**Use this model to derive ‘target’ enterprise value multiples that are consistent with specified value drivers, including measures of growth, return on investment, margins and capital intensity. The model is based on an underlying 2-stage DCF methodology. We explain its derivation, the key assumptions and how to select appropriate value driver inputs. **

**See our article Linking value drivers and enterprise value multiples for more about how to use this model.**

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Valuation multiples are, in effect, a discounted cash flow calculation expressed as a single summary statistic. An enterprise or equity valuation multiple can be derived from the same value drivers and underlying methodology as used in DCF. The multiple represents the valuation that is implied by those input value drivers.

Our target enterprise value multiple model is based on an underlying 2-stage DCF framework with specified value drivers for each stage. The results of the model are expressed in the form of five ‘target’ enterprise value multiples.

An implied or target multiple model is an excellent way to better understand how key value drivers impact value and multiples. However, the model summarises very complex businesses in a limited number of value drivers and, inevitably, cannot faithfully reflect all of the factors that would be included in a comprehensive discounted cash flow analysis. You should use the model with this in mind.

The key assumptions that underlie the model are:

- Growth and returns are constant during each of the two stages specified in the model.

- A single cost of capital applies to all periods.

- Growth and incremental returns fully describe the reinvestment rate and, as a result, the difference between profit and cash flow.

- Profit metrics are 12-month forward forecasts and should include the expected (average) amount of non-recurring or exceptional items (see model inputs).

- Multiples are based on the concept of ‘core’ or ‘operating’ enterprise value that is consistent with the definition of the after-tax operating profit (NOPAT). See our article
*EV/EBITDA multiples must be consistent’*for an explanation about why this is important.

- NOPAT is stated after depreciation and amortisation, except for the amortisation related to those intangibles that will not be replaced in the ordinary course of business. See our article
*Should you ignore intangible amortisation*.

**Growth**

This is the expected rate of growth in the post-tax operating profit, commonly called net operating profit after tax (NOPAT).

The model assumes that growth is constant during each stage. For the initial phase this may be simplistic considering that actual growth forecasts may differ for each period. However, in most cases, using an average expected rate should 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 the long-term growth rate, it is important to use a sustainable rate considering market and economic conditions. Remember that this long-term growth rate is applied in perpetuity. The model will not accept a growth rate greater than the cost of capital. Such a scenario is impossible anyway because, theoretically, such a growth rate produces an infinite valuation and the company would eventually end up bigger than the economy.

**Excess return on incremental investment** (ROII)

This is the post-tax return on all capital invested in the business. It can also be expressed as a return on net operating assets.

The model input should be a return premium over the cost of capital, not the full expected return. Entering zero would mean the company’s return would be equal to the cost of capital. You could even enter a negative amount if the company is expected to generate returns below the cost of capital. The formulae shown in this article are based on ROII being the full return before deducting the cost of capital. However, we decided to use the excess return in the model (ROII – WACC) as the return input because we believe this ensures that investors focus on whether or not returns can be sustained above the cost of capital or not.

The return should also be incremental and hence forward looking; in other words, it is the return expected to be earned in future periods on the incremental investment that is recognised in the balance sheet. The historical aggregate return on capital that divides NOPAT by balance sheet invested capital should not be used, although this may help as a starting point in estimating forecast incremental returns.

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 capture the expenditure that will be capitalised in the balance sheet. The model uses this return to determine the difference between reported profit and the cash flow that ultimately drives value.

The difference between accounting returns and economic returns is largely 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 return on investment used in the model for a company would generally be high for a company where it is primarily intangible investment that drives value.

**Cost of capital**

This is the normal economic weighted average cost of capital that captures both the cost of debt, equity and any other claims that are reflected in enterprise value. Cost of capital is the overall required return of all investors in respect of their investment in the core enterprise (the full business less any non-core assets and investments that are excluded from enterprise value).

**Profit **

NOPAT, EBIT and EBITDA are not themselves model inputs because the output of the model is implied multiples not an implied value or stock price. However, it is important to apply the model output to the correct profit metric when using the model to derive target values.

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

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 (ROIC).

ROII is defined as the forecast increase in profit divided by the forecast increase in invested capital:

{ \sf { ROII \,= \,\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 \,= \,ROII * r \,= \,\dfrac{(NOPAT_{t1} \,– \,NOPAT_{t0})} {NOPAT_{t0} }}} \qquad …(5)

And therefore:

{ \sf { r \,= \,\dfrac{g} {ROII}} } \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/ROII)} {(WACC \,– \,g)}}} \qquad …(8)

Expanding and rearranging (8) produces:

{ \sf { EV \,= \,\dfrac{NOPAT \,(ROII \,– \,g) } {ROII \,(WACC \,– \,g)} }} \qquad …(9)

Which gives the target EV/NOPAT multiple of:

{ \sf { \dfrac{EV} {NOPAT} = \dfrac{ (ROII \,– \,g)} {ROII\, (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{(ROII \,– \,g)} {ROII \,(WACC \,– \,g)} \,(1 \,– \,T) }}

{ \sf { \dfrac{EV} {EBITDA} = \dfrac{(ROII \,– \,g)} {ROII \,(WACC \,– \,g)} \, (1 \,– \,T) \,(1 \,– \,D) }}

{ \sf { \dfrac{EV} {Revenue} = \dfrac{(ROII \,– \,g)} {ROII \,(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{(ROII \,– \,g)} {ROII \,(WACC \,– \,g)} \,(1 \,– \,\dfrac{g} {ROII}) }}

**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{ (ROII_1 \,– \,g_1)} {ROII_1\, (WACC \,– \,g_1) } \, \bigg(1 \,- \, \dfrac{(1 \,+ \,g_1)^n } {(1 \,+ \,WACC)^n } \bigg) \,+\,…}}

{ \sf { \dfrac{ (ROII_2 \,– \,g_2)} {ROII_2\, (WACC \,– \,g_2) } \,*\, \bigg( \dfrac{ (1 \,+ \,g_1)^n } {(1 \,+ \,WACC)^n } \bigg)}}

**Terms used**

WACC = Weighted average cost of Capital

ROII = Return on incremental investment

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

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