# DCF versus residual income: A difference in returns

Residual income based valuations are a useful alternative to the more common discounted cash flow. While both approaches must produce the same answer for a given set of assumptions and value drivers, we think it can be easier to derive realistic inputs using the residual income approach, considering the focus on return on investment.

However, residual income also poses challenges. The approach requires ‘clean surplus’ accounting, return inputs must allow for accounting distortions due to the lack of recognition of intangibles, and terminal growth assumptions may need to differ from those used in DCF – as we demonstrate using an interactive model.

Although discounted enterprise cash flow seems to be the dominant discounting based valuation approach in practice, we often come across analysts referring to residual income (economic profit) valuation techniques. It seems that some investors perceive residual income as a different approach that produces a different, and potentially superior, valuation.

DCF and the residual income model (RIM) approaches are mathematically equivalent and, for a given set of assumptions, should produce the same valuation. However, in practice, DCF and RIM do not always give the same answer because of:

• Misunderstanding of the models: We think that many investors struggle to understand the underlying assumptions and methodology of residual income and consequently can mistakenly incorporate errors in their valuations.
• A different focus on returns: Because residual income directly uses return on invested capital as a basis for valuation, this can lead to different (and potentially more realistic) assumptions being applied in a valuation model.

We think more investors should explore residual income as a basis for valuation. But if you do, be careful to avoid inconsistencies (particularly in relation to intangible assets) and errors (particularly the calculation of terminal values) in your analysis.

## How residual income works

Residual income is defined as profit less a charge representing the cost of capital applied to the (accounting) capital invested in the business.

Residual income = Profitt1 – Invested Capitalt0 x Cost of Capital

The same result can also be obtained using the aggregate return on investment as an input:

Return on Investment = Profitt1 / Invested Capitalt0

Substituting this into the calculation above produces:

Residual income = Profitt1 x (1 – Cost of Capital / Return on Investment)

There are essentially two ways to approach residual income. These mirror the general distinction between direct equity valuations and indirect valuations using enterprise value.

• Equity residual income: The residual income attributable to common shareholders is net income (after deducting income attributable to non-controlling interests and other non-common share equity) less shareholders’ equity multiplied by the cost of equity (COE).

Equity residual income = Earnings – Shareholders’ equity x COE

• Enterprise residual income: From an enterprise value (EV) perspective, residual income is the profit available for all providers of capital (the claims on the business included in EV) less a capital charge reflecting the rate of return required by all those providers of capital. This capital charge is calculated as the invested capital multiplied by the weighted average cost of capital (WACC). The profit must be post-tax but before you deduct interest on debt finance and other debt-like claims included in EV. It must also be before any income derived from non-core assets that are excluded from the invested capital and (operating) EV. This profit is often referred to as net operating profit after tax or NOPAT.

Enterprise residual income = NOPAT – Invested capital x WACC

In any EV based valuation, the definition of EV should be consistent with the profit to which it is related and, in the case of residual income, consistent with the definition of invested capital.1We discuss this in our article ‘Enterprise value: Calculation and mis-calculation’. It is also possible to define EV in different ways, such as whether a specific liability is regarded as financing and included in EV, or operating and therefore excluded. Extended trade payables and decommissioning liabilities are items that may be treated differently. The same applies to non-core or non-operating assets, including whether investments in associates are regarded as non-operating (and therefore deducted in calculating EV) or not.

A residual income valuation is the sum of the valuation date invested capital plus the present value of forecast residual income. The discount rate is the same as for DCF – in other words, the cost of equity for a direct equity residual income valuation or WACC for an enterprise value based approach.

Equity value = Shareholders’ equityt0 + PV of forecast equity residual income

or

Enterprise value = Invested capitalt0 + PV of forecast enterprise residual income

Like DCF, a residual income valuation will likely include an explicit forecast for a number of years, with the present value of residual income thereafter based on simplified (often constant growth) assumptions. However, as we explain below, you need to be careful about using the same constant growth assumption for both profit (or cash flow) and residual income, as they may not be the same.

#### Comparison of Residual Income and DCF valuations

Where: COE = Cost of Equity and WACC = Weighted Average Cost of Capital

At first sight, it seems that it would be difficult to reconcile residual income and DCF, given that one is earnings-based and the other cash-flow based.

What is perhaps most odd about the identity between the two methods is how invested capital is an input only for residual income valuations. Actually, invested capital is not a driver of value at all because it is a sunk cost and has nothing directly to do with future cash flows. In the residual income model it features twice, as the initial book value of invested capital, where higher invested capital adds to the final valuation, but also in the charge for the use of capital (invested capital x weighted average cost of capital), where higher invested capital reduces the valuation.

Overall, the influence of invested capital is neutral such that the same final answer should be obtained whatever invested capital is used, provided the profit measure is consistent with, and based on the same accounting policies used to derive, invested capital. As we demonstrate in the model below, DCF and residual income are actually mathematically identical. Invested capital should always be the difference between the present value of cash flows and residual income.

Residual income is based on the accounting profit and invested capital. Some practitioners advocate that accounting metrics should be adjusted to obtain measures that are closer to economic returns, such as additional capitalisation of intangibles. These adjustments should not directly alter the output of a correctly formulated RIM valuation, considering that they would not alter cash flows and RIM is equivalent to DCF. However, accounting adjustments may make it more likely that realistic assumptions are used in the model.

The mathematical equivalence of DCF and residual income valuations does not necessarily mean that you should be indifferent between the two approaches. The residual income approach has both advantages and additional challenges as we explain below.

## Terminal values:  DCF versus residual income

One of the challenges in using residual income as a basis for valuation is getting the terminal value calculation correct. It is common to assume a constant rate of growth in profit and free cash flow for a terminal value in DCF. However, using the same rate of growth for a residual income terminal value may be inconsistent and lead to a different valuation.

For residual income to grow at the same rate as profit and cash flow, invested capital must also grow at that same rate, which means that the incremental return on future investment (the increase in profit divided by the increase in invested capital) must be the same as the aggregate return on existing investment.

To illustrate, assume high historical investment by a company has resulted in low aggregate return, but this return is forecast to improve because the incremental return on new investment is expected to be much higher. The impact is that invested capital will grow at a lower rate than profit or cash flow and, as a consequence, residual income will grow at a higher rate.

The interactive DCF versus residual income model below reflects this scenario. When first loaded the aggregate ROIC is 8% in the first forecast year. However, the value driver assumptions include more optimistic incremental returns, including in respect of the terminal value calculation where the long-term incremental return model input is assumed to be 20%. The result of these assumptions is that in the first year of the terminal value period (year 6) the growth in residual income is greater than the growth in profit (NOPAT) and cash flow (2.8% rather than 2%).

If the assumed long-term profit growth is applied in the terminal value of the residual income valuation, the value will be understated and inconsistent with the input value driver assumptions. Unfortunately, the growth in residual income will vary over time and, as a result, the terminal value calculation becomes more complex.

It is possible to calculate the correct terminal value (one that is consistent with the input assumptions) using a somewhat complex formula.2Here it is …

{ \sf TV_{n} = IC_{n} \, x \, \dfrac{(ROIC_{n+1} - WACC)} {WACC} \, + \, \Bigg( NOPAT_{t+1} \, x \, \dfrac{g} {WACC} \, x \, \dfrac{(iROIC - WACC)} {WACC} \, x \, \dfrac {1}{WACC - g)} \Bigg) }

Where:
TVn = Terminal value in year n
ROIC = Aggregate return on invested capital
iROIC = Incremental return on incremental investment
WACC = Weighted average cost of capital
NOPAT = Net operating profit after tax
g = Growth in NOPAT
However, the calculation that is perhaps easiest to follow is to separately calculate residual income for each year in the terminal value period. We have applied this approach in the model below to also illustrate how residual income growth and aggregate returns vary if iROIC does not equal ROIC.

If you change the input value drivers in the model, notice that the DCF value and (correct) residual income valuations are always the same.

#### Interactive model: Economic Profit versus Discounted Cash Flow

— iPhone and iPad users: This model formats best if viewed in Google Chrome — The terminal value calculation in the DCF model is based on the incremental return on invested capital value driver approach that we explain in our article ‘DCF terminal values: Returns, growth and intangibles’. More explanations about this model can be found in the version that is available for download.

We recently saw a claim that residual income valuations are superior to DCF based values because the terminal value in residual income is a smaller proportion of the overall value. Terminal value, and the impact of forecasts beyond the explicit forecast period, is a major challenge in valuations, with small variations in estimates of long-term growth and other valuation inputs making a significant difference to the final answer.

It would seem logical, therefore, that a valuation technique which minimises the impact of terminal value estimates is preferable. However, this particular reason for favouring residual income is incorrect. While it is generally true that a terminal value in a residual income model is lower than that in DCF, this does not affect the overall sensitivity of the valuation to changes in long-term assumptions. Long-term assumptions for growth, margins, risk, etc. have exactly the same impact on value when this is measured using residual income, discounted cash flow or any other valuation technique.

Although residual income valuations may be no better in coping with long-term value effects, we think there are other reasons why a residual income approach can be useful. The focus on return on investment and the ability to introduce ‘fade’ to those returns can help in establishing realistic forecasts – more on this later.

## Residual income and clean surplus accounting

In addition to ensuring that growth assumptions used in a residual income terminal value calculation are correct, there is a further factor that needs to be considered in ensuring residual income models are valid. For DCF and residual income to give the same result (and for residual income to provide the correct result) the data on which the residual income is based must follow what is called ‘clean-surplus accounting’. This is where the profit (earnings or NOPAT) and change in capital (shareholders’ equity or invested capital) are consistent and follow this relationship:

Closing capital = Opening capital + profit – distributions to capital providers

The distribution to capital providers is the same as the free cash flow (FCF) that is included in a DCF valuation. For an equity valuation this represents dividends plus (net) share repurchases. For an EV based valuation, FCF is the distributions in the form of interest and dividends, net share repurchases as well as the change in net debt, and other debt equivalent liabilities that are included in enterprise value.

You may think that the above relationship is automatic in financial reporting because it is, in effect, the basis of accounting. However, there are two reasons why this rule can be violated and, as a result, a residual income valuation would be incorrect and inconsistent with input assumptions.

It is common to base valuations on adjusted rather than GAAP metrics. If income or expense items that are reflected in changes in balance sheet items are excluded from the profit used for residual income, the residual income based valuation will be incorrect. You must use the forecast GAAP profit and not an adjusted non-GAAP measure. This may not be a problem if adjusted profit merely excludes non-recurring items because, generally, such items are forecast at zero anyway. However, sometimes recurring gains and losses are excluded from non-GAAP profit, such as value changes and restructuring costs, for which forecasts may be non-zero. If you exclude these items from profit used in a residual income, or indeed a DCF valuation, you will produce an invalid answer.3For more about how to deal with non-GAAP adjustments in valuation metrics see our article ‘Don’t use non-GAAP metrics in equity valuation’.

Intangible assets represent a particular challenge in valuations. The amortisation of intangible assets arising from business combinations (if replacement assets are not capitalised – we use the term ‘replacement-expensed’), is often excluded from performance metrics used in equity analysis. However, for residual income valuations, excluding amortisation of purchased intangibles but including the intangibles in invested capital, will lead to a false valuation. Including or excluding these intangibles produces a valid answer, but you must be consistent.

### Other comprehensive income

Accountants often talk about clean surplus accounting in the context of other comprehensive income (OCI) or movements in equity. If gains and losses are reported in OCI and are not later reclassified to profit and loss (a feature of IFRS but not US GAAP) or are included directly in equity, then clean surplus does not apply. This results in the change in invested capital during the period not equalling the difference between profit and cash flow, which invalidates a residual income valuation.

Fortunately, in a forecast model, most gains and losses that in prior periods may have been excluded from profit and loss and reported in OCI, will be forecast at zero. However, this may not always be the case. Pension remeasurements and the changes in value of certain equity investments under IFRS both produce items in OCI that are not likely to have a zero forecast in investor models.

## Why we like residual income

We think that investors should consider using the residual income formulation of discounted cash flow more often. Although there can be challenges in determining the terminal value and in ensuring the validity of the model due to the clean surplus requirement, the approach can help investors. The key benefit is the focus on aggregate returns. We think that a realistic valuation may be more likely when using the residual income approach, given the greater clarity regarding this key driver. Furthermore, aggregate returns can be decomposed into margin and asset utilisation components which we think further aids analysis.

In standard DCF models there is no explicit recognition of the aggregate return on capital. An incremental return on incremental investment is implicit in any DCF model and can be used as an explicit input to generate a reinvestment rate. This is the approach we have used in the DCF model above. However, aggregate returns are also important.

Companies that currently earn high excess aggregate returns may be susceptible to declining returns and, particularly, declining margins, as the industry matures. This ‘fade’ factor can more easily be incorporated into a residual income valuation.

DCF models often seem to be based on an assumption of margins being maintained together with growth in profit and limited incremental investment (i.e. high iROIC). The resulting valuations may be too optimistic. Fading aggregate returns in a residual income framework, even if included with growth in revenue, can produce declining profit as returns ‘normalise’. This approach may be more realistic in a situation where a young growth company is expected to mature into a ‘utility proxy’.

Additionally, if high investment in the past has resulted in a modest current aggregate return on investment, then this may well predict continuing modest returns on future incremental investment and consequently lower cash flows relative to profit. For this reason, we think that even if you only use a standard DCF valuation, always consider aggregate returns in your overall analysis.

## Returns and intangible asset accounting

However, a word of warning regarding return on investment. ROIC and ROE are accounting measures of return that may not necessarily reflect economic returns. In particular, the limited and inconsistent recognition of intangible assets presents a problem. Most intangible assets are internally developed rather than purchased, with few being recognised in the balance sheet. Only where intangibles are acquired in a business combination are intangibles fully recognised, but even here the cost of replacement assets would mostly be immediately expensed.

The result of this is that when return on investment is based on unadjusted reported data, the aggregate returns depend on the nature of the business (the importance of intangible investment) and the past development of the business (organic versus acquisition led growth). Where unrecognised intangibles are significant then returns will be high and may be persistently high, even in a competitive and mature industry.

The intangible asset problem does not invalidate residual income valuations. As we explain (and demonstrate in the interactive model above) the residual income framework is not actually dependent on the amount of past investment or what is capitalised in the balance sheet. However, you must be conscious of the effect of intangible assets when projecting returns in the model. This especially applies if you are using an approach of fading returns where the end point of that fade may be a relatively high return and certainly one that is structurally above the cost of capital.

In our article ‘Missing intangible assets distorts return on capital’ we explain more about the influence of intangible asset accounting on return on capital. You will also find an interactive model in this article which shows how returns can be corrected to allow for the lack of accounting recognition.

## Insights for investors

• Discounted cash flow and residual income valuation approaches may appear to be quite different, and therefore likely to result in different answers; however, this is incorrect. For the same input assumptions both approaches must give the same result.
• DCF does not directly factor in an aggregate return on investment. Value effectively depends on the incremental return earned on new investment. Past investment is a sunk cost and does not (directly) affect value.
• Although residual income is based on aggregate returns and past investment affects those returns, ultimately value is not directly affected by the aggregate return. Aggregate return on investment affects value only if these returns give some insight into forward looking incremental returns and growth.
• Growth in residual income may not equal growth in profit or cash flow. Be careful when including constant growth assumptions in terminal value calculations.
• The focus on aggregate returns is both a complication but also an advantage of residual income valuations. Directly considering return on investment, including the potential for returns to ‘fade’, may help in estimating realistic value drivers.

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