Valuing the debt interest tax shield

The fact that the cost of debt finance is tax deductible, whereas the cost of equity is not, seems to give a structural advantage to debt finance. The value (if any) of this ‘tax shield’ is either an explicit or more likely implicit component of any equity valuation.

The most commonly quoted calculation of the value of the debt interest tax shield understates value by ignoring growth but, potentially, overstates value by ignoring the effect of personal taxes. We explain how to incorporate these often-ignored factors in your analysis.

Many of you will be familiar with the capital structure theories of Modigliani and Miller (M&M). They demonstrated that, under certain assumptions, including no taxation, capital structure does not affect value. Business or enterprise value, and consequently the combined value of debt and equity claims on that business, is unaffected by leverage.

Relaxing the M&M no-taxation assumption reveals that, in most tax jurisdictions, there is an inherent advantage to debt financing (and a value gain from higher leverage) due to debt interest payments being tax deductible, which is not the case for dividends and equity returns. A company with higher leverage pays less tax, thereby creating a value loss for government and a gain for shareholders.

In M&M’s own expanded theory, the relationship between the enterprise value of a levered (VL) and unlevered (Vu) business is given by: 

{ ~~\sf V_{L} = V_{U} + D.T{_C} ~~~~}
VLEnterprise value (value of an enterprise with financial leverage)
VUEnterprise value of an equivalent business with all equity financing
DMarket value of debt finance
Tc Rate of corporate tax

Click on the formula to see a list of notations

The term D.Tc is the present value of the tax savings due to the payment of debt interest, which is derived as follows:

  • Interest payments on outstanding debt equal the amount of debt multiplied by the cost of debt (D.Kd).1This may not strictly be true. The calculation D.Tc is based on market value and market interest rates; however, the tax saving would more likely reflect book values and historical interest rates on outstanding debt. It is possible to allow for this difference, but the effect is unlikely to be material in practice.  
  • Multiplying this by the tax rate produces tax savings of D.Kd.Tc.
  • If debt is assumed to be constant in perpetuity then, discounting at the cost of debt, the tax savings has a present value of D.Kd.Tc/Kd  which simplifies to D.Tc. The discount rate is set equal to the cost of debt because the risk associated with the tax savings is assumed to be the same as the risk related to the interest payments themselves.

The problem is that, while commonly quoted in practice, the above is too simplistic.

The calculation D.Tc is based on an assumption of constant debt in perpetuity and a tax shield that only reflects corporate taxes. Neither assumption is realistic in practice. Furthermore, the calculation assumes that the cost of debt discount rate correctly reflects the risk of the tax shield, which may not necessarily be the case. Using the standard calculation may produce incorrect answers.

Getting the right value for the tax shield matters for several aspects of valuation

Getting the right value for the debt interest tax shield matters. Sometimes the tax shield is explicitly referred to, such as in evaluating the value effect of a change in financing policy, or when using Adjusted Present Value (APV) techniques for business valuation or project appraisal.

However, the debt tax shield is also implicit in other aspects of finance and valuation, and you may not even be aware of when you are incorporating it (and certain related assumptions) into your analysis. For example, the tax shield affects leveraging and deleveraging calculations for equity beta and, potentially, also the risk-free rate and equity risk premium used to calculate cost of capital.

There are two factors that affect the value of the debt interest tax shield which may, under certain circumstances, mean that the calculation D.Tc is incorrect. These are (1) how expected changes in debt are dealt with and, related to this, the choice of discount rate; and (2) tax considerations beyond purely corporate taxes.

Debt tax shield – growth and discount rate

The most commonly quoted calculation for the value of the debt interest tax shield (VTS) is the M&M formula we explain above:

{ \sf VTS = D.T{_C} }

The assumption that debt is constant is unrealistic in almost all valuation exercises. In business valuation long-term growth is probably accompanied by increasing debt if, as is likely, companies seek to maintain a target amount of financial leverage. In project appraisal, debt capacity only lasts as long as the project itself and may decline rather than increase over time.

The appropriate discount rate for debt tax savings may not always be the cost of debt

The problem is that there seems to be little agreement amongst academics or practitioners on how to modify the tax shield calculation to take varying debt amounts into account, and what discount rate should be used in this situation. Of particular concern in business valuation is whether it is appropriate to use the cost of debt as a discount rate for all debt interest tax savings when the amount of debt increases along with business growth. The additional tax shield arising from additional debt in future periods is linked to business risk, which suggests a higher discount rate may be appropriate for at least this component of the tax shield.

In our view, the best approach to growth and discount rate is one we think was first proposed by the academic Pablo Fernandez2See ‘The value of tax shields is not equal to the present value of tax shields’. Our formula below is mathematically the same as that given by Prof. Fernandez but rearranged to more clearly identify the components. This approach has certainly been criticised by other academics; however, we think this may be due to the unfortunate title of the paper (the calculation is very much a present value of the tax shield) and the way Prof. Fernandez presented the calculation. Out of all of the theories and suggested calculations, we think this approach most appropriately reflects the economics of the debt tax shield (subject to our extension described below).. He produced the following calculation for the value of the debt interest tax shield, under an assumption of constant growth.

{ ~~ \sf VTS = D.T{_C} + \dfrac{D.g.T_{C}}{K_{U} - g} ~~~~ }
VTSValue of debt interest tax shield
DMarket value of debt finance
TcRate of corporate tax
Growth in the business and in the amount of debt
KuCost of equity assuming zero leverage

In this approach part of the tax shield is discounted at the cost of debt, but the growth component is discounted at the higher unleveraged cost of equity.3This means that the overall discount rate applied is somewhere between the cost of debt and the unleveraged cost of equity. Disaggregating the tax shield into cost of debt and unleveraged cost of equity components provides for a more practical, and we argue more realistic, approach.

The first term in the calculation above (D.Tc) represents the value of the tax shield for the amount of debt currently in place, where the tax savings are discounted at the cost of debt. This is the same as the M&M no growth tax shield we explain above. We agree that the appropriate discount rate for this component is indeed the cost of debt. The tax saving simply reduces the interest cost of debt and with it the burden of debt for equity investors. Applying a factor (1 – Tc) to both interest and to the debt claim captures this effect. In so doing, the tax savings are discounted at the same rate as the debt itself.

The second term (D.g.Tc / (Ku-g)) is the present value at the unleveraged cost of equity of the incremental tax shields arising in future periods due to the assumed business growth. The incremental tax shield in year 1 (if debt grows by g% and is valued on the same M&M basis above) is D.g.Tc. These additional tax shield ‘flows’ will grow by g% p.a.

Incremental tax shields due to business growth have higher risk

By dividing (D.g.Tc) by (Ku-g), the future incremental tax shields due to business growth are discounted at the higher rate of Ku – the unleveraged cost of equity. The reason for the higher rate is that the incremental debt in future periods is related to business growth and hence each incremental tax shield can, in effect, be viewed as a component of enterprise free cash flow, with the same risks.

We think this dual discount rate approach is a good solution, which can be applied even where growth is not constant using an explicit forecast of changes in debt.

The only problem is that not all changes in the amount of debt are necessarily related to business growth; some may arise from an expected change in funding policy. A more generalised approach would be to differentiate between the two, with the debt tax shield related to current debt and changes due to planned revised financing policy (∆Dp.Tc) discounted at Kd, and other changes related to business growth (∆Dg.Tc ) discounted at the risk adjusted rate Ku.

In the case of business valuations, long-term growth in debt is likely to be linked to growth in the business, in which case the incremental tax shield benefits would all be discounted at Ku and the formula proposed by Fernandez would be appropriate. However, for project appraisal, debt (or debt capacity) changes may be more likely to simply relate to changes in planned funding. 

Here is our more generalised version of the dual discount rate approach:

Valuing the debt interest tax shield

The Footnotes Analyst

Dp and Dgrepresent the change in debt each period due to a change in debt policy and business growth respectively. We use T* rather than Tc in the calculation for the reasons set out below.

Allowing for investor taxes

The effect of taxation on asset pricing and returns is not limited to corporate taxes. How returns to investors are taxed at the investor level is also relevant. Investors will accept a lower gross return on an asset, and hence pay a higher price, if the income from that asset is taxed at a lower rate than that from an alternative investment. It is important that this effect is built into valuation.

Lower personal tax rates for equity returns reduces the overall value of the debt tax shield

The difference between the effective personal tax rate on income from equity, compared with that for debt investment, affects the value of the debt interest tax shield. If equity returns are taxed at a lower rate than debt returns (which in many jurisdictions they are) the cost of equity should be lower than it would be without this tax advantage which, in turn, partly offsets the benefit of the corporate tax savings from debt interest. Lower personal tax for equity investors, in effect, creates an equity return tax shield that offsets part, or potentially even all, of the debt interest tax shield.

Although the original M&M theory only allowed for corporate taxes, a subsequent paper by Miller4The debt and taxes paper by Merton Miller can be found here. showed the importance of also considering different personal taxes on equity (Tpe) and debt (Tpd). Miller provided the following calculation of the net tax advantage of debt (often referred to as T*).

{~~ \sf T^*~ = ~ 1 - \dfrac{(1 - Tc)~x~(1 - Tpe)}{(1 - Tpd)} ~~~~}
T*Effective tax advantage of debt after allowing for personal tax effects
TcRate of corporate tax
TpeEffective rate of personal tax on returns from equity investments
TpdEffective rate of personal tax on returns from debt investments

If the personal tax rates on equity and debt are the same, the tax advantage of debt remains the rate of corporate tax (T* = Tc). However, if the personal tax payable by equity holders is less, this tax advantage for equity offsets the debt interest tax shield, which reduces the overall advantage of debt finance (T* < Tc).

One way to appreciate why investor taxes affect value in addition to corporate taxes, is to think of government as having a claim on enterprise cash flows equal to the tax it receives. This tax collection includes not just corporate level taxes but also tax paid on distributions to the providers of capital. Any change in the overall amount of tax received by government, both personal and corporate, must impact the value of the government claim and therefore the value attributable to the debt and equity claims on the business. Only if higher leverage reduces the overall tax taken by government can there be an increase in the value of the enterprise attributable to the providers of capital.

The net effective tax advantage of debt can perhaps be better understood by rearranging the above calculation. The personal tax advantage of equity (Tp’) is the amount by which post personal tax equity returns exceed those for debt (assuming the same pre-tax return).

{~~ \sf Tp'~ = ~\dfrac{(1 - Tpe)}{(1 - Tpd)} - 1 ~~~~}
T*Effective tax advantage of debt after allowing for personal tax effects
Tp’The personal tax advantage of equity
TpeEffective rate of personal tax on returns from equity investments
TpdEffective rate of personal tax on returns from debt investments

Substituting this into the equation for T* above and rearranging gives:

{~~ \sf T^*~ = ~ Tc - Tp'.(1 - Tc) ~~~~}
T*Effective tax advantage of debt after allowing for personal tax effects
Tp’The personal tax advantage of equity
TcRate of corporate tax

This shows the two opposing tax effects that alter the net interest cost of debt finance relative to the cost of equity (assuming equity has the same risk) …

  • Tc represents the reduced interest cost because interest payments are tax deductible.
  • Tp’.(1-Tc) represents the higher interest payable for debt, compared with the return that would be demanded by equity investors (assuming the same risk), due to differences in personal tax, less the corporate tax saving that applies to this extra interest.

Estimating the overall tax advantage of debt – T*

Estimating T* is difficult. Many companies are subject to different tax regimes due to the international nature of their operations and the international spread of their investors. In addition, different investor groups, such as pension funds, corporate investors and private investors, are subject to different personal taxes. However, the challenge of estimating T* does not mean that the tax shield should necessarily be ignored, or that it should simply be assumed to be the rate of corporate tax on the basis that this is generally much easier to determine.

There are two extremes for T*, either T* = Tc or T* = zero. Understanding when each applies will enable a more informed decision about what value to use in practice.

Classical tax system: T* = Tc

A so-called classical tax system is where the personal taxation of debt and equity returns is the same and there is no ‘imputed’ tax credit provided for equity investors. In this environment Tpd = Tpe and the net personal tax advantage to equity (Tp’) is zero. The net tax advantage for debt financing is therefore only the tax deductibility of interest. This produces a tax shield value equal to the rate of corporate taxes.

However, even in a fully classical tax system there could be a difference between Tpd and Tpe if, for example, capital gains are taxed differently. Equity returns are more likely to be in the form of capital gains compared with returns on debt, and either a lower rate of tax on gains, or simply the benefit of deferring gains until realised, will result in an overall lower value of the debt tax shield.

Imputation tax system: T* = zero

In some jurisdictions corporate taxes are ‘imputed’ to equity investors. This means that corporate tax is treated as a part-payment of equity investor personal taxes, with an explicit tax credit given to investors. Alternatively, the same effect may be achieved by taxing equity investors at a lower rate on their income compared with that applied to debt investors, with the difference fully or partially based on the corporate taxes already paid.

In a full imputation system, the difference between Tpe and Tpd gives a value for the net personal tax advantage for equity that exactly offsets the tax deductibility of debt interest, which results in a tax advantage of debt of zero. However, imputation or differential tax systems, rarely fully impute corporate taxes to investors, such that tax advantage of debt may still be positive, but less than the rate of corporate tax.

The challenge of estimating personal tax rates, and the net value of the debt interest tax shield, is why personal tax effects are often ignored in practice, and T* is assumed to equal Tc. That was certainly the approach we adopted at UBS.

Implications for valuation

The absolute value attributed to the debt tax shield, and the estimated value of T* that determines its value, affects a number of different aspects of valuation. We will explain more on this subject in further articles, but here is a high-level summary:

Beta leverage adjustment:

Where beta is delevered to determine an asset beta, or an industry asset beta is relevered to determine an equity beta, the calculations should include T* not Tc. For example, if debt is risk free (a common assumption, although not necessarily true in practice) and the tax shield (excluding the value attributable to business growth) is discounted at the cost of debt, the asset and equity beta relationship becomes:

{~~ \sf Beta_{asset}~ = ~ Beta_{equity} ~x~ \dfrac{E}{D (1 - T^*) + E} ~~~~}
EFair value of equity
DFair value of debt
T*Effective tax advantage of debt after allowing for personal tax effects

Risk free rate:

The risk-free rate used for the calculation of cost of equity (including the unleveraged cost of equity in APV calculations) should be lower than the rate observed in the debt markets if there is a personal tax advantage to equity and T* is less than Tc. The adjustment is:

{~~ \sf Rf_{(E)}~ = ~ \dfrac{Rf_{(D)}}{(1 - Tp')} ~~~~}
Rf(E)Risk free rate applicable to equity
Rf(D) Risk free rate applicable to debt
Tp’The personal tax advantage of equity (see above)

Equity risk premium:

The ERP should also allow for personal taxes. The relationship between the ERP applied to debt (assuming CAPM is used for the cost of debt) and the ERP for equity is the same as given above for the risk-free rate.

Adjusted present value:

APV valuations should include the value of the tax shield based on the expanded calculations we explain above.

Enterprise DCF based on WACC:

Where DCF analysis uses WACC as the discount rate there is no need to explicitly include the value of the tax shield because it is implicit in WACC itself. However, remember to allow for the above effects of T* on beta leverage adjustments and the risk-free rate and ERP components of CAPM. If T* = Tc, no special adjustments are required.

For more about these implications see our article ‘Equity beta, asset beta and financial leverage’ and to to see the calculation of the value of the debt interest tax shield applied in a downloadable DCF model see ‘DCF valuation: Financial leverage and the debt tax shield’.

Insights for investors

  • The commonly quoted value for the debt interest tax shield of D.Tc is based on the assumption of constant debt and a classical tax system where the tax advantage of debt equals the rate of corporate tax.
  • If debt is forecast to change, do not necessarily discount all of the tax shield at the cost of debt. Business risks are likely to be relevant in selecting an appropriate discount rate.
  • The value of the debt interest tax shield to equity investors is less than the rate of corporate tax if equity investor personal taxes are reduced by imputed tax credits or lower rates of tax.
  • Use the net tax advantage of debt (T*) rather than the rate of corporate tax when evaluating the value of debt financing and when delevering and relevering beta factors.
  • If the net tax advantage of debt is less than the rate of corporate tax you will need to adjust CAPM inputs, including the risk-free rate.

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