become, post-crisis. At the risk of repeating myself, the Fed has, at best, had only a marginal impact on interest rates during the last six years and it is my guess that rates would have stayed low with or without the Fed during this period.

Negative Interest Rates
Turning to the question at hand, is it possible for nominal interest rates to be negative, based upon fundamentals? The answer is yes, but with a caveat. If the preference for current consumption over future consumption dissipates or gets close to zero and you expect deflation in a currency, you could end up with a negative interest rate. In fact, that is the common thread that runs through the economies (Japan, the Euro Zone, Switzerland) where rates have become negative.

Now, comes the caveat. If you have nominal negative interest rates, why would you ever lend money out, since you have the option of just holding on to the money as cash. Historically, that has led many to believe that the floor on nominal rates should be zero. As rates go below zero, it is time to reexamine that belief. One way to reconcile negative interest rates with rational behavior is to introduce costs to holding cash and there are clearly some to factor in, especially in today's economies. The first is that while the proverbial stuffing cash under your mattress option is thrown around as a choice, you will increase your exposure to theft and may have to invest in security measures that are costly. The second is that there are some transactions that are extraordinarily cumbersome to get done with cash; imagine buying a million dollar house and counting out the cash for the payment. The Danish, Swiss and Japanese governments are embarking on a grand experiment, perhaps, of how much savers will be willing to pay for the convenience of staying cashless. In effect, the lower bound has shifted below zero but there is still one. To those who are convinced that negative interest rates have nothing to do with fundamentals and that they are entirely by central bank design, I would argue that the only reason that these central banks have been able to push rates below zero, is because real growth and inflation have become so low in their economies that the intrinsic rate was close enough to zero to begin with. There is no chance that the Brazilian and Indian central banks will follow suit.

Interest Rates, Financial Assets and the Real Economy

When central banks in these currencies strongly signal their intent to drive interest rates to zero and below, what could be the motivation? Put simply, it is the belief that lower interest rates lead to higher prices for financial assets and more real investment in the economy, either through the mechanism of "lower" hurdle rates for investments or a weaker currency making businesses more competitive globally. In this central banking heaven, where central banks set rates and the world meekly follows, this is what unfolds:

So, why has it not worked? As interest rates in the US, Europe and Japan have tested new lows each year for the last few, we have not seen an explosion in real investment in these countries, and while stock prices have risen, the rise has had as much to do with higher earnings and cash flows, as it has to do with lower interest rates. In my view, the fundamental miscalculation that central banks have made is in assuming that their actions not only affect other pieces of this puzzle but are also read as signals of the future.  In particular, central bankers have failed to incorporate three problems: that interest rates do not always follow the central bank lead, that risk premiums on equity and debt may increase as rates go down and that exchange rate effects are muted by other central banks acting at the same time. In this reality-based central banking universe, the lowering of rates by central banks can have unpredictable and often perverse consequences, lowering financial asset prices, reducing real investment and making a currency stronger rather than weaker.

This is all hypothetical, you may say, but there is evidence that markets have become much less trusting of central banking and more willing to go their own ways. For instance, as the risk free rate has dropped over the last few years, note that the expected return for stocks has stayed around 8% during that period, leading to higher and higher equity risk premiums.

While bond markets initially did not see this phenomenon, last year default spreads on bonds in every ratings class widened, even as rates dropped. Interestingly, the most recent ECB announcement that they would push the rates they control lower was accompanied by news that they would enter the bond market as buyers, hoping to keep default spreads down. That is an interesting experiment and I have a feeling that it will not end well.

Dealing with Negative Interest Rates
My interests in negative interest rates are primarily in the context of valuation and corporate finance. In both arenas, the hurdle rates we use to pick investments and value businesses build off a long term risk free rate as a base and having that base become a negative value is disconcerting to some. There are two choices that you have:

1. Switch currencies: You can value Danish companies in Euros or US dollars, where long term rates are still positive (albeit very low). This evades the problem, but you can run but you cannot hide. At some point in time, you will have to work in the negative interest rate currency.
2. Normalize risk free rates: This is a practice that has become more prevalent in both the US and Europe, where risk free rates have dropped to historic lows. To compensate, analysts are using the average rate across long periods as a normalized risk free rate. I have problems with this approach at three levels. The first is that normal is in the eye of the beholder and what you call a normal 10-year T.Bond rate is more a function of your age than scientific judgment. The second is that given that the risk free rate is where you plan to put your money if you don't make your real investment, it seems singularly dangerous for this to be a made-up number. The third is that using a normalized risk free rate with the high equity risk premiums that are prevalent today will lead to too high a hurdle rate, since the latter are primarily the result of low risk free rates.
3. Leave the risk free rate negative: So, what if the risk free rate is negative? In valuation, you almost never use the risk free rate standing alone, but only in conjunction with a risk premium. If you can update those risk premiums, they may very well offset the effect of having a negative risk free rate and yield a cost of equity and/or debt that does not look different from what it did prior to the negative interest rate setting. There is one other adjustment that I would make. In stable growth, I have been a proponent of using the risk free rate as your cap on the stable growth rate. With negative risk free rates, I would stick with this principle, since, as I noted earlier in this post, negative interest rates signify economies with low or no real growth combined with deflation and the growth rate in perpetuity for stable companies in these economies should be negative for those same reasons.

What Real Negative Interest Rates Signify

When interest rates of from being really small positive numbers (0.25% or 0.50%) to really small negative numbers (-0.25% to -0.50%), the mathematical consequences are small but I do think that breaching zero has consequences and almost all of them are negative.

1. The economic end game: For those who ultimately care about real economic growth and prosperity, negative interest rates are bad news, since they are incompatible with a healthy, growing economy. 
2. Central banks insanity, impotence and desperation: As I watch central bankers preen for the cameras and hog the limelight, I am reminded of the old definition of insanity as trying the same thing over and over, expecting a different outcome. After six years of continually trying to lower rates, with the expectation of economic growth just around the corner, it is time for central banks to perhaps recognize that this lever is not working. By the same token, the very fact that central banks revert back to the interest rate lever, when the evidence suggests that it has not worked, is a sign of desperation, an admission by central banks that they have run out of ideas. That is truly scary and perhaps explains the rise in risk premiums in financial markets and the unwillingness of companies to make real investments. 
3. Unintended consequences: As interest rates hit zero and go lower, there will be some investors, in need of fixed income, who will look in dangerous places for that income. A modern-day Bernie Madoff would need to offer only 4% in this market to attract investors to his fund and as I watch investors chase after yieldcos, MLPs and other high dividend paying entities, I am inclined to believe that is a painful reckoning ahead of us. 
4. An opening for digital currencies: In a post a few years ago, I looked at bitcoin and argued that there will be a digital currency, sooner rather than later, that meets the requirements of trust needed for a currency in wide use. The more central bankers in conventional currencies play games with interest rates, the greater is the opening for a well-designed digital currency with a dependable issuing authority to back it up.

In the next few weeks, I am sure that we will read more news stories about central banks professing to be shocked that markets have not done their bidding and that economies have not revived. I am not sure whether I should attribute these rantings to the hubris of central bankers or to their blindness to market realities. Either way, I feel less comfortable with the notion that central bankers know what they are doing and that we should trust them with our economic fates.

YouTube Video

Datasets

1. Central Bank Rates & Government Bond Rates - March 10, 2016
2. Intrinsic and Actual T.Bond Rates - 1954- 2015
3. Risk Premiums on Stocks and Bonds - 1960-2015

The Value and Pricing of Cash: Why low interest rates & large cash balances skew PE ratios

For an asset that should be easy to value and analyze, cash has been in the news a lot in the last few months, both when it has been returned (in buybacks especially) and also when it has been accumulated either domestically or offshore. Since companies have always returned cash and held cash balances, you may wonder why these stories are news worthy but I think that the cash is under the spotlight because of a convergence of factors, including the rise of technology companies in the market cap ranks, a tax law in the US that is increasingly a global outlier, and low interest rates.

Accounting for, Valuing, and Pricing Cash

I start my valuation class with a simple exercise. I hold up an envelope with a $20 bill in it (which everyone in the class has seen me put into the envelope) and ask people how much they would pay for the envelope.  While some find this exercise to be absurd, it does bring home a very simple rule, which is that valuing cash should not require complicated valuation models or the use of multiples. Unfortunately, I see this rule broken on a daily basis as investors mishandle cash in companies, both in intrinsic valuation and pricing models.

To illustrate the divide between risky assets and cash, assume that you are trying to value a software company, with a cash balance (which is invested in liquid, riskless or close-to-riskless investments) of $200 million. Let's assume that the accounting income statement & balance sheet for the company looks as follows:

If you believe the accounting balance sheet, this company is half software and half cash but that is misleading for two reasons. The first is that assets on accounting balance sheets are not marked to market and can remain at low values, even as their earnings power rises. The second is that accounting rules (absurdly) treat R&D, the biggest capital expenditure at technology firms, as operating expenses, which then results in those assets never showing up on the balance sheet. The ripple effects of understating the book value of equity can be seen in the high returns on equity that I report for the firm.

Having established that book-value cash ratios will be skewed by the changing composition of the market, let's turn to the question of valuing this company. For simplicity, let's assume that the cost of equity for investing in the software business is 10% and that the expected growth in income from software is 2% in perpetuity. If we assume that the company can maintain its existing return on equity of 36% on its new investments in perpetuity, the value of the software business is:

• Expected net income from software = $72 million
• Expected reinvestment to generate growth = 2%/36% = 5.56%
• Value of Software business = 72 (1-.0556)/ (.10-.02) = $850 million

The cash is invested in liquid, riskless investments earning 2% (pre-tax). The fact that cash earns a low rate of return does not make it a bad investment, because that low rate of return is what you should expect to make on a short-term, riskfree investment. If you decide to do an intrinsic valuation of the income from cash, you should discount the income at the risk free rate:

• Expected pre-tax income from cash = $ 200 (.02) = $4 million
• Cost of equity = Riskfree rate = 2%
• Value of equity = 4/.02 = $200 million

The intrinsic value balance sheet for this company is shown below:

Note that the software business is now worth a lot more than it was in the accounting balance sheet but that cash value remains unchanged. The value of equity on the balance sheet is an intrinsic equity value.

In pricing, the tool used in comparisons is usually a multiple and the most commonly used multiple is the PE ratio. To set the table for that discussion, I have restated the intrinsic value balance sheet in the form of PE ratios for the software business, cash and equity overall.

The PE ratios for software and cash are computed by dividing the intrinsic values of each one by the after income generated by each. The PE ratio for cash can be simplified and stated as a function of the risk free rate and tax rate:

The PE ratio for cash is much higher than the PE for software (11.81) and it is pushing up the PE ratio for equity in the company to 14.11. Put differently, if the stock is priced based on its intrinsic value, it should trade at a PE ratio of 14.11.

How will bringing in debt into this process change the game? Let's assume that you borrowed $300 million and bought back stock in this company, while leaving the existing cash balance unchanged. Reducing your market cap by roughly $300 million will augment the effect of cash on PE and make the non-cash PE ratio even lower.

Cash Balances and PE: Determinants

In the market, we observe the PE ratios for equity in companies, and those PE ratios will be affected by both how much cash the company holds and the interest rate it earns on that cash.  To the extent that cash balances (as a percent of value) vary across time, across sectors and across companies, the conclusions we draw from looking at PE ratios can be skewed by these variations. To observe how much of an impact the cash holdings have on the observed PE ratio for a company, I varied the cash balance in my software company from 0% to 50% of the intrinsic value of the company; at 50%, the cash balance is $850 million and is equal to the value of the software business. The PE ratio for equity in the company is shown in the graph below, with the cash effect on PE highlighted:

The effect of holding cash is accentuated when the interest rate earned on cash, which should be a short term risk free (or close to risk free) rate, is low relative to the cost of equity. In the table below, I highlight the interest rate effect, by holding the cost of equity fixed at 8% and varying the risk free rate from 1% to 5%:

Thus, a cash balance that amounts to 20% of firm value will push PE ratios from 15.38, when the short-term, risk free rate is 1% and to only 14.08, when it is 5%.

It is true that companies with global operations are accumulating some of their cash overseas to avoid US taxes. Bringing in trapped cash into this process is easy to do and requires you to separate cash balances into domestic and trapped cash; the biggest problem that you face is getting that information, since most companies are not explicit about the division. While the domestic cash balance is its stated value, the trapped cash will see its value reduced by the expected tax liability that will be incurred when the cash is repatriated (which will require assumptions about when that will be and what the differential tax rate paid on repatriation will amount to.)

The US Market: PE and Cash
At this point in this discourse, you may be wondering why we should care, since companies in the US have always held cash and had to earn close to a short-term risk free rate on that cash. That is true but we live in uncommon times, where risk free rates have dropped and corporate cash holdings are high, as is evidenced in this graph that looks at cash as a percent of firm value (market value of equity+ total debt) for US companies, in the aggregate, from 1962 to 2015 and the one-year treasury bill rate (as a proxy for short term, risk free rates):

Data from Compustat & FRED: Computed across all money-making companies

With short-term risk free rates hovering around zero and cash balances close to historical highs, you would expect the cash effect on PE to be more pronounced now than in the past. To measure this effect, I computed PE ratios and non-cash PE ratios each year for US companies, using the following equations:

The interest income from cash was estimated using the average cash balance during the course of the year and average one-year T.Bill rate for that year. In the graph below, I look at the paths of both measures of PE from 1962 through 2014. Note that while while both series move in the same direction, the divergence has become larger since 2008; in 2014, the non-cash PE was almost 30% lower than the conventional PE.

Update: The PE effect is large, especially in the last five years. It is perhaps being exaggerated by the inclusion of financial service firms in the sample, since cash and short term investments at these firms can be huge and are really not comparable to cash holdings at other companies. If you remove them from the sample, the cash effect does get smaller. Rather than pick and choose which data I will report, I have included the year-by-year averages for the US for four sets of data: all companies, only non-financial service companies, all money-making companies and all non-financial money-making companies in this link. 

I know that the talk of a bubble gets louder each day, and while there may be legitimate reasons to worry about the level of stock prices, those who base their bubble arguments entirely on PE ratios (normalized, adjusted, current) may need to revisit their numbers. All of the versions of the PE will be "pushed up" by the cash holdings of US companies and the low interest rate environment that we live in.

Sector Differences in Cash and PE

Cash balances have varied not only across time but they are also different across sectors and within sectors, across companies. Consequently, comparing PE across sectors or even across companies within a sector, without adjusting for cash, can be dangerous, biasing you away from companies with large cash balances (which will look expensive on an unadjusted PE) and especially so during periods of low interest rates.

In the first part of the analysis, I estimated cash as a percent of firm value, PE ratios and non-cash PE for each sector in 2014. (I eliminated financial service companies from my sample, since I am not sure that I can categorize cash as a non-operating asset for these companies). While all of the industry averages can be downloaded at the link below, the sectors where the cash effect on PE was greatest are listed below:

In the second part of the analysis, I computed the cash effect on PE for individual companies and then looked at the distribution of this cash effect across all companies:

It delivers the message that there is no simple rule of thumb that will work across all companies or even across companies within a sector.

Perhaps, the best way to check out the effect of cash on PE is to pick a company and take it through the cleansing process, a very simple one that requires relatively few inputs. Use this spreadsheet to try it on your favorite (or not-so-favorite) company.

Rules for dealing with cash

In an investing world full of complications, simple measures like PE retain their hold because they are easy to compute and easy to work with. However, there is a price that we sometimes pay for this simplicity, and in periods like this one, where interest rates are at historic lows, we may need to reassess how we use these measures to compare companies. In particular, I think we have to separate companies into their cash and operating parts, and deal with the two separately, because they are so different in terms of risk and earnings power. Thus, it we are using multiples, enterprise value multiples will work better than equity multiples, and with equity multiples, non-cash versions (where the cash is stripped from market capitalization and net income is cleansed of the cash effect) will be more reliable than cash versions. This will also mean that the time honored way of estimating PE, i.e., dividing the market price today by the earnings per share, will have to be replaced by an approach where we use use aggregated market value, cash and earnings, rather than per share numbers. 

Spreadsheets

1. Intrinsic value of cash and operating assets (to back up example in post)
2. PE Cleanser (to compute non-cash PE for a company)

Datasets

1. Cash and non-cash PE ratios by year: All US companies
2. Cash and non-cash PE ratios by sector in 2014