# Price earnings ratios – DCF in disguise

Last updated 23 March 2023

Are you trying to identify what is ‘priced in’ to a current stock price or work out a terminal value in a DCF analysis? A target valuation multiple calculation may be the answer. We present a simple interactive model.

Many dismiss valuation multiples as being too simplistic; however, multiples are just DCF in disguise. You can derive a price earnings ratio with the same value drivers as you would use in a discounted equity cash flow model.

Target multiples represent a deserved value, expressed in the form of a multiple, that reflects specified value driver inputs. The model we include in this article derives a prospective target price earnings ratio. It is a two-stage model with specified growth, incremental return on equity and cost of equity inputs for an initial forecast period and then in perpetuity thereafter. The model is clearly simplistic as it captures the complexities of a company in only a handful of value drivers, but we believe it is still extremely useful for:

• Understanding how differences in growth and returns affect value;
• Back-solving to identify what is priced into the current stock valuation;
• Calculating a terminal value in a DCF analysis that is actually more sophisticated than the commonly applied perpetual growth model; and
• Investigating whether differences in stock ratings can be justified by differences in fundamental value drivers.

#### Interactive model: Price earnings ratio implied by value drivers

— iphone and ipad users: This model formats best if viewed in Google Chrome — The target price earnings ratio is based on an underlying discounted equity cash flow valuation. The cash flows are derived from earnings, combined with a cash conversion that is a function of a forecast incremental return on equity and forecast growth inputs.

## Understanding the model inputs

#### Growth

This is the expected rate of growth in earnings. For the initial phase it may be simplistic to assume that growth is constant when actual growth forecasts differ for each period. However, in most cases, using an average expected rate will not have a significant effect on the target multiple. If the initial phase is long and growth is high and volatile then using an average rate could be a problem and a more sophisticated multi-period approach would be necessary.

For long-term growth, it is important to consider what rate is a sustainable, considering the market and economy as a whole. Remember that this rate is applied in perpetuity. The model will not accept a rate greater than the cost of equity. It is an impossible scenario anyway because, theoretically, such a rate produces an infinite valuation and the entity would eventually end up bigger than the economy.

#### Incremental return on equity

The return input is a forward-looking incremental return expected to be earned on incremental investment. It represents the forecast increase in profit in a given period divided by the increase in equity capital. The historical return on equity calculation of earnings divided by shareholders’ equity is backward looking as regards the investment and should not be used. Historical investment by equity investors is a sunk cost and does not directly impact value. However, historical returns may be relevant when estimating forecast incremental returns as efficient use of capital previously invested and a high historical return may well indicate that future incremental returns will also be high.

Incremental returns used in the model are accounting returns, which may not necessarily be the same as economic returns. The additional investment used in the calculation of incremental returns should be what is capitalised in the financial statements. The reason is that the model uses this return to determine the difference between reported earnings and the cash flow that ultimately determines value.

The difference between accounting and economic returns is often due to the limited recognition of intangible investment in financial reporting; most investment in intangible assets is immediately expensed rather than capitalised and amortised. As a result, the returns used in the model would generally be high for a company where it is primarily intangible investment that drives value . Unfortunately, the relationship between accounting and economic returns is a complex one (and perhaps a subject for a future article).

#### Cost of equity

This is the normal economic cost of equity capital; in other words, it is the required return of equity investors in respect of their investment in the entity. Make sure this reflects differences in risk and leverage. CAPM may be a good starting point.

#### Earnings

The earnings metric should be forecast not historical. To be precise, a forward 12-month prospective earnings should be used (usually a combination of first and second year prospective earnings). However, in practice using the first-year prospective metric is generally good enough. Whatever earnings figure is chosen, remember the forecast growth input applies to future periods beyond the period of that forecast earnings. You should also ensure that the earnings measure is realistic and comprehensive. Do not exclude expenses that have a non-zero expected value in future periods merely because they are volatile, they are so-called ‘non-cash’, or because a company has excluded them from their adjusted ‘non-GAAP’ metrics.

Although earnings is not itself an input of the above model, it is important to apply the model output to the correct earnings metric, hence the inclusion in this list.

## How to use a target multiple model

#### What is in the price analysis

How do you determine whether a particular valuation multiple is deserved or not? One approach is to try and construct a set of value drivers that replicates the multiple. Consider whether you think those implied value drivers look conservative or aggressive and that will help you reach better conclusions on value.

For example, at the time of the first publication of this article, Amazon tradeed on a forward price earnings ratio of 59x based on analyst consensus earnings forecasts provided by Reuters. Use the model above to try and identify a set of value drivers that replicates this multiple. Now consider whether you believe Amazon is likely to achieve this or not. Remember that your implied value drivers need to be mid points in a distribution, they should not be the ‘success scenario’. One of the common mistakes in valuation is to consider value based only on the assumed successful implementation of a company’s strategy. Values need to reflect potential downside as well as upside, which is why forecasts need to be true expected values allowing for differing outcomes.1For more about the importance of using expected values in equity valuation see our article Most likely profit may not be the most relevant profit.

#### Terminal value calculations

A terminal value in DCF analysis can be calculated based on an implied multiple derived from value drivers, instead of the more commonly applied constant terminal rate of growth.  The advantage of a target multiple approach is that it effectively adjusts implied reinvestment to reflect the selected growth. This is a common mistake in DCF where changes in terminal growth are done without considering the effect this has on required reinvestment and hence on the terminal cash flow itself.

#### Quantify a valuation premium or discount

How do you know whether a multiple is too high or too low? Comparisons with other companies or with historical ranges helps, but it is difficult to explicitly allow for differences in value drivers. You may think that a stock is higher quality than the comparable companies, but what valuation premium does that justify? Using the target multiple approach to identify what is priced into comparable company stock prices and then adjusting for value driver differences can help in estimating that premium or discount.

## Model limitations and assumptions

A target multiple model, such as this for price earnings ratios, is an excellent way to better understand how key value drivers impact value and multiples, but it is obviously simplistic and has its limitations.  For example, the model is based on simplistic growth assumptions and does not allow for a more complex development of earnings and equity. Clearly the approach should not be your only basis for equity analysis and valuation.

Also remember that this model assumes:

• That there are no other equity claims in the entity’s capital structure, such as derivatives on own equity or other classes of share capital, or that if these do exist suitable adjustments are made to earnings and the cost of equity;
• That no forecast gains and losses are excluded from forecast earnings and that there are no distortions arising from a non-zero forecast of other comprehensive income; and
• That forecast earnings and earnings growth is not impacted by the accounting treatment of gains and losses that arise in prior periods only to be recognised subsequently. In other words, the model assumes no distortions from recycling of OCI.

## Insights for investors

• Price earnings ratios (and all other valuation multiples) can be reconciled with the same value drivers that determine DCF values. Multiples are DCF valuations summarised in a single metric.
• Incremental rate of return on equity, expected growth in earnings and the sustainability of that growth are key drivers of value and hence of a price earnings ratio.
• Use a target multiple approach to estimate what is priced into the current valuation of a company – in effect a simplified reverse DCF.
• Use a target multiple approach to identify a multiple to apply in a terminal value calculation for a DCF model.
• Remember that target multiple model is based on a number of simplifying assumptions and is not a substitute for a full DCF analysis.

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