**If DCF terminal values are based on continuing forecast cash flow, it is important that the reinvestment assumption is consistent with long-term return expectations. We provide an interactive DCF model that demonstrates four alternative cash flow growth-based terminal value calculations, along with related returns analysis.**

**One of the challenges when using returns in equity valuation is the limited recognition of intangible assets. Adjustments to capitalise intangible investment do not change cash flow but can help in ensuring that the assumptions that drive forecast cash flows are realistic.**

In a discounted enterprise cash flow valuation, value equals the present value of all expected cash flows that a business is forecast to generate. While an explicit forecast, considering detailed modelling of a business and its financials, is possible for a certain period (usually around 3 to 7 years), at some point a different approach is required.

A DCF terminal value is a calculation of the value of cash flows beyond the explicit forecast period, based on a simplified or summarised calculation. This may be based on an assumed rate of growth in the forecast cash flow after the explicit forecast period or may reflect an assumed multiple of that cash flow, or of profit, based on observed multiples of a peer group of comparable companies. Usually, the terminal value represents a large proportion of the overall valuation. Consequently, how the terminal value is calculated, and whether the assumptions used are realistic, matters a lot.

In this article we focus on how a cash flow growth based terminal value can be improved, particularly with regard to reinvestment assumptions and implied returns. Nevertheless, even in a cash flow growth model, it is important to cross check any resulting enterprise values against multiples. The model below reconciles the perpetuity cash flow growth approach with valuation multiples.

First, we consider the basic cash flow growth model and its limitations.

**Terminal value approach 1 – Constant cash flow growth**

The most common terminal value calculation is to assume that the enterprise free cash flow at the end of the explicit forecast period grows in perpetuity at a constant rate. The following calculation of the value of a growing perpetuity of cash flows should be familiar to all investors:

{ \sf { Value_{t0} \,= \,\dfrac{Cash \,flow_{t1}} {(Discount \,rate \,– \,Growth)}}}

When applied in a terminal value calculation following, for example, a 5-year explicit forecast this becomes:^{1}The formula reflects the more common discounted enterprise cash flow valuation, where the discount rate is the weighted average cost of capital. For a discounted equity cash flow approach the discount rate would be the cost of equity.

{ \sf { Terminal \,value \,at \,year \,5 \,= \,\dfrac{FCF \,in \,year \,5 \,x \,(1 \,+ \,g)} {(WACC \,– \,g)}}}

The interactive model below shows a typical enterprise DCF valuation with a terminal value based on this constant FCF growth approach. Because the terminal value, and hence the overall value, is materially impacted by both the long-term growth and the discount rate, a sensitivity table may be used to illustrate how changes in these variables affect value. We have included this in our model, albeit presented as a percentage change in value from the base case rather than as alternative absolute values that is perhaps more common.

**Interactive model: DCF with constant growth terminal value and sensitivity table**

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*You can download our terminal value model using the link below. This contains 5 alternative approaches to calculating a terminal value, including one based on comparable companies, which we will address in a separate article.*

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All three variables in the constant cash flow growth terminal value calculation are challenging to estimate and forecast. However, in this article, we focus on the cash flow component and, in particular, the implicit reinvestment assumption.

Enterprise free cash flow can be expressed as the post-tax operating profit (NOPAT) less the additional investment in net operating assets in the period (capital expenditure in excess of depreciation plus any increase in net working capital and other net operating assets).

{ \sf { FCF \,= \,NOPAT \,less \,reinvestment}}

The reinvestment component of free cash flow is itself linked to return on capital, specifically the incremental return on capital.

Aggregate return on capital (post-tax) equals NOPAT divided by net operating assets. The incremental return on capital is the increase in NOPAT in a specified period divided by the related increase in net operating assets. Incremental returns in any one period can be very volatile as they are affected by profit changes unrelated to the increase in net operating assets. However, incremental returns are particularly relevant where long-term steady state assumptions are used, such as in DCF terminal values.

In our model above we show the implicit incremental return for each of the explicit forecast periods and the implied terminal (steady state) incremental return based on the input long-term growth assumption, including for the differing growth rates used in the sensitivity table. The reason why the implied incremental return is high in the explicit period (based on the data in the model when first loaded) is that we have assumed reasonably high growth in profit, which likely comes from sources other than investment, such as margin improvements. Based on the terminal growth assumption, the incremental return seems to be more realistic and potentially sustainable in the long-term (21.1% based on the base-case growth assumption in the model). It is important to check whether implied incremental ROIC, particularly that implied by terminal value assumptions, is sustainable.

You will notice that in the sensitivity table the implied incremental return varies significantly depending on assumed long-term growth. We think this results in a valuation that is more sensitive to different terminal growth assumptions than is realistic. The solution to this is to make the long-term incremental return a model input.

**Terminal value approach 2 – Investment moderated cash flow growth**

The problem with the typical DCF model we discuss above is that the level of net new investment in the terminal period is not linked to the assumed long-term growth. In our view reinvestment, at least in part, drives growth. When the growth rate input in the model is changed the amount of investment does not change (other than the effect of the year 6 growth rate) such that the implied return on capital varies. This is likely to be unrealistic and invalidate the sensitivity analysis.

One approach to ensuring that the net new investment in the terminal period is realistic, and consistent with the rate of growth, is to independently derive that investment and not assume that the net new investment component of the year 5 cash flow simply grows at the long-term profit growth rate.

Growth, reinvestment and return on capital are linked in the following way:

{ \sf { Growth \,= \,Reinvestment \,rate \,x \,Incremental \,return \,on \,invested \,capital}}

The reinvestment rate is the net new investment divided by NOPAT and the incremental return on invested capital is the additional profit (i.e. NOPAT) derived from that additional investment.

Using this relationship, and adding incremental ROIC as a model input, the net new investment in year 6 consistent with these inputs can be calculated.^{2}We have constructed the model such that the incremental return for year 6 is the increase in profit for year 6 divided by the additional investment in year 6. An alternative approach is to lag the additional investment such that the year 6 incremental return is based on the additional investment in year 5. There is no perfect approach given the approximations made in DCF analysis. This means that when the long-term growth rate is flexed, so too is the level of investment. The result is a terminal value that is less variable for given changes in assumed growth, as can be seen by comparing the sensitivity table with that above for approach 1.

Approach 2 gives precisely the same answer as approach 1 if the explicit input for incremental returns in approach 2 is the same as the incremental return implied by the investment in approach 1.

**Interactive model: DCF with assumed incremental return input used for terminal value**

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Notice that the sensitivity of the overall DCF value to changes in terminal growth assumption is now lower (and in our view more realistic) compared with the sensitivity shown in the first model. Using the incremental return as an input assumption means changes in the growth rate drive the net new investment. Try it for yourself – change the terminal value growth rate input and observe how the implied incremental investment component of the year 6 cash flow changes.

How sensitive the DCF value is to changes in growth depends on the input incremental return. A lower incremental return results in lower sensitivity to changes in the growth rate because growth adds less value. In fact, if the incremental return is set equal to the cost of capital, additional growth adds no value at all and the overall DCF valuation does not change with different growth rates, other than the year 6 impact.^{3}Had we constructed the model so that incremental returns are based on the prior year investment then the DCF value would have been unaffected by a change in growth assuming the incremental return is set equal to the discount rate.

**Terminal value approach 3 – Target exit multiples**

A variation on the above approach of linking investment to growth is to use a target exit multiple calculation to derive a terminal value. This calculation is based on the same inputs for a cash flow growth-based terminal value, namely the cost of capital (WACC), forecast growth (g) and expected incremental return on net new investment (iROIC).

{ \sf { Target \,exit \,NOPAT \,multiple \,=\, \dfrac{ (iROIC \,– \,g)} {iROIC\, (WACC \,– \,g) }}}

This calculation derives a target first year prospective multiple such that applying this to the year 6 forecast NOPAT produces a terminal value at the end of year 5. For more explanation about target multiples, including how the above calculation is derived and access to our interactive target enterprise value multiples model see our article *Interactive model: Target enterprise value multiples*.

Target multiples are not the same as using a comparable company analysis to derive an exit multiple (which we will return to in a future article). A target multiple based terminal value is still a calculation of the present value of cash flows beyond the explicit forecast period but with the calculation presented as a target multiple.

It is generally much easier to make judgements about how realistic or otherwise a DCF valuation is if the answers are derived from, or are cross-checked with, suitable multiples. It is for this reason that in both models we show the exit multiple and overall current multiple that are implied by the DCF model valuation. We have only presented the implied EV/NOPAT multiple in this case, but you would probably also want to calculate and use similar implied multiples of other metrics, such as EBITDA. All of this will help in refining model inputs.

## Terminal value approach 4 – **Multiple stage target multiples**

For some companies it may not be appropriate to assume that steady state conditions (constant growth and returns) start from the end of the explicit forecast period. This particularly applies to those companies experiencing high growth or that are in an early stage of development. In this case adding an interim ‘medium-term’ growth phase can be useful. This can be done in several ways, including extending the explicit forecast period itself. The interim period may have a medium-term growth rate applied to FCF in an extended forecast or maybe a growth rate that fades gradually to the assumed long-term rate.

The two-stage terminal value approach we show here is the same as the terminal exit multiple approach above, except that the target year 5 EV/NOPAT multiple is derived based on two stages with differing growth and incremental returns.

**DCF terminal values based on target multiples**

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**Dealing with the intangible asset problem**

In other articles we have discussed how the limited and inconsistent recognition of intangible assets presents challenges for investors. This includes DCF valuation and especially the calculation of DCF terminal values.

Of course, cash flow itself is unaffected by whether expenditure on intangibles is recognised as an asset in the balance sheet or as an expense in the income statement. Therefore, the accounting treatment should not ultimately affect DCF values. However, when forecasting, it is very difficult to focus purely on cash flows without using wider accounting information. Almost certainly you will need a full summarised financial statement model to be confident that the cash flow projection fairly reflects the underlying economics. If free cash flow is derived from the accounting profit less net new investment and if a returns-based analysis is used to ensure that the reinvestment rate is realistic (as we suggest) then the accounting treatment of intangibles matters a lot.

There are two things we would emphasise regarding intangibles and DCF terminal value calculations: (1) the need to exclude from NOPAT the amortisation of ‘replacement-expensed’ intangibles arising from business combinations; and (2) the need to allow for the lack of intangible asset recognition when using an incremental return input.

**NOPAT and intangible amortisation**

Unless you use a fully intangible asset adjusted returns approach (see below) it is best to exclude from NOPAT the amortisation of those intangibles arising from past business combinations that will not be replaced by new capitalised intangibles. This is a common adjustment when management present adjusted performance measures (APMs) – also called non-IFRS or non-GAAP measures. We think such adjustments are valid and provide a better basis to assess profitability and returns, particularly the incremental returns we use in our DCF terminal value calculations above.

For more about this topic see our article Should you ignore intangible amortisation?

**Lack of intangible asset recognition**

Most internally generated intangibles are not recognised as assets in financial statements, with the expenditure incurred in developing those assets being immediately expensed. The consequence is that measures of return are overstated. The incremental return on capital used as an input in the terminal value calculations we describe above should take this generally favourable impact of lack of recognition of intangibles on returns into account. For sectors where (expensed) intangible investment is high you would need to use a higher incremental ROIC and often one that is structurally above the cost of capital, even if no excess economic returns are expected. An examination of historical ROIC measures for the company and sector will help; although for this purpose it is best to exclude any intangibles arising from past business combinations. An aggregate historical ROIC calculated on this basis will be more consistent with the incremental ROIC input required for a terminal value calculation.

An alternative, and arguably better, approach is to fully adjust for unrecognised intangible investment. This does not alter free cash flow but it does affect NOPAT and the net new investment that make up that free cash flow, and hence the incremental ROIC. The resulting adjusted aggregate and incremental returns may be a better approximation of economic returns, notwithstanding the subjectivity involved. Consequently, it should be easier to make judgements about the incremental ROIC input for a DCF terminal value. Indeed, in many valuations it would likely be appropriate to set that intangible adjusted incremental return equal to the cost of capital. Furthermore, the link between net new investment and growth that we have emphasised is enhanced and should further reduce the sensitivity of DCF terminal values to different growth assumptions.

For more discussion about the inconsistent recognition of intangible assets in financial statements, the effect on returns, our suggested adjustments and an illustrative interactive model, see our article *Missing intangible assets distorts return on capital.*

**Insights for investors**

**Realistic terminal values are essential in DCF models. Focus on NOPAT and reinvestment and calculate the incremental return on capital implied by your inputs to help ensure investment and growth assumptions are consistent.**

**The assumption of constant growth in free cash flow for terminal values may not result in realistic incremental investment. Consider using an explicit return input to generate free cash flow in the terminal period.**

**A target multiple approach to terminal values can also be used to ensure realistic reinvestment assumptions.**

**Valuation multiples are an important reality check of terminal values and overall DCF value. Calculate implied EV/NOPAT, EV/EBITDA and other metrics relevant to the sector.**

**Remember that performance metrics and returns can be significantly impacted by inconsistent recognition of intangible assets in financial statements. Always measure NOPAT before deducting the amortisation of ‘replacement-expensed’ intangibles acquired in a business combination.**

**To obtain better insight into returns. Consider more comprehensive adjustments to capitalise and amortise the investment in intangibles that is expensed under conservative accounting rules.**