Enterprise value multiples, such as EV/NOPAT and EV/EBITDA, can be derived from underlying value drivers, including growth, return on investment, and cost of capital. These calculations benefit from the rigour of an underlying DCF methodology but present the results as familiar valuation multiples.
Our popular target multiple calculator can be used in both absolute valuations and to derive value drivers implied by current market prices. In a new expanded version of the model we add a disaggregation of growth inputs and a more refined measure of return on investment. The interactive model is free to download.
One of the most frequently downloaded models available on The Footnotes Analyst is our Target Enterprise Value Multiple calculator. This links key value drivers, such as growth and return on investment, to the valuation multiples that reflect those drivers. The output is a 12-month forward target EV/NOPAT, and variations thereof, such as EV/EBITDA.
The model is based on an underlying discounted cash flow methodology, but one that is simplified and does not require an explicit cash flow forecast. It can be used to derive a target valuation, but it can also be used in reverse to identify what is priced into the current market price multiples for a particular investment, such as estimating the period of abnormal growth that is built into the current price of a growth stock.
We have used this model for many years and find it is particularly useful to help investors in conceptually thinking about valuation multiples and their underlying value drivers in absolute terms, rather than simply using multiples in a relative comparison.
The Footnotes Analyst target enterprise value multiple calculator
The Footnotes Analyst. See below for a download link.
Loose references to differences in value drivers to justify differences in multiples
Relative comparison of multiples is all very well, but without some way of explicitly including value drivers in the analysis, investors are left to subjectively explain observed multiples. In our experience, analysts often seem to justify differences in valuation multiples with loose references to differences in growth and margins, whereas the target multiple calculator requires investors to first identify the key value drivers and, as a result, provides a more robust underpinning of differences in valuation.
The model also features as a component of our approach to DCF. We prefer to use a target ‘exit’ multiple calculation for DCF terminal values rather than simply apply the common constant growth in cash flow formula. We think including a return on investment input in the terminal value in addition to growth, and the potential for a 2-stage approach, should result in investors deriving a more realistic terminal value.
You will find more about using target multiples in DCF analysis, and a downloadable model that illustrates 5 different approaches to terminal values, in our article ‘DCF terminal values: Returns, growth and intangibles’.
Target multiple models are simplified – a full DCF analysis may be preferred
Of course, all models are simplified representations of the real world. The target multiple model may have more value-driver inputs than, for example, a simple constant cash flow growth approach, but it is still simplified compared with full DCF analysis. Fewer inputs is a good thing in that it forces analysts to focus on the most significant drivers of value. However, it can also be a problem in that it becomes more difficult to fully capture all value drivers, which is why a full DCF-based analysis that includes an explicit cash flow forecast for a number of years is often to be preferred.
A key simplification in the target multiple model recently caught the attention of a Footnotes Analyst reader, who sent us an interesting email proposing an extension to the model …
“I particularly enjoyed your article, “Linking value drivers and enterprise value multiples”. While exploring the mathematics, I noted that the model assumes all growth comes from reinvestment, with the return on existing assets held constant. This inspired me to try to derive an expanded version that also incorporates growth from efficiency gains on existing assets. I wanted to share my derivation and would be very interested to hear your thoughts. ….”
We like the suggestion, and have produced a new version of the model that features a disaggregation of forecast growth and a separate input for efficiency gains.
Incremental ROIC versus return on new investment
Our original model shown above features an input of the incremental return on invested capital (iROIC). We define this as the forecast increase in profit for a given period divided by the increase in capital for the prior period. Combining this measure with a forecast growth input gives a reinvestment rate, from which cash flow and value is derived.
We define:
iROIC = Increase in NOPAT / Increase in IC
Growth = Increase in NOPAT / NOPAT
Reinvestment rate = Increase in IC / NOPAT
Combining the above and cancelling produces:
Growth = iROIC x Reinvestment rate
Therefore:
Reinvestment rate = Growth / iROIC
Cash flow = NOPAT x (1 – Reinvestment rate) = NOPAT x (1 – Growth / iROIC)
It is from this relationship that all the target multiples presented in the model are derived. In a single stage model the target EV/NOPAT multiple is given by:
{ \sf { \dfrac{EV} {NOPAT} = \dfrac{ (iROIC \,– \,g)} {iROIC\, (WACC \,– \,g) }}}
Click here for more about the underlying maths …
The model is based on an underlying DCF methodology where enterprise value is the present value of expected enterprise free cash flow (FCF) discounted at the weighted average cost of capital (WACC). Below is the derivation of the formulae that applies when growth is constant in perpetuity, i.e. a single stage model.
Single stage target multiple formula and derivation
If growth in free cash flow (FCF) is expected to be constant, then enterprise value (EV) is:
{ \sf { EV = \dfrac{FCF_1}{(WACC \, – \, g)}}} \qquad ...(1)
But FCF can also be written as the post-tax operating profit (NOPAT) multiplied by one minus the reinvestment rate (r). The reinvestment rate is the percentage of profit that is reinvested in the business for growth.
{ \sf { FCF \,= \,NOPAT \,* \,(1 \,– \,r) }} \qquad ...(2)
Growth (g) can also be written as the product of reinvestment rate and the incremental return on invested capital (iROIC).
ROII is defined as the forecast increase in profit divided by the forecast increase in invested capital:
{ \sf { iROIC \,= \,\dfrac{(NOPAT_{t1}\,–\, NOPAT_{t0})} {(Invested \,Capital_{t1}\,– \,Invested \,Capital_{t0}) }}} \qquad ...(3)
And the reinvestment rate can be expressed as the additional investment divided by profit:
{ \sf { Reinvestment \,Rate \,(r) \,= \,\dfrac{ (Invested \,Capital_{t1} \,– \,Invested \,Capital_{t0})} {NOPAT_{t0}}}} \qquad ...(4)
Combining (3) and (4) and cancelling produces growth in NOPAT equal to the incremental return multiplied by the reinvestment rate:
{ \sf { g \,= \,iROIC * r \,= \,\dfrac{(NOPAT_{t1} \,– \,NOPAT_{t0})} {NOPAT_{t0} }}} \qquad ...(5)
And therefore:
{ \sf { r \,= \,\dfrac{g} {iROIC}} } \qquad ...(6)
Combining (2) and (1) gives:
{\sf { EV \,= \,\dfrac{NOPAT \,(1\, – \,r)} {(WACC \,– \,g)}}} \qquad ...(7)
Substituting (6) into (7) and assuming that growth and returns remain constant gives:
{ \sf { EV \,= \,\dfrac{NOPAT \,(1 \,– \,g/iROIC)} {(WACC \,– \,g)}}} \qquad ...(8)
Expanding and rearranging (8) produces:
{ \sf { EV \,= \,\dfrac{NOPAT \,(iROIC \,– \,g) } {iROIC \,(WACC \,– \,g)} }} \qquad ...(9)
Which gives the target EV/NOPAT multiple of:
{ \sf { \dfrac{EV} {NOPAT} = \dfrac{ (iROIC \,– \,g)} {iROIC\, (WACC \,– \,g) }}} \qquad ...(10)
To calculate target EV/EBIT and EV / EBITDA and EV / Revenue multiples the difference between NOPAT and these metrics must be included in the formulae above. If T = the effective tax rate, D = depreciation and amortisation as a percentage of EBITDA and M is the operating margin (EBIT / Revenue), all in respect of the first year forecast period, then:
{ \sf { NOPAT = EBIT \,* \,(1 \,– \,T) }} \qquad ...(11)
{ \sf { NOPAT = EBITDA \,* \,(1 \,– \,D) \,* \,(1 \,– \,T) }} \qquad ...(12)
{ \sf { NOPAT = Revenue \,* \,M \,* \,(1 \,– \,T) }} \qquad ...(13)
Target EV / EBIT, EV / EBITDA and EV / Revenue multiples can be derived from the target EV / NOPAT multiple by substituting (11), (12) and (13) into (10):
{ \sf { \dfrac{EV} {EBIT} = \dfrac{(iROIC \,– \,g)} {iROIC \,(WACC \,– \,g)} \,(1 \,– \,T) }}
{ \sf { \dfrac{EV} {EBITDA} = \dfrac{(iROIC \,– \,g)} {iROIC \,(WACC \,– \,g)} \, (1 \,– \,T) \,(1 \,– \,D) }}
{ \sf { \dfrac{EV} {Sales} = \dfrac{(iROIC \,– \,g)} {iROIC \,(WACC \,– \,g)} \,M\,(1 \,– \,T) }}
A target EV / Free cash flow multiple can be derived by substituting (2) and (6) into (10)
{ \sf { \dfrac{EV} {FCF} = \dfrac{(iROIC\,– \,g)} {iROIC \,(WACC \,– \,g)} \, * \,\dfrac{1} {(1 \,– \,g/iROIC} }}
Two-stage target multiple formula
The above analysis shows the derivation of calculations for target multiples based on an assumed perpetuity single-stage DCF approach. It can easily be expanded to allow for two growth periods with differing growth rates and returns.
The target EV / NOPAT multiple then becomes:
{ \sf { \dfrac{EV} {NOPAT} \,= \, \dfrac{ (iROIC_1 \,– \,g_1)} {iROIC_1\, (WACC \,– \,g_1) } \, \bigg(1 \,- \, \dfrac{(1 \,+ \,g_1)^n } {(1 \,+ \,WACC)^n } \bigg) \,+\,...}}
{ \sf { \dfrac{ (iROIC_2 \,– \,g_2)} {iROIC_2\, (WACC \,– \,g_2) } \,*\, \bigg( \dfrac{ (1 \,+ \,g_1)^n } {(1 \,+ \,WACC)^n } \bigg)}}
Terms used
WACC = Weighted average cost of Capital
iROIC =Incremental return on invested capital
g = Growth in profit
r = Reinvestment rate
n = Number of years for growth period 1
FCF = Enterprise free cash flow
Invested capital = Aggregate investment in balance sheet net operating assets
NOPAT = Net operating profit after tax
EBITDA = Earnings before interest, tax, depreciation and amortisation
EBIT = Earnings before interest and tax
A key simplification in the above calculations is that we assume that the increase in profit and capital are linked; however, this may not always be the case, at least directly. A company may increase profit without any additional investment, for example, by reducing expenses, improving margins through a more advantageous product mix, or simply generating more output from the existing asset base. While it may not be possible to maintain such profit growth in the long-term, many companies will likely be expected to show such effects in the short-term (i.e. in ‘period 1’ in our model). This ‘growth requiring zero investment’ is referred to by our reader as ‘efficiency gains’ in the quote above.
In our original model, efficiency gains are simply rolled into the overall incremental ROIC. In effect iROIC is a combination of the actual return on new investment (RONI) plus the effect of efficiency gains. Higher efficiency gains result in a higher iROIC, even though the actual return from new investment may itself be more modest. The problem is that, while iROIC is a perfectly valid approach to derive target multiples, estimating this in practice may be difficult if there are also efficiency gains to consider.
Separate efficiency gains to facilitate better forecasting
The proposal is therefore to disaggregate the forecast growth into that derived from new investment (the increase in the invested capital base) and that which does not require new investment – efficiency gains derived from the existing asset base. The reinvestment rate is then obtained by combining the growth from investment only (total growth less the efficiency gains element) with the estimated return from that investment (RONI). In other words, using RONI instead of iROIC in the model.
The revised target EV/NOPAT multiple calculation is:
{ \sf { \dfrac{EV} {NOPAT} = \dfrac{ (RONI \,– \,g_i)} {RONI\, (WACC \,– \,g) }}}
Where g is the total forecast growth in NOPAT and gi is the growth derived from reinvestment, with the difference between them being the forecast efficiency gains. RONI is the incremental return on new investment.
Here is the revised model:
Target EV multiple calculator modified to include disaggregated growth
The Footnotes Analyst
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The two alternative returns measures used in each model are linked. If inputs are consistent with each other, they will produce the same reinvestment rate and the same overall value and valuation multiples. The calculations of the reinvestment rate are:
Reinvestment rate = Total forecast growth / iROIC = Growth from reinvestment only / RONI
And therefore:
RONI = iROIC * (Growth from reinvestment only / Total forecast growth)
For example, in our original model, an iROIC of 25% and a growth rate of 12% produces a reinvestment rate of 48%. However, if 5% of the growth is forecast to be achieved from efficiency gains, the iROIC is higher than the actual return on new investment (RONI). In the revised model the same reinvestment rate is obtained from the combination of the growth due to reinvestment only and the return on that investment.
Reinvestment rate = 48% = 12% / 25% = 7% / 14.6%
As can be seen from the results in the two versions of the model above, the answers are the same (assuming the inputs are consistent, which they are in the data shown when you first load this page). So why bother with the modified version and the added effort of disaggregating the growth rate? The answer is that it may provide a better basis for analysis and forecasting and is therefore more likely result in realistic valuations.
Efficiency gains are likely to be short lived for many companies, which is why we have included zero as the ‘period 2’ input in the model data above. For many companies it is reinvestment and the return that can be achieved on that new capital that will likely dominate what determines the deserved valuation multiples today.
A focus on aggregate return on invested capital
One of the advantages of separately forecasting and modelling efficiency gains (growth requiring zero investment) is that the revised return input RONI – the incremental return on new investment only – is more logical and perhaps easer to forecast. RONI is consistent with the existing historical aggregate rate of return on invested capital (NOPAT / Invested capital) such that the historical return should be a better starting point for a forecast of RONI than it is a forecast of iROIC.
Analysing aggregate ROIC may help in forecasting both efficiency gains and RONI
Furthermore, if growth in aggregate ROIC arises from an increase in the NOPAT component, the forecast percentage change in ROIC will equal the efficiency growth input in the model. The increase in ROIC may come from improved margins and/or higher asset turnover (more revenue from the existing asset base). Each of these may themselves be analysed into different contributing factors using the familiar DuPont style analysis.
However, you do need to be careful with using forecast changes in ROIC to estimate efficiency gains. If ROIC is expected to increase due to a reduction in net operating assets, this has a value effect that differs from growth in NOPAT, which cannot easily be incorporated in our simple target multiple model.
Value effect of higher ROIC depends on the source of the increase
Increasing ROIC by reducing invested capital results in a value increase equal to the amount of that capital release. This is most likely to be reflected in a reduced amount of net debt in a valuation model. There could also be a second order effect in that the incremental return on new investment could be higher if the more efficient use of capital can be extended to forecast investment returns. In the case of an increase in ROIC due to higher NOPAT, we think this is more likely to produce a permanent increase in profit and cash flow, which will result in a value change equal to the increase in profit multiplied by the valuation multiple applicable to that profit.
If the existing asset base is expected to change you will probably need to resort to a more sophisticated full DCF analysis to fully capture the resulting effects on value.
ROIC and intangible asset accounting
One of the challenges of using accounting return on investment metrics in equity valuation is the inconsistent recognition of intangible fixed assets. While purchased intangibles are recognised much like tangible assets, this mostly occurs in the context of business combinations where intangibles form part of the assets acquired. Most other intangible assets are internally generated through investment in research and development, customer relationships, branding and other ‘future-orientated’ expenditure. Few of these investments are recognised in the balance sheet as intangible assets under IFRS or US GAAP accounting rules.
The result of the limited capitalisation of intangibles is that ROIC and other similar measures of return tend to be overstated and higher than the true underlying economic return. Investors can deal with this in two ways. Neither approach is perfect.
- Allow for return overstatement when selecting valuation model inputs: If no adjustment for unrecognised intangibles is made when deriving valuation metrics such as NOPAT, the return input will need to be higher to reflect the degree to which ROIC is overstated.
- Adjust the financials to recognise the estimated missing amount of intangible assets: This means NOPAT will likely differ (probably be higher) and the returns metrics used in valuation models should be based on the revised capital base.
For more about these techniques, and the impact of intangibles on returns and performance metrics, see our article ‘Missing intangible assets distorts return on capital’. This article also includes a simple model that should help to quantify the effect of limited intangible asset recognition.
Insights for investors
- Valuation multiples can be more than just a tool for the relative comparison of stock prices. Target multiples derived from a simplified DCF approach facilitate both an absolute view and the analysis of value drivers implied by market prices.
- Target EV/NOPAT reflects forecasts of the key value drivers – growth, returns, and cost of capital. Other target EV multiples, including EV/EBITDA, can be derived from EV/NOPAT.
- The calculation of target multiples requires a forward looking measure of incremental return on investment. Historical investment is a sunk cost – aggregate invested capital and ROIC are not direct valuation inputs.
- If growth is not disaggregated, the required return input is iROIC, defined as the forecast increase in profit divided by the increase in invested capital.
- If growth is disaggregated to separately identify efficiency gains, the return input in the target multiple model becomes RONI – the return on new investment. RONI excludes the effect of efficiency gains.
- Disaggregating growth, and the resulting alternative target enterprise value multiple model, produces the same result as our earlier model, assuming consistent inputs. However, the alternative approach may make it more likely you will derive realistic valuations.
With thanks to Florian for sending the email that prompted this article.