Concepts & Commentary : Demystifying the P/E Multiple

Demystifying the P/E Multiple (8 votes)

People in finance regularly talk about the inverse of the Price/Earnings (or P/E) multiple being the cost of equity, but they seldom know why this is the case. And while the P/E multiple is far and away the most commonly used trading multiple, have you ever wondered why that might be?

Assume a company earns $100 million of pretax income. Assuming a 40% tax rate, this translates into $60 million of earnings (or “E”). Further assuming a 10x P/E multiple, this implies an equity value of $600 million.

10x P/E multiple × $60mm of earnings = $600mm in equity value

Now consider these earnings in the context of fundamental corporate finance. Assuming the company pays out all of its earnings in the form of dividends (100% payout ratio), this $60 million is a perpetual stream of cash flows to equity holders. To the extent the earnings stream grows every year, it is not only a perpetual stream of cash flows but a growing perpetual stream of cash flows.

PV_perpetuity = Cash Flow (CF )
Discount rate (r)

In the example above, CF = $60 million and the present value = $600 million (based on a 10x P/E multiple). Applying the perpetuity formula, you can calculate an implied discount rate (r) of 10%.

$600mm = $60mm
Discount rate (r)

Begin by multiplying both sides by the discount rate (r) and re-write the formula as:

$600mm × Discount rate (r) = $60mm

To solve for the discount rate (r), divide both sides by $600mm:

$600mm × Discount rate (r) = $60mm
$600mm $600mm

You now have the answer for the discount rate (r):

r = $60mm / $600mm
= 0.10, or 10%

The implied discount rate in this example is 10%, and the inverse of 10% is 10 (1 / 0.10 = 10), which is the P/E multiple. One important thing to note here: the perpetual cash flow in this simplified valuation is earnings, which means that it is a cash flow that flows only to equity holders in the form of dividends (debt holders have already been paid through the medium of interest expense). Therefore, the inverse of the P/E multiple is the implied equity discount rate (r) using the perpetuity method of valuation.

Investors use the P/E multiple for valuation purposes because it’s a proxy for a perpetuity valuation. It’s a shorthand way of saying: if I as an investor assume the company will pay out all of its earnings in dividends (or will reinvest those earnings at a rate of return equal to its equity cost of capital), then the value of equity should be equal to the present value of the earnings stream in perpetuity. Therefore, using the P/E multiple is a shortcut method of discounted cash flow valuation to an equity holder. If the inverse of the P/E multiple represents a perpetuity discount rate for equity, then multiplying earnings by a P/E multiple is effectively using the perpetuity method of valuation.

Earnings × P/E multiple = Present value of equity
$60mm × 10x = $600 million

Which is the same as:

Earnings     /     Discount rate        = Present value of equity
Earnings     /     Inverse of P/E       = Present value of equity
$60 million /     10% or 0.10          = $600 million

Assuming a growing perpetuity, the formula changes only slightly:

PV_perpetuity = Cash Flow (CF )
Discount rate (r) - growth rate (g)

Assuming that earnings, the “E” in the P/E multiple, is a growing perpetuity rather than a static perpetuity, the inverse of the P/E multiple is equal to the amount (r – g) rather than just (r) as it was in the first example above. Therefore, as the growth rate (g) increases, the quantity (r – g) decreases and the resulting “net” discount rate also decreases. And as the discount rate decreases, the implied present value of equity increases. Therefore, companies with higher growth rates should trade at higher implied valuations (at any given level of earnings, or “E”) than companies with lower growth rates. The reason has to do with the underlying math. Perhaps an example may help to clarify the situation.

Assume two companies, 1 and 2, with the following characteristics.

	Company 1	Company 2
P/E Ratio	25x	10x
Implied cost of equity¹	4% (1/25)	10% (1/10)
Earnings	$100mm	$100mm
Implied equity value	($100 / 0.04) = $2,500mm	($100 / 0.10) = $1,000mm

¹ After accounting for perpetual growth (g)

Company 1 with a higher P/E of 25x will have a lower cost of equity (1/25, or 4%) than Company 2 with a lower P/E of 10x (1/10, or 10%). This means that the present value of Company 1’s equity will be higher than the present value of Company 2’s equity for any given level of earnings, ($100mm in this example). This has nothing to do with the level of earnings, and everything to do with the divisor, the implied cost of equity. Recall from math class that the smaller the divisor, the larger the quotient. Similarly, the larger the divisor, the smaller the quotient. We can now use that math truism to draw some other conclusions, namely that if the divisor becomes smaller for any reason, the quotient—in this case the equity valuation—will grow larger. Now recall that for a growing perpetuity, the divisor is not the equity discount rate (r) but the equity discount rate (r-g). The “g” is the growth rate of the equity earnings. Assuming “g” is a positive number, the amount of “r-g” will be less than “r” alone. And since a smaller divisor leads to a larger quotient, the equity valuation for any company will be higher if the growth rate “g” is higher. This is why companies with higher growth rates are valued more highly in the market (for any given level of earnings) than companies with lower growth rates. Again, it is a function of the perpetuity (or, in this case, the growing perpetuity) method of valuation. As with discounted cash flow analysis, the perpetual growth rate (g) must be a steady-state growth rate for the long-term. It should not be a short-term growth rate.

What are the benefits of using the P/E multiple for valuation?

Using the P/E multiple for valuation is straightforward and does not require a tremendous amount of effort. The math is easy (it is simply the P/E multiple × EPS) and companies report their earnings, or “E”, every quarter. Moreover, equity research analysts typically produce a predicted “E” for each quarter for the next two fiscal years. As a result, investors are able to estimate value using little more than simple multiplication. Also, since all public companies report their earnings, the P/E multiple is one of the few metrics that can be used to compare relative pricing across all industries.

What are the shortcomings of using the P/E multiple for valuation?

One of the biggest shortcomings in using a P/E multiple is that it implicitly assumes a steady state level of earnings, or “E”. As you may recall from corporate finance, applying the perpetuity method of valuation or the growing perpetuity method of valuation should only be done when a company or stream of cash flows has reached its steady state level (this is why people spend so much time trying to normalize earnings). If cash flows are not yet at a steady state, then a year-by-year discounted cash flow analysis followed by a perpetuity method in the terminal year is more appropriate. This is consistent with the principle in performing discounted cash flow analysis that you cannot arbitrarily choose a terminal value year; instead, one should ensure that the company under analysis has reached a steady state by the terminal value year. The corollary is that if the company has not reached a steady state, then you need to extend your projection model until a time when the company has reached its steady state. Another challenge of the P/E multiple is that it assumes that the company will either pay out the entirety of its “E” in dividends (100% payout ratio) or reinvest the “E” in the business and earn at least its cost of equity capital on those reinvested proceeds while doing so. To the extent that the company under analysis is not necessarily doing this, the P/E method of valuation can lead to faulty decisions. Another potential shortcoming occurs if the company under evaluation has erratic “E” (certain companies, for example, employ depreciation methods based on events during the year, which causes the “E” to change significantly from year-to-year) since it will be difficult to conclude if and when such a company has reached a steady state level of earnings. In this situation (common with oil and gas companies, for example), other valuation metrics such as price to cash flow multiples (P/CF) might provide better valuation guidance. Lastly, as with any multiples-based comparables analysis, using a P/E multiple to value a company assumes the company you are valuing is truly comparable to the company whose P/E multiple you are applying, and no two companies are perfectly comparable.

Earnings yield and accretion/ dilution analysis

The inverse of the P/E multiple is also referred to as the earnings yield of a company. When performing accretion/dilution analysis, people often assume that “equity is more expensive than debt” and therefore that “the more stock (equity) consideration there is in a deal, the more dilutive (or less accretive) it will be, and the more cash/debt consideration there is in a deal, the more accretive (or less dilutive) it will be.” Many times we have seen analysts and associates racking their brains trying to figure out why, in their accretion/dilution model, the accretion goes up (or dilution goes down) when they increase the amount of stock consideration (as opposed to the opposite, which is what one often sees). When performing accretion/dilution analysis, compare the acquiror’s earnings yield to its after-tax cost of transaction debt (earnings yield being the inverse of the P/E and not the theoretical cost of equity using CAPM). To the extent the earnings yield (the cost of equity, which is already an after-tax number) is lower than the after-tax cost of debt, the deal will actually be more accretive (or less dilutive) the more stock there is in the transaction. To the extent the earnings yield is higher than the after-tax cost of debt (which is the more common situation), the deal will be more dilutive (or less accretive) the more stock there is in the transaction. Said differently, a transaction will be more accretive (or less dilutive) to EPS if more of a lower cost form of capital is used. Similarly, a transaction will be more dilutive (or less accretive) to EPS if more of a higher cost form of capital is used. This is why accretion/dilution results change with changes in the proposed capital structure, even though there may be no change at all in the income statements of both Acquiror and Target or the other transaction assumptions.

This is also why companies with high P/E multiples often use stock as their acquisition currency relative to cash/debt. A company, for example, that is trading at 30x forward earnings has an earnings yield of 3.3% (1/30 = 0.033 or 3.3%). Therefore, its after-tax cost of debt needs to be less than 3.3% in order for acquisition consideration of cash/debt to be more accretive (or less dilutive) than acquisition consideration of stock. Assuming a 7% cost of debt, let’s see which form of capital is less expensive:

P/E multiple                            = 30x

Inverse of P/E multiple              = 1/30, or 3.333%
_{(already an after-tax number)}

Cost of debt                            = 7.0%

After-tax cost of debt                = 7.0% × (1 – 40%) = 4.2%

Earnings yield (3.33%)            < After-tax cost of debt (4.2%)

Therefore a company with a 30x P/E multiple, a pretax cost of debt of 7.0%, and a corporate tax rate of 40% would fund all of its acquisitions with stock as the lower cost form of capital if EPS accretion/dilution were its only concern. There are, of course, many other tactical and strategic issues involved in deciding whether to use cash vs. stock as acquisition currency, such as determining whether the pro forma P/E multiple will expand or compress since the extent to which it compresses (if it does) impacts whether there is “value” accretion/dilution.

Let’s revisit the earlier example of Company 1 and Company 2.

	Company 1	Company 2
P/E Ratio	25x	10x
Implied cost of equity	4.0% (1/25)	10.0% (1/10)
Earnings	$100mm	$100mm
Implied equity value	($100mm / 0.04) = $2,500mm	($100 / 0.10) = $1,000mm
Pretax cost of debt	7.0%	7.0%
Tax rate	40.0%	40.0%
After-tax cost of debt	4.2%	4.2%
Lower cost form of capital	Equity	Debt

Any transaction will become more accretive to EPS (or less dilutive) if more of the lower-cost form of capital is used, and any transaction will become more dilutive (or less accretive) to EPS if more of the higher-cost form of capital is used. In the example immediately above, all else being equal, Company 1 should use more equity (as the lower cost form of capital) in order for a transaction to be more accretive (or less dilutive). Similarly, in this example, Company 2 should use more debt (as the lower cost form of capital) in order for a transaction to be more accretive (or less dilutive). Alternatively, if Company 1 were to use more debt (as the more expensive form of capital), the transaction would be more dilutive (or less accretive). Similarly, if Company 2 were to use more equity (as the more expensive form of capital), the transaction would be more dilutive (or less accretive). Note that a 25x P/E multiple is relatively high (but not unrealistic; in fact many companies trade at this level) and a P/E multiple in the 10x - 20x range (implied cost of equity of 10% - 5%) is considered more common. Thus it is more common that the after-tax cost of debt is lower than the (already after-tax) cost of equity, which is why, when faced with a dilutive transaction, practitioners often suggest as a first course of action an increase in the amount of cash consideration and a decrease in the amount of equity consideration. However, as you now know, this will only be more accretive (or less dilutive) to the extent that the cost of debt capital is less than the cost of equity capital.

Final Thoughts

Judicious use of the P/E ratio can enable one to effectively draw valuation conclusions with relatively little information and effort. However, blind reliance on the P/E ratio can result in errant analysis and conclusions. Also, when it comes to how much cash vs. stock to use as acquisition currency in an M&A deal, EPS accretion/dilution is just one of many factors a company would need to consider. Other considerations include tax ramifications, desires and goals of the selling shareholders, and the pro forma impact on acquiror’s credit quality, to name a few.

For more information, please see the chapters on Financial Statement Basics, Strategic Transactions, Accretion Dilution Analysis, and Acquisition Currency in The Practitioner’s Guide to Investment Banking, Mergers & Acquisitions, Corporate Finance, which is available online at http://www.scoopbooks.com/.