Wednesday, May 27, 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. 


  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)


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


Ak said...

Are you adjusting the cash balances (in your PE graph) as you mentioned for tax liability after repatriation? I find it nearly impossible to discern this information in most public companies and it makes me wonder how much I may be missing in my valuation by using just the balance sheet number.

Kevin Erdmann said...

Great article, as usual.

If I am not mistaken, doesn't this also mean that if you adjusted your equity risk premiums for leverage and cash balances, they would be higher than the published levels? This would be especially interesting since unadjusted ERP is already high.

Aswath Damodaran said...

You are right. If you take out the cash from equity and compute an equity risk premium on only the non-cash assets, it would be higher than my already high number.
I wish I had the information to make the adjustment but I do not. Companies are not required (yet) to break out their trapped cash and tell us what it is invested. Interestingly, it looks like Apple has much of its trapped cash invested in long term investments (but does not specify what they are) rather than liquid, short term investments.

Kevin Erdmann said...

Aswath, I linked to your post on my blog. One of my readers questioned the large current difference between the PE and non-cash PE, and I don't have an answer. Do you have the explanation? Here is his comment:

I enjoyed your post and found it very interesting, but it is quite a larger magnitude fo difference than I would have thought. Are you sure this is correct?

Thus would imply that cash to market cap is close to 30%, by my guess – if you assume that interest on cash is close to zero, lets call it 1% of earnings





Market cap


Earnings ex cash


Ex cash P/E


Market cap




Cash to market cap


That seems like quite a lot to me – the S&P500 is currently valued at $19.2tn, so that would suggest cash balances were north of $5tn which sounds an awful lot ie its $10bn per stock

What am I missing and have you or Aswath checked that data, please?

Aswath Damodaran said...

The market-wide numbers come from adding up market cap and cash balances across all companies in the market, including financial service companies and that skews up this ratio. (The data services just throw cash and ST investments into this item and for financial service companies, that can add up to huge values).
If you look at only non-financial service company, the cash ratio drops to closer to 15% of market capitalization and the effect on non-cash PE is reduced. But the across time effect stays no matter which dataset you look at. If I get a chance, I will also compute market wide numbers for only non-financial service US companies, by year, and put that data up online as well.

Callum Thomas said...

Quick question, your example is a company with no liabilities, but what do you do with short-term (or long-term) liabilities?

Anonymous said...

To follow up on Callums question. Would not debt lead to the complete opposite effect, and given that companies still have more debt than cash your conclusions for the market should be completely opposite?

With your way of calculating it, Apple leaving cash abroad and borrowing in the US to buy back shares pushes down the non-cash PE, as far as I can understand.

Anyway, interesting thoughts and well explained.

Anonymous said...

agreed, not sure it makes sense to adjust for gross cash balances without netting out debt?

Aswath Damodaran said...

On the last comment, netting our debt from what? If you are suggesting that I subtract debt out of market cap, that makes no sense. That would be double netting out debt.

The prior comment raises an interest question of whether adding debt to the equation would change the equation. If you borrow money to buy back stock, while holding on to your cash (which is effectively what Apple did), the cash effect on PE will be greater, because cash as a percentage of market capitalization will increase.

Anonymous said...

On your Apple comment "the cash effect on PE will be greater, because cash as a percentage of market capitalization will increase.". The way you calculate it for the market it will, but is that really correct?

Let's turn the initial example on it's head and change your original company to:

Assets: Software 850
Liabilities: Debt 200, Equity 650

And let's assume they pay 2% interest on their debt as well (for simplicity).

The intrinisic PE of the Software business is still 11.81, the intrinsic PE of the debt 83.33, but what is the intrinsic PE of the equity now? Wouldn't that be 650/(72-2.4) = 9.34.

Clearly, most companies cannot borrow at the risk free rate, but are you not just looking at one side of the story? As your Excel sheet shows companies have more debt than cash, even though they have high levels of cash.

Aswath Damodaran said...

My point was not that the PE would be higher but that the cash effect on PE would be higher, with a higher debt ratio and a given mix of software/cash. One reason everything gets trickier with debt, is that introducing debt will lower the intrinsic PE for the software business, since my cost of equity will rise, as my debt ratio increases. It is one reason why I prefer to work with pre-debt numbers and compute enterprise value.
I think your focus on bringing in debt into the picture is the right one, since you can borrow and leave that borrowing sitting as cash. I am working on a follow-up post on incorporating the effects of debt on PE and hope that I can provide a cleaner more comprehensive way of adjusting for both cash and debt on PE.

Anonymous said...

An update would be great.

Let's say you can borrow at 2% and invest the cash at 2%. Increasing the debt and leaving what you borrow in cash will then increase the cash effect on PE, but you will have a "debt" effect on PE which will offset the higher cash effect, so the intrinsic PE of the equity does not change.

I don't agree that introducing debt will lower the intrinsic PE of the software business either though. It is still the same business. E.g. your 10% is really the cost of capital for the software business, and leaving issues such as tax shield of debt etc. aside the cost of capital does not change when you introduce debt. The cost of equity will rice though and therefore the intrinsic PE of equity will go down, as my simple illustration above shows (based on your illustration).

The challenge with introducing debt, I would think, is that corporates obviously does not borrow at the 1-year T.Bill rate. And most of the debt is not short term.

Unknown said...

Your point is that cash have always been distorting PEs. But now, this distortion are bigger than ever, since US companies have big amounts of cash yielding lower than ever interest rates.

You chart “PE and Non-cash PE: US companies” shows that cash used to add around 1 point to PE (that’s it: PE – Noncash PE), but since year 2000, this difference started to grow and now is adding almost 5 points to PE (in 2014 PE was 16,58x and Non-cash PE was 11,90, so cash added 4,68x to PE).

But, you stated that US companies have huge amount of cash overseas. And you make the simplistic assumption that all this cash is being invested on US 1 year T-bill. But if this money is being invested abroad, how can we be sure that it not being invested in assets yielding more than 1 year T-bill?

In fact, what if, before year 2000, companies were doing exactly what you supposed (that´s it: getting something on the range of US 1-year T-bill on their cash), but since then, they started to invest more and more of their cash overseas, yielding more than US 1-year T-bill, in a way that this would offset the excess cash? Summing up: in this scenario, maybe the final effect on PE would be something neutral (cash would still be adding around 1 point to PE)…

How can we be sure that this is not the case?

Aswath Damodaran said...

Good point about trapped cash, but I don't think it is as big a factor as you think. The trapped cash is at best about 25% of total cash, looking across all US companies, and a big chunk of that cash is in Europe earning even even less than it does in the US. In fact, there is a simple way to tell. If the cash is being invested to generate significant income, it has to show up as interest income and that interest income number for companies where it is available is actually well below 1%.

Apprentice of Agamas said...

Shouldn't the Return on equity on software be 18% and not 36% ?
Here's how I got 18%
Net income from software = $72
Equity = $400
So return on equity on software = 72/400 = 18%
Since you explicitly mentioned Balance sheet, I'm assuming this was a yearly balance sheet and not a 6 monthly ? (though the 36% seems to indicate it was a 6 monthly snapshot)
Thank you!

Anonymous said...

I don't work in finance, but I try to understand a rational approach to the markets as explained in your blog. I'm hoping you can clarify a few calculations that have me lost

If we assume that the company can maintain its existing return on equity of 36% on its new investments in perpetuity

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

I'm thinking reinvestment is the growth needed in fixed assets to generate the 2% income growth. If the fixed assets did not grow then the income would not grow. To generate 2% growth, with a return on fixed assets of 36%, requires an increase of 5.56%

But then the value of the software business has me stumped. The investment is not based on 72, which is the numerator, but on 200. 200 needs to grow by 5.56%, so the net income from software seems like it should be 72 decreased by that amount not by 5.56%

Unknown said...

Very good post. I have opined that lower interest rates tend to cause higher P/E ratios. Also a very good point about cash on the balance sheet. I forget which stock, but my broker did the very same calculation on a very cash rich company. He took the price, subtracted out the cash per share, and then recalculated the Price to Earnings Ratio.

As far as debt on the balance sheet, there is a counter argument that there is a cost of capital to the owners equity (assets minus debt) on the balance sheet. The argument is made that the owners equity has a higher cost of capital than the debt. The business owners (shareholders) demand a higher rate of return than what is represented by the interest payments on the company debt. In a very low interest rate environment, adding low interest debt to the balance sheet would reduce cost of capital. If a larger portion of your balance sheet is low interest debt your cost of capital would be decreased.

For example, a strong balance sheet is 75% equity and 25% debt. Let's say the company levers up a bit and goes to 60% equity and 40% debt. If the market return of stocks is expected to be 6-7% and market interest rates are at 3%, it would seem to be a no brainer that a 60/40 balance sheet would have a lower cost of capital than a 75/25 balance sheet. You can see why companies will issue debt and then retire some of their outstanding stock, particularly if the dividend yield on the stock is higher than the coupon on their bonds! And that is exactly what companies have done.

A counterargument to all of this is that it is no shock to the market that Apple has a lot of cash
on its balance sheet. That is priced into Apple's stock price. Also the fact that companies have floated a lot of debt is also priced in.