In my last post, I looked at the leavening effect that large cash balances have on PE ratios, especially in a low-interest rate environment. In making that assessment, I used a company with no debt to isolate the effect of cash, but many of the comments on that post raised interesting points/questions about debt. The first point is that while cash acts as an upper for PE, debt can act as a downer, with increases in debt reducing the PE ratio, and that if we are going to control for cash differences in the market across time, we should also be looking at debt variations over the years. The second is the question of which effect on PE dominates for firms that borrow money, with the intent of holding on to the cash. In this post, I will start by looking at debt in isolation but then move to consider the cross effects of cash and debt on PE.

**Debt and PE: A simple illustration**

To examine the relationship between PE and debt, I went back to the hypothetical software firm that I used to evaluate the effect of cash on PE. Initially, I assume that the firm has no cash and no debt and is expected to generate $120 million in pre-tax operating income next year, expected to grow at 2% a year in perpetuity. Assuming that the cost of equity (and capital) for this firm is 10%, that the tax rate is 40% and that its return on equity (and capital) on new investments is 36%, the company's income statement and intrinsic value balance sheet are as follows:

Now, assume that this firm chooses to move to a 40% debt ratio with a pre-tax cost of borrowing of 4%. The effects of the debt on the are traced through in the picture below:

Note that the value of the business has increased from $850 million to $988.37 million, with

__the bulk of the value increase coming from the tax subsidies generated by debt__.
The effects of borrowing show up everywhere, with almost almost every number shifting, and the effects at first sight seem to be contradictory. Higher debt

__raises the cost of equity__but__lowers the cost of capital__,__reduces net income__but__increases earnings per share__and results in a__lower PE ratio__, while increasing the__value per share__. The intuition, though, is simple. Borrowing money to fund the business increases both the expected returns to equity investors (captured in the EPS increase) and the riskiness in those equity returns (pushing the PE ratio down) and at least at a 40% debt ratio, the benefits outweigh the costs. In fact, if you are able to continue to borrow money at 4% at higher debt ratios, the PE ratio will continue to drop and the value per share continue to increase as the debt ratio increases.Note that at a 90% debt to capital ratio, the PE ratio drops to 2.75 but the value per share increases to $11.41. If it is sounds too good to be true, it is, because there are two forces that will start to work against debt, especially as the debt ratio increases. The first is that the

__rate at which you borrow will increase as you borrow more__, reflecting the higher default risk in the company. The second is that at a high enough debt level, with high interest rates,

__the interest expenses may start to exceed your operating income__, eliminating the tax benefits of debt. In the table below, I highlight the effects on PE and value per share of different borrowing rates:

The breakeven cost of borrowing, at least in this example, is around 8.6%; if the company borrows at a rate that exceeds 8.6%, debt reduces the value per share. The effect on PE, though, is unambiguous. As you borrow more money, the PE ratio decreases and it does so at a greater rate, if the borrowing rate is high.

**Debt, Cash and PE: Bringing it all together**

Now that we have opened to the door to cash and debt separately, let's bring them together into the same company. A measure that incorporates both cash and debt is the net debt, which is the difference between the cash and debt balances of the company.

Net Debt = Total Debt - Cash and Marketable Securities

This number will be negative when cash balances exceed total debt, zero, when they offset each other, and positive, when debt exceeds cash. In the table below, I have estimated the PE ratio for the company with different combinations of debt ratios (from 0% to 50%) with cash ratios (from 0% to 50%), with debt borrowed at 4% and cash invested at 2%:

Numbers in red are declines in value/share |

Note that both the cash effect, which pushes up PE ratios, and the debt effect, which pushes down PE ratios, is visible in this table. Interesting, a zero net debt ratio (which occurs across the diagonal of the table) does not have a neutral effect on PE, with PE rising when both debt and cash are at higher values; thus the PE when you have no cash and no debt is 11.81, but it is 12.66 when you have 40% debt and 40% cash. Before you view this as a license to embark on a borrow-and-buy treasury bills scheme, note that the value per share effect of borrowing money and holding it as cash is negative; the value per share declines $0.22/share when you move from a net debt ratio of zero (with no debt and no cash) to a net debt ratio of zero (with 40% debt and 40% cash). Again, there is no mystery as to why. If you borrow money at 4% and invest that money at 2%, which is effectively what you are doing when cash offsets debt, you are worse off than you would have been if you had no cash and no debt. In fact, the only scenario where the value effect of borrowing money and buying T.Bills is neutral is

__when you can borrow money at the risk free rate__but even in that scenario, the PE ratio still increases. In short, the cash effect dominates the debt effect and you can check it out for yourself by downloading the spreadsheet that I used for my computations.**Cash and Debt Effects on PE: US Stocks from 1962 to 2014**

In my last post, I noted the difficulty with dealing with cash balances at financial service firms, where the cash serves a very different purpose than it does at non-financial service firms. That statement is even more applicable when it comes to debt, since debt to a financial service firm is less a source of capital and more raw material. Hence, I will focus entirely on non-financial service firms for this section. The first set of statistics that I will estimate relate to debt and cash. In the graph below, I look at cash as a percent of firm value (estimated as market capitalization plus total debt), total debt as a percent of that same value and the net debt ratio (the difference between total debt and cash, as a percent of value) for non-financial service firms in the US from 1962 to 2014.

Raw data from Compustat: All money-making, non-financial service firms |

Note the median values for cash and debt are highlighted on the graph. In 2014, the cash holdings at non-financial service companies in the US amounted to 7.30%, higher than the median value of 7.23% for that statistic from 1962 to 2014, and the total debt was 24.20% of value, lower than the median value of 28.39 for that ratio from 1962 to 2014. Since cash pushes up PE ratios and debt pushes down PE ratios, the 2014 levels for both variables are biasing PE ratios upwards, relative to history.

Unlike the cash effect, which I was able to measure with relative ease by netting cash out of the market capitalization and the income from cash from the net income, the debt effect is messier to isolate. If you assume that cash is the only non-operating asset (i.e., that companies do not have cross holdings and other non-operating investments), the debt effect can be computed approximately. First, if cash and debt is zero for a company, and there are no other non-operating assets, the net income for that company will be its after-tax operating income (EBIT (1-tax rate)). Second, the value of the company, if it it had no cash and debt, can be approximated with its enterprise value, leading to the EV/EBIT(1-t) providing an approximate measure of what the earnings multiple would have looked like with no cash and no debt. (The enterprise value does include the value effect of debt and is hence not a clean measure of what the value would have been, if the firm had no debt and no cash.)

Debt Effect = EV/ EBIT (1-t) - Non-cash PE

To estimate these numbers for my sample, I used the average effective tax rate each to compute the after-tax operating income in that year, in recognition of the reality that US companies would not be paying the marginal tax rate on taxable income, even if they had no interest expenses. The graph below summarizes the cash and debt effects on stocks from 1962 through 2014:

Source: Compustat; All money-making, non-financial service US firms |

At the end of 2014, the PE ratio was 17.73, the non-cash PE was 16.05 and the EV/EBIT(1-t) was 19.44. So, what do these numbers mean? All three measures are higher than the median values over the last 55 years, which would be ammunition you could use to argue that stocks are overvalued. However, as I noted in my post on PE ratios last year, the treasury bond rate, at 2%, is also much lower than the historic norm, and if you don't buy into the bubble story, could be used to explain the higher multiples. I don't this post is the forum for examining the heft of these arguments, but I did try to provide my views in this post last year on bubbles.

**PE Ratios: Three Rules for the road**

Like most investors, I like the simplicity and intuitive feel of PE ratios, but they are blunt instruments that can get us into trouble, when used casually. A low PE ratio can be indicative of cheapness, but it can also be the result of high debt ratios and low or no cash holdings. Conversely, a high PE ratio can point to over priced stocks, but it can be caused by high cash balances and low debt ratios. Based on the last two posts, I would suggest three simple rules for the use of PE ratios.

*When comparing PE ratios across companies, don't ignore cash holdings and debt*. As the diversity of companies within sectors increases, the old notion of picking the lowest PE stock as the winner is increasingly questionable, since you may be choosing most highly levered company in the sector.*When comparing PE ratios across time, don't ignore cash holdings and debt*. In these last two posts, I have noted the ebbs and flows in both cash as a percent of firm value and debt as a percent of value across time, sometimes due to shifts in the numerator (cash and debt values changing) and sometimes due to shifts in the denominator (market value of equity changing). Whatever the reasons, these shifts can affect the PE ratios for the market, making it look expensive when cash balances are high and debt ratios are low.*Any corporate action that changes the cash or debt as a percent of value will change the PE ratio*. Consider a company that has a large cash balance and is planning on using that cash to buy back stock. Even if nothing else changes, the PE ratio for the company should decrease after the buyback, as (high PE) cash leaves the company. Thus, the practice of forecasting earnings per share after buybacks and multiplying those earnings per share by a constant PE will overstate value. This effect will be even more pronounced, if the company borrows some or all of the money to fund the buyback, since a higher debt ratio will also push down the PE even further.

Finally, if you are at the receiving end of an investing pitch (that a stock or market is cheap or expensive), based just on PE ratios, you should be skeptical, no matter how credentialed the person making the pitch may be, and do your own due diligence.

**Spreadsheets**

## 13 comments:

Why not just adjust the PE Ratios to take into account net cash/debt?

P = Equity Value - Net Cash/Debt

E = Earnings

So a company that has a P/E of 20 and a Equity Market cap of 1B with 100m of cash and Earnings of 50m would have an adjusted P/E of 18.

Just a thought.

If you adjust for net debt, you no longer have P. You have EV. If you have EV in the numerator, you have to look at after-tax operating income in the denominator.

Thanks Professor. I generally agree with these conclusions. However, if you assume the example company does a levered recap to facilitate a special dividend (rather than a buyback) then your analysis would suggest that the stock price should drop by the amount of the special dividend payment, which is generally not the case in practice (if you compare the unaffected stock price to the price on the ex-date). If you could address this point it would be most appreciated.

Why would you use pre-tax in the denominator for P/E, but after-tax for EV? Shouldn't it be opposite: EV/Pre-tax and Market cap/After tax?

As per your calculation at a 90% debt to capital ratio, the PE ratio drops to 2.75 but the value per share increases to $11.41.

However, I note that while PE is at 2.75, value per share comes to 2.07, not 11.41. This is because at 90% debt, the following hold true - 1) Value of firm = 1240.88 2) Debt = 1116.79 3) Equity = 124.09 5) Net income = 45.20 6) PE = 124.09 / 45.20 = 2.75 7) Price per share = 124.09 / 60 = 2.07

Cost of debt = 4%

Same is true for value per share at other debt ratios. I think as equity value reduces (due to increase in debt ratio) value per share should keep going down rather than going up because you are keeping # shares fixed at 60.

Could you please elaborate how you got 11.41 per share value?

Thanks

Why is your number of shares frozen at 60? When you go to a 90% debt ratio, you should have only 10 million shares outstanding.

I don't keep my number of shares fixed. It starts at 100 but changes as the debt and cash change.

Prof. Damodaran,

can you please explain how the number of shares outstanding change with debt? In the example, the initial count was 100M but with 40% Debt, the number became 60M. I did not follow the formula you used to come to this number.

Thanks for your help!

Professor - A question if you can help.

Is this post simply explainable by the fact that Beta is a function of levarage i.e. a company with, say, lots of cash and zero debt will, perhaps, have a negative Beta leading to a cost of equity even lower than the so-called 'risk free rate'? Lower cost of equity implies a very high P/E. That explains, cash has a higher P/e and debt has a lower p/e

Thanks in advance.

I know that there are lots of moving parts in the PE ratio computation, especially when debt and cash change and while I tried to make it transparent, it is still opaque enough to be confusing. Rather than respond to each comment, let me try to address them all.

1. Special dividend: I am puzzled as to the point about stock prices and special dividends. On the ex-divdidend day, the stock price will drop by roughly the amount of the special dividend, with any difference being almost rounding error. If it did not, I could make money by buying stocks just before ex-dividend days and collecting the special dividend. Put differently, the effect on equity is the same whether I have a buyback or a special dividend but the value per share will be different.

2. Why shares change as you borrow money or increase cash: The trickiest part of the spreadsheet is adjusting the number of shares for new debt and new cash. The easier adjustment is for debt. When you change the debt ratio for an existing firm, then the way to do it is through a recap and that that will require borrowing money and buying back shares. The math actually is very simple. To get from a debt ratio of 0% to 40%, I will have to buy back 40% of the shares outstanding and I will be paying the updated value per share on the buyback (one reason why there is circularity in the spreadsheet). If I want to add to my cash balance without borrowing money, I need to issue new shares and these will be issued at the prevailing price, since cash by itself does nothing for my value per share.

3. Beta and PE: Shailesh, I think you are mistaking the symptom for the cause. The beta effect is the symptom, not the cause of the change in PE. The PE is changing because equity becomes riskier in a business when it borrows money. I have chosen to show the effect on beta, but even if you use an alternate model for cost of equity, you should be showing this effect.

Thanks for the response. However, my point on special dividends was a bit different. Let's say a company has a stock price of $10. The company then announces a special dividend of $1 / share. Therefore, one might expect the stock price to be $9 on the ex-date. However, in practice, often the stock price is bid up by the amount of the special dividend between the announcement date and the day before the ex-date such that there is little net change between the unaffected price (pre-announcement) and the price on the ex-date after the stock price is reduced by the amount of the dividend. The stock price goes up to $11 and then the dividend of $1 comes out at the ex-date so the price remains $10. Therefore, the multiple has actually increased in these cases, rather than decreased. That is the observed effect that I wanted to get your perspective on in the context of this post. Is this an example of the market being inefficient or is there something else at play here? Thanks very much.

I am so sorry but there is no way that your contention can hold up in theory or in practice and here is why. First, if this is true, you have found a true money machine. Companies should keep paying special dividends until they liquidate themselves because you are creating value out of nothing. Second, when you say in practice, what exactly are you basing this on? The evidence I have special dividends suggests that the only value effects they leave behind are the effects that come out of leverage and that they carry no signaling or other benefits that regular dividends do. You may have anecdotal evidence of prices being bid up after the announcement of special dividends but you cannot generalize from that small sample.

Thanks Prof. This is so great!

Is it safe to assume that I can ignore all these complications with PE by pricing stocks with the EV/EBITDA multiple? It's capital structure neutral and always nets cash against the debt.

With regards to the special dividend discussion, I have observed a few cases (not a statistical sufficient sample), where the announcement of special dividends increased the stock value indeed, but my gut feeling tells me, that in these situations I watched the implicit assumptions drove the stock price. And of course not the payout itself, which nets out.

And my assumption in these situations is, that shareholders either (1) where happy to see the special dividend, because they haven't trusted management with the excess cash and were afraid of subdued investments, sometimes even lobbying for special dividends for that reason or (2) the announcement of a special dividends bolstered the outlook (or the confidence in the given outlook), as it's kind of reassured with a payout and (hopefully) therefore confidence of management is high enough to really earn sufficient cash flows in the future.

A third case I could imagine is, that from a valuation point of view holding cash doesn't change the valuation, as cash flows from the operation are discounted with the cost of capital and then the value is adjusted by (market) net debt. But if you as a company retain excess cash you cannot properly invest, but the investor would invest the money into another opportunity, the investor may appreciate the excess cash paid out. From a total investor point of view, the (consolidated) cost of capital would probably change as well, but still an investor in equity may charge all its equity investments with cost of equity and not just the operational firm value part of its equity.

Not sure about the last argument here.

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