**Defined benefit pension schemes create two leverage effects – financial leverage due to the debt-like nature of pension deficits, and asset allocation leverage if pension assets are not matched with pension liabilities. In DCF valuation these effects must be correctly, and consistently, included in both the discount rate and free cash flow.**

**We use an interactive model to demonstrate four possible DCF approaches based on enterprise and equity cash flows. Our preferred approach uses enterprise free cash flow with the effects of asset allocation leverage excluded from the discount rate.**

Defined benefit pensions create challenges for investors with regard to both the discount rate and free cash flow applied in discounted cash flow analysis.^{1}It is not just DCF valuations that are affected; so too are the calculation and analysis of valuation multiples. After all valuation multiples are, in effect, just a simplified form of DCF. For a discussion of the link between multiples and DCF and for interactive models to derive target valuation multiples based on underlying DCF drivers, see our articles *Linking value drivers and enterprise value multiples* and *Price earnings ratios – DCF in disguise**.* Many companies have significant pension schemes. Often these are in deficit (and sometimes are completely unfunded) which creates financial leverage similar to debt financing.

Even if fully funded, schemes create risk if the fund is invested in risky assets (such as equities) that do not effectively match the liability cash flows. Both financial leverage and pension asset allocation leverage affect the cost of capital.

Pension related risks also impact cash flows. Asset allocation leverage reduces the expected cash outflow due to the spread between the expected pension fund asset return and the interest accretion for the liability. Financial leverage arising from a pension fund deficit results in additional contributions.

There are four possible DCF approaches depending on whether pension financial leverage and/or pension asset allocation leverage are included, or not, in the determination of the discount rate. Two of these approaches are based on enterprise free cash flow (FCF), the discounting of which initially produces a target enterprise value that then must be adjusted to deduct the pension claim to derive a target stock price. The other two are based on an equity free cash flow approach which directly derives an equity value.

Only if pension risks and cash flows are dealt with in a consistent manner will a DCF calculation be correct. But before we explain the four approaches and demonstrate each one using an interactive DCF model, we first need to examine and disaggregate pension risk and pension cash flows.

**Pension leverage and cost of capital**

A defined benefit pension obligation almost always creates leverage and increases equity risk. Pension payments to scheme members are (largely) a fixed obligation and similar to long-term debt finance. The existence of pension fund assets results in two leverage components – asset allocation leverage and, if the scheme in in deficit, financial leverage.^{2}The principles for DCF analysis we outline also work if the pension scheme is in surplus (try it in the embedded model below), but for simplicity we will assume a deficit for the purposes of our explanations. Only if a scheme is fully funded and asset-liability matched, is there no financial risk.^{3}There can be other risks. Pension payments are uncertain considering changes to expected longevity and other factors such as salary growth and staff turnover. We do not consider these risks here. However, we do not believe these affect cost of capital in the same manner as financial risks, given the generally uncorrelated (unsystemic) nature of these risk factors.

**Asset allocation leverage:**If the assets of the pension fund produce cash flows that exactly match the expected pension payments in terms of duration and other characteristics, then there is no asset allocation risk for the company. However, if the company’s pension fund is not invested in matching assets then this creates additional ‘asset allocation’ risk for the equity investors. The additional risk does not necessarily reduce the equity value because a higher risk asset allocation would be expected to reduce the company’s future cash contributions to the pension fund.

**Financial leverage:**To the extent that the scheme is under-funded, the deficit creates financial leverage similar to other debt finance. Like debt, pension deficits result in an interest expense and a ‘debt’ repayment when the pension deficit is corrected via a company contribution or when the company has to make future pension payments directly to retired scheme members because the pension fund has insufficient assets.

The leverage effect of pensions can be illustrated using CAPM beta factors that are commonly used to derive a DCF discount rate.

**Pension risk and beta factors**

Most investors will be very familiar with the idea of asset, equity and debt betas. An operating asset beta (boa) reflects the (systemic) risk of the operating business. This risk is shared between the various claim holders. Typically, claims are simplified^{4}Regular readers of The Footnotes Analyst will be familiar with our expanded view of enterprise value to encompass different types of equity and debt claims. See for example *Enterprise value: Calculation and Miscalculation*.to equity holders and debt holders, with operating asset beta being the average of the equity (be) and debt (bd) betas, weighted by the market value of each claim (E & D) relative to enterprise value (EV). Therefore:

{ \sf { {\large \beta} oa = {\large \beta} e \dfrac{E}{EV} + {\large \beta} d \dfrac{D}{EV}}}

Due to the prior charge of debtholders the debt beta is typically relatively low compared with the asset beta.^{5}It is not uncommon to see this calculation simplified by assuming the debt beta is zero. This may be acceptable for companies with modest financial leverage and investment grade debt but in other cases the simplification can result in material errors. The higher financial leverage results in a higher equity beta.

A funded defined benefit pension scheme adds two additional terms to the above. The gross (before deducting pension assets) pension liability (PL) is a further claim but this is offset, in part or completely, by pension assets (PA). We need to keep each component separate and not just focus on the net pension deficit because the pension assets and liability may have different risks and beta factors. The relationship now becomes:

{ \sf { {\large \beta} = {\large \beta} e \dfrac{E}{EV}\,+ {\large \beta} d \dfrac{D}{EV} + {\large \beta} pl \dfrac{PL}{EV} - {\large \beta} pa \dfrac{PA}{EV}}}

This can be rearranged to separate the financial leverage and asset allocation leverage effects arising from pensions. If the pension deficit^{6}These calculations also apply if there is a pension fund surplus; just reverse the sign. is represented by PD and PD = PL – PA, then the above can be expressed as:

{ \sf { {\large \beta} = {\large \beta} e \dfrac{E}{EV}\,+ {\large \beta} d \dfrac{D}{EV} + {\large \beta} pd \dfrac{PD}{EV} - \left[ ({\large \beta} pa - {\large \beta} pl ) \dfrac{PA}{EV} \right] }}

What do these beta factors represent?

**Equity beta:**This is the standard equity beta factor representing the systemic risk for equity investors. It reflects all risk factors, both underlying business risk and all leverage effects, including those arising from pension schemes. The equity beta of a company can be observed (with a certain statistical confidence interval) in the market through standard regression analysis.

**Debt beta:**This reflects the credit risk of debt and the resulting exposure of debtholders to underlying asset risk. A debt beta can be estimated based upon the observed debt yield to maturity or calculated using an option pricing approach.

**Pension assets beta:**This reflects the average risk of the assets in the pension fund. For example, a 100% weighting to equity would likely result in a beta close to 1.0.

**Pension liability beta:**This reflects the sharing of risk with the pension scheme members and represents the liability non-performance risk. Due to the members having a prior charge similar to debt and also the potential existence of a ring-fenced fund, the pension liability beta should be low and often similar to the debt beta. Risky asset allocation, a weak sponsor and the ability of the sponsor to modify benefits all increase the pension liability beta.

The final term in the above calculation (in square brackets) is the effect of pension asset allocation leverage. This risk factor is reflected in the equity beta, given that it is the shareholders who are subject to this risk. The deduction of this term in the calculation produces an asset beta that only reflects operating asset risk.

In DCF valuation it is important that the correct pension risk component is included in the cost of capital calculation. There are four approaches, with either no pension risk factor included, one of them or both.

**Cost of capital and pension risks**

**From beta to cost of capital**

Each of the above betas can be combined with the risk-free rate and equity risk premium to produce a CAPM cost of capital. The asset betas produce two versions of WACC and the equity betas produce two versions of the costs of equity.^{7}Strictly speaking an asset beta produces an unlevered cost of equity. However, because we have not included any debt finance in the model, there is no debt interest tax shield to consider and the asset beta applied in CAPM produces the same result as a traditional WACC calculation.

An alternative approach to calculating an enterprise free cash flow discount rate is to simply take the weighted average of the costs of different forms of finance in a traditional WACC calculation. How this should be done depends on whether asset allocation risk is being included or not which, in turn, depends on how the cash flow is defined.

If asset allocation risk is excluded from the discount rate applied in a DCF valuation then the WACC calculation must include the gross pension liability and pension assets with their respective rates of return, but with a negative weighting applied to the expected return on the assets. Separating the effect of asset allocation leverage in the same way as we did above for beta factors, this produces:

{ \sf { WACC = COE \dfrac{E}{EV}\,+ COD \dfrac{D}{EV} + COP \dfrac{PD}{EV} - \left[ (PA\,return - COP ) \dfrac{PA}{EV} \right] }}

Where: COE, COD and COP are the costs of equity, debt and the pension liability respectively and PA return is the expected return from the pension fund assets.

All of these alternative beta factor and cost of capital calculations are illustrated in our interactive model below. To keep the model simple, we have not included any debt finance, mainly because this adds the challenge of dealing with the debt interest tax shield.

**Pensions contributions and free cash flow**

The overall pension cash flow for a funded defined benefit pension scheme is simply the payment by the company to the pension fund. However, it may not be correct to include the full payment to the pension fund in the free cash flow to be discounted.

To identify the right cash flow, we need to disaggregate the overall payment into its various components. The pension payment to the fund, in effect, comprises:

**(1) Service cost:** The value of pension rights granted in the period adds to the gross pension liability. Part of the pension cash flow covers this cost.

**(2) Expected gain from asset allocation:** If the pension fund is invested in assets with a higher expected return than the interest accretion of the liability, then this spread, in effect, subsidises the expected cash flow cost of paying pensions. All other things being equal, a company would expect lower cash funding payment as a result of taking asset allocation risk.

**(3) Interest accretion on a pension deficit:** If the fund is in deficit then this will rise in line with the unwind of the discount rate. Part of the cash payment to the fund must cover this accretion.

**(4) Deficit reduction or increase:** This is the difference between the actual payment to the pension fund and the sum of each of the other components.

**(5) Unexpected asset returns and changes in discount rate:** If the actual return on pension assets differs from that expected, or if the liability is affected by a change in discount rate, then these affect the funding position. For historical periods this component is likely to be large and offset by the deficit reduction or increase (4).

In cash flow forecasts for DCF analysis, the unexpected asset return and changes in discount rate (5) will automatically be zero. This leaves us with four components of the total forecast cash flow. Which of these should be included in free cash flow in a DCF calculation depends on whether the DCF is based on enterprise or equity cash flow and how the expected gain and associated leverage from asset allocation is dealt with. There are therefore four possible cash flows.

An enterprise free cash flow approach, where the pension deficit is treated as a form of debt, must exclude the debt cash flow. Therefore, the pension cash flow should exclude those components that represent the interest accretion expense (3) and the changes in the forecast deficit (4). In an equity free cash flow approach these components would be included. Furthermore, in each of the enterprise and equity FCF approaches the asset allocation effect could be included or excluded, depending on the discount rate selected. The table below shows the resulting four cash flow amounts to be included in FCF.

**Alternative pension components of forecast free cash flow**

**Enterprise to equity bridge**

The fundamental difference between an enterprise and an equity approach to DCF valuation is how debt and other non-common share claims are dealt with. For an enterprise approach, debt cash flow (the cash paid to debt holders in respect of debt repayments and interest) is not included in free cash flow but instead the absolute value of the debtholders’ claim is deducted in the enterprise to equity bridge.

This also applies to pensions. If the components of pension payments representing the interest accretion and paydown of any scheme deficit are included in free cash flow, then you should not also deduct the absolute amount of the deficit. Only in the case of an enterprise free cash flow approach is the pension liability deduction necessary.

**Including the effect of taxation**

Both the cost of capital and cash flows in a DCF valuation need to include tax effects. Generally, for defined benefit pension schemes, the contributions made by the company to the fund are tax deductible, rather than the amount reported in profit and loss. A scheme deficit creates a deferred tax asset – the asset represents the tax savings that will arise when the deficit is corrected.

Because both the deficit interest accretion and the liability repayments are tax deductible, the tax effect of pensions is not the same as for regular debt finance. For pensions, all that needs to be done is to use after-tax amounts for the pension cash flow, gross pension assets, gross liability and deficit.

**Tax effect on beta factors and cost of capital:**Use after-tax weightings for pension assets and liabilities. Do not also use an after-tax cost of capital because this would double count the tax effect. For example, the asset beta calculation now becomes:

{ \sf { {\large \beta} = {\large \beta} e \dfrac{E}{EV}\,+ {\large \beta} pl \dfrac{PL(1-T)}{EV} - {\large \beta} pa \dfrac{PA(1-T)}{EV}}}

Where EV includes the post-tax pension deficit

**Tax effect for free cash flow:**Use an after-tax amount for each of the cash flow measures described.

**Tax effect for enterprise to equity bridge:**Deduct the after-tax deficit from EV when calculating a target equity value.

**Putting it together – 4 approaches**

Having identified four different measures of risk, and consequently four discount rates, together with four different measures of pension cash flow, we are now in a position to put them together to produce our alternative DCF approaches. Each will produce the same ultimate target equity value, as we demonstrate in the interactive model below.

What is important is to not mix up the cash flows and discount rates.

**Alternative approaches to including pensions in DCF valuation**

The interactive model below shows how each of the four approaches described above can be successfully used to produce a valuation. The model includes a typical explicit forecast period plus a terminal value based on a constant growth assumption. All blue input figures can be changed.

**Interactive model – Pensions in enterprise and equity free cash flow DCF**

— iphone and ipad users: This model formats best if viewed in Google Chrome —

*Further analysis, including the derivation of the different beta factors and costs of capital, plus the detailed roll forward of the pension assets and liability, is available in the downloadable excel version of this model.*

Please enter your email address to receive an excel version of this model

To learn more about the model inputs, underlying methodology and assumptions click on the links below.

This DCF model shows four alternative methods to include a pension scheme in DCF valuation. The model uses a standard explicit forecast (in this case four years) and terminal value, based on constant growth in perpetuity. To keep the model as simple as possible and to be able to emphasise the effect of pensions, we have not included any debt or other claims on enterprise value apart from the pension liability.

The blue figures are input cells and can be freely changed. You will notice that some of the year 4 inputs are model calculations. These are needed to ensure that a true steady state is achieved for the terminal value calculation such that the leverage effects from pensions remain constant in the terminal period (i.e. the gross and net pension liability grow at the same rate as the business). If this were not the case, the equity FCF based DCF approaches would not be accurate using a single discount rate in the terminal period.

The discount rate calculations start with an assumed asset beta. This is the risk of the operating assets excluding any effects of the pension scheme. We assume this asset risk remains constant (although the approaches would still work with changes to asset risk over time).

In addition to pure asset risk, three other measures of risk are calculated that include pension asset allocation risk or pension leverage risk or both pension risk factors. These beta factors are then applied in a CAPM framework to derive the discount rates for the DCF 4 calculations.

The cash flows used in each calculation include a different measure of pension cash flow. If the discount rate includes all pension risk, then the full cash payment to the fund is included in FCF within an equity flow framework. Where elements of pension risk are excluded from the discount rate so are the related components of pension cash flow.

Aside from the usual assumptions implicit in any DCF analysis based upon CAPM, the model is also based on the assumption that pension leverage is fully reflected in the equity beta and that no advantage, other than the lower expected cash flow, arises from asset allocation leverage. This results in pension asset allocation being value neutral.

If, for example, you change the input for the pension asset beta (which would represent a different asset allocation) you will notice that the DCF value does not change. This is because any change in asset allocation risk is assumed to be exactly offset by a change in cash flow. The effect of pension fund asset allocation on corporate value is itself an interesting subject, with some claiming that, in practice, investment in risky assets increases value and others claiming the opposite, but this is not something we discuss here or have tried to reflect in the model.

**Pension asset and liability inputs:** Enter the gross pension asset and gross pension liability amounts. The model then calculates the pre-tax and post-tax pension deficit (or surplus).

**Pension beta factors:** The pension asset beta should reflect the assumed asset allocation of the scheme. The pension liability beta should reflect the non-performance risk related to the pension obligation and would be affected by the credit quality of the sponsor, the degree of funding for the scheme and the asset allocation. For example, if the scheme is fully funded and asset-liability matched then the liability beta (and pension asset beta) would be zero, even though the credit rating for the sponsor may indicate that its other debt is risky. The pension beta factors are assumed to be constant over time.

**Pension cash flows: **The *‘Company contributions to the pension fund’* input is the cash payments by the sponsor to the fund. This is then disaggregated for the purpose of the different DCF approaches. The other cash flow input ‘*Pension and other payments from the fund’* represents distributions by the fund to retired employees plus other disbursements, such as in respect of a pension buy-out. This second cash flow is not directly used in the DCF, but it does determine the changes in pension funding and hence how pension risks evolve over time.

**Long-term incremental return on invested capital (iROIC):** This is the forecast post-tax incremental return on incremental capital invested. We use this to derive the additional investment in the terminal period. It is a technique to better ensure that the terminal value calculation is realistic and does not reflect overly optimistic assumptions about the investment required to generate long-term growth.

**So which DCF approach is best?**

There are a number of factors that can affect the choice of an enterprise or equity free cash flow basis for DCF. On balance, we prefer an enterprise FCF approach. Allowing for debt and other claims as an absolute deduction from a target enterprise value is easier than identifying the related non-common share cash flow which needs to be included in equity free cash flow. This is particularly the case where the non-common share claims have contingent features, such as convertibles or options. In addition, the discount rate applied to an enterprise DCF is more likely to be constant over time. The cost of equity in an equity free cash flow DCF needs to change as leverage (including the two forms of pension leverage) changes. This can be mitigated by building in assumptions of constant leverage, with debt cash flow determined on this basis, but this adds further complication regarding the cash flows themselves.

For pensions, we believe it is best to treat these as a financing claim within an enterprise DCF model and to exclude the expected gains due to asset allocation from the enterprise free cash flow and the related leverage effect from the cost of capital. This means deducting only the pension service cost in FCF. For cost of capital, it is important to not only include the pension deficit as a component of WACC but also to deal correctly with pension asset allocation leverage. In other words, we favour the first approach in the above model.

The advantage of our preferred approach is that there is no need to forecast any of the pension flows other than the service cost or to forecast changes in pension funding and hence the effect on cost of capital. However, it is important that you get a consistent discount rate and ensure that both forms of pension leverage are removed from the asset beta and that a WACC calculation takes account of not just the pension deficit but the gross asset and liability positions.

Of course, as we demonstrate in our interactive model, different approaches to DCF, if applied correctly and based on the same underlying assumptions, should all lead to the same fundamental value.

Actively considering material pension schemes and ensuring that the discount rate and cash flow calculations are consistent is a must in DCF valuation. Just ignoring it is likely to lead to inconsistencies. An easy to make error is to only include the service cost in free cash flow (based upon this being included in EBIT and NOPAT from which FCF is derived), to calculate WACC using only the costs of equity and debt and to deduct the pension deficit in the enterprise to equity bridge. This approach will understate DCF value because it leaves pension related risks in the discount rate while excluding their cash flow effect from free cash flow.

**Insights for investors**

**Defined benefit pension schemes create financial leverage if there is a net deficit, and asset allocation leverage if scheme assets do not exactly match the liabilities.**

**Pension cash flow is the expected payments to the fund. This can be analysed into different components depending on the DCF approach used.**

**Investment in higher risk pension assets increases the cost of equity and reduces expected cash contributions.**

**Discounted enterprise and discounted equity free cash flow approaches should always give the same answer, provided that they are based on the same assumptions. But be careful with terminal values, particularly those for discounted equity cash flow models, to ensure the data truly reflects steady state.**

**If enterprise free cash flow DCF is based on NOPAT that is net of only the pension service cost, then make sure that the discount rate excludes any asset allocation risk. This means including both gross pension liability and gross assets in the WACC calculation.**

**Use after tax pension assets and liabilities for beta factor and WACC calculations; deduct the after-tax deficit in the enterprise to equity bridge.**

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