Leverage, Cost of Capital and Bank Valuation

In this paper we present a model that demonstrates the effect of debt on cost of capital and value for banks with risky assets. Using a static partial equilibrium setting, both in a steady state and steady growth scenario, we derive a bank- specific valuation metric which separately attributes value to assets and debt cash flows in the form of a liquidity premium and a tax-shield. The asset side model proposed does not require the assumption of stable capital structure, typical of the currently applied DCF equity side methods. Furthermore, the theoretical framework we present is helpful in reconciling asset and equity side approaches in banking.


Introduction
Banks represent a particular case in valuation, as they create value from both the assets and liabilities side of their balance sheet due to the liquid-claim production (DeAngelo and However, the main critical issue in dealing with in the application of a DCF disaggregate model in a banking context is its consistency with the theories of MM. First, the extension of MM's propositions is debatable because of the incompatibility of the assumptions underlying the theoretical framework of the theorems due to the role of banks in reducing information asymmetries in MM's world. Second, more technically, a formal restatement of MM's first and second propositions might be complicated owing to the criticalities in separating operating from financial management, in terms of both cash flows and cost of capital. In order to overcome these issues, a formal restatement of MM's propositions for banking firms exploiting the segmented-markets model has been put forward (Merton 1990;DeAngelo and Stulz 2015). This permits the existence of banks in a perfect and complete financial market. Hereafter, using a static partial equilibrium model as in MM (1958), we separate the contribution of assets from liabilities to bank enterprise value in line with the original framework of disaggregate models for non-financial firms.
In summary, this model helps to directly and explicitly reveal the value creation determinants of banks by providing a more general leverage-cost of capital theory in the absence of distress costs.
The use of a disaggregate asset-side model for banks can help to overcome problems typical of DCF aggregate models and, in particular, cost of equity and weighted average cost of capital redetermination when leverage changes over time. Besides assuming a disaggregate view of value, the model also provides a sort of binary approach to bank valuation which is useful in taking into account their specifics on the asset and liabilities side. On the one hand, the model assigns a portion of value to assets in relation to their cash flows and expected return. On the other hand, the disaggregate approach explicitly attributes a significant portion of value to banks' debt when they better manage financial structure in terms of composition and pricing.
A separated view of value also makes it possible to analyse the cost of capital implications over banks' debt management strategies. The theoretical framework presented in this paper offers an explanation in terms of value on why banks hold an incentive to fund their assets through deposits or other marked-down financial instruments. The liquidity premium gained on this type of debt mitigates the effect of the cost of increasing leverage on cost of equity, with direct effects in terms of valuation. Thus, in the presence of macroeconomic conditions where banks retain wide margins on mark-down management and in the absence of distress costs, the higher the stock of marked-down debt, the greater the value creation. More generally, this paper contributes to the literature by providing a theoretical framework for banks valuation which enables us to choose between an asset or equity side valuation, thereby removing the drawbacks of current DCF equity side models.
The remainder of the paper is organized as follows. The next section introduces the theoretical model. Section Three introduces a bank valuation framework in a steady state and in a steady growth scenario and discusses implications of the cost of capital. Section Four compares equity and asset side methods in terms of banks' capital structure and Section Five concludes.

Capital structure and bank total value
The effect of leverage on firm value and cost of equity are usually analysed in the light of MM's propositions. If the leverage irrelevance principle is valid for banking firms as predicted by the first proposition, a variation of financial leverage would imply a proportional variation in the cost of equity, maintaining stable the overall cost of funding. The agreed view in the literature is that MM's theorems cannot be applied to banks in perfect and complete financial markets, because the absence of information asymmetries makes unnecessary the presence of financial intermediaries (Mehran and Thakor 2011). DeAngelo and Stulz (2015) offer a viable solution for such alleged incompatibility introducing a segmented-markets model (Merton 1990) which assumes two financial markets with different levels of information availability: a first perfect and complete financial market and a second financial market with frictions. In their model, banks act in the first market, and at the same time, extend loans to agents in the second financial market, maintaining their role in reducing information asymmetries between agents, following MM's assumptions.
With regard to investigating the effect of financial structure on value, MM require a clear split between operating and financial cash flows. But this cash flow break-down is not easily achieved, because for banks financial management is part of operating management. In order to overcome this problem, we reconsider cash flow generation and separate cash flows from assets and from liabilities. In asset cash flows, we take into account not only the positive components arising from loans and securities, but also the negative components related to intermediation costs, which depend on bank scale and size (DeAngelo and Stulz 2015).
Combining the segmented financial market assumption and the distinction between asset and debt cash flows, we exploit a static partial equilibrium model to analyse the effect of leverage on bank value.

A static partial equilibrium model for banks
We consider two banks with the same class of risk and the same operating expected return (X) given by the net profit of the intermediation activity, before the deduction of financial expenses paid on debt. Both banks operate in the first perfect and complete financial market, and are intermediaries on the second, imperfect and incomplete financial market. The first bank (1) is financed only by equity ( ! ), while the second bank (2) has a financial structure composed of equity ( ! ) and safe debt in the form of deposits ( ! ). Bank 2 gains a liquid-claim premium ( ), equal to the difference between the perfect and complete market interest rate ( ! ) (risk free) and the liquid financial claim interest rate ( ! ). Specifically, the liquidity premium is reached paying debt at ! rather then ! , with ! < ! .
The existence of the two different interest rates in a frictionless market is justified by the presence of intermediation costs: they eliminate arbitrage across the two markets and, consequently, make possible a liquidity-claims rate lower than risk free rate. On this basis, according to the seminal work of MM (1958), we are able to demonstrate that for an agent operating in a first perfect and complete financial market, the results of "homemade leverage" and "mixed portfolio" strategies converge to those of a levered equity portfolio and unlevered equity portfolio respectively.

2.2"Homemade leverage" strategy
If an investor holds a fraction of bank 2 equity, its return ! would be equal to: The same investor could replicate the capital structure of Bank 2 selling his stocks, borrowing on his own credit an amount of debt equal to ! and purchasing on the market an amount of equity of Bank 1 equal to ! + ! . He would thus acquire a percentage of equity equal to ! + ! / ! . The return Y ! for the so called "homemade leverage" strategy would be equal to: where ! + ! is equal to ! and ! is equal to ! , while ! is the interest rate paid on debt by the investor himself in a perfect and complete market. The investor would have the incentive to sell his stocks of Bank 2 and purchase stocks of Bank 1 only when ! > ! and until the increase in Bank 1 equity and the decrease in Bank 2 equity make equal the return on Bank 2 with the return on "homemade leverage" strategy ( ! = ! ):

"Mixed portfolio" strategy
If the investor holds a fraction of Bank 1 (unlevered) equity, its return ! would be equal to: The investor can switch all his equity unlevered portfolio to a mixed portfolio (comprising equity and debt) selling his stocks and acquiring a proportional amount of equity of Bank 2 equal to ! ! ! ! ! ! and an amount of debt of As long as the investor acts in a perfect and complete financial market, he would be able to achieve an interest rate on debt equal to the risk-free rate, rather than the lower interest rate obtained by agents of the imperfect and incomplete financial market. Therefore, the total return on the mixed portfolio (on equity and debt -! ) is: The first term of (5) represents the yield on equity and the second term the yield on debt. The investor would have the incentive to sell his stocks in Bank 1 and acquire stocks of Bank 2 if ! > ! and until the increase of Bank 2 equity and the decrease of Bank 1 equity makes equal the return on Bank 1 with the return on mixed portfolio strategy ( ! = ! ): This table summarises the pay-off strategies for investors. Firstly we report the cost and pay-off associated with buying levered bank stocks and a "homemade leverage" strategy. Secondly, we report the cost and payoff of buying unlevered bank stocks and a "mixed portfolio" strategy. An investor can gain an equal premium, with both strategies given by the spread between the market interest rate and interest rate on deposits (the liquidity premium banks earn on deposits). The wider the spread, the higher the value of the levered compared to the unlevered bank. In Table 1 S is equity, D is debt, V is value, CF is cash flow, rf is the market interest rate and rl is the cost of deposits.

Leverage effect on bank value
Expressed in terms of ! , (3) and (6) together lead to (7) in equilibrium: We can now define ! / as the factor of proportionality 1/ ! or the inverse of expected rate of return, that is, the cost of equity for the unlevered bank associated with a specific class of risk. Hence, (7) is formally MM's first proposition when deposits are priced considering a liquidity premium ! − ! , in line with the view of Hanson et al. (2015) on traditional banks. Accordingly, the more a bank levers up, other things remaining equal, the higher the bank firm value. Note that if the bank does not gain a liquidity premium, the interest rate on debt is the same as the market rate ( ! = ! ). As a consequence, the enterprise value of the unlevered bank (Bank 1) and levered bank (Bank 2) are equivalent and MM's leverage irrelevance principle still holds true. On the other hand, if Bank 2 issues debt at lower rates than the market rate ( ! − ! = > 0), then the enterprise value of the levered bank will be higher than the unlevered bank ! > ! . In this case, debt will be the preferred source of funding and, consequently, the leverage irrelevance principle does not hold.
If (7) is re-expressed as a function of the unlevered cost of capital, the enterprise value of the bank would be equal to: The first term of the equation is the Present Value of Liquidity Premium (PVLP), while the second term is the bank's asset cash flow discounted at the cost of capital of the unlevered bank in a steady state framework. In a perfect and complete financial market, banks can transform risky assets to riskless assets by following a policy of hedging. On this basis, our model would converge to that of DeAngelo and Stulz (2015) in which free cash flows to equity (and as a consequence the asset cash flow) are discounted at the risk-free rate. However, the bank's firm value does not only depend on the value of its assets, but also on the value created by other financial services such as investment banking and the many other activities that banks typically undertake to increase their profits. The risk associated with this type of businesses cannot be totally eliminated through hedging strategies, so the discount rate of these cash flows should be higher than the risk free rate.
Thus, in a similar manner to MM's application for non-financial firms, asset cash flows should be discounted at ρ ! > r ! . The presence of risky assets implies a lower capacity of issuing safe debt. In facts, banks could lever up without losing the liquidity premium until debt is equal to the value of perfectly hedged assets and, as a consequence, less than 100% of its enterprise value. The same conclusion is reached by DeAngelo and Stulz (2015) for cases when only an imperfect hedging strategy is possible, which makes capital requirements useful to cover unexpected losses.

Leverage, cost of capital and valuation for banking firms
In line with an asset-side disaggregate valuation model used for non-financial firms, the bank valuation scheme proposed in the previous section separates the unlevered bank value from debt benefits. Specifically, in the case of industrial firms, the asset-side disaggregate model determines the enterprise value as the sum between the value of the unlevered firm and the value of tax benefits of debt. In the case of banks, as noted above, debt creates value not only through the deductibility of interest expenses, but also by a liquidity premium on deposits.
In this section, we present the bank valuation model which takes into account both the tax and liquidity premium benefits in two configurations: the steady state and the steady growth scenario. In each scenario, we make distinct assumptions on the discount rate for the benefits of debt. The approaches we introduce have different implications in terms of weighted average cost of capital and cost of equity.

The steady state valuation
Following MM, we can choose to discount the fiscal and liquidity premium benefits using the unlevered cost of equity (MM 1958) or the cost of debt (MM 1963). In the first case, debt benefits in the form of both liquidity premium and tax-shields are discounted at the cost of capital for the unlevered bank. Thus (8) becomes: where is the Present Value of Liquidity Premium, is the Present Value of Tax Shield, is the tax rate and ! is the net bank's assets cash flow before interest expenses. According to Hanson et al. (2015), the interest rate on liquid-claims is calculated as the interest rate on deposits divided by deposits. More concisely, Equation (9) can be written as: is the Present Value of Debt Benefits (the sum of PVLP and PVTS) while is ! is the unlevered bank value. As we noted above, the valuation approach provides a useful independent view of bank value, enabling us to understand the contribution of assets, liquidity premium and tax-shields to the enterprise value of a bank. However, as in the case of non-financial firms, this valuation model should be equivalent to an asset-side aggregate model in which free cash flows are discounted at the weighted average cost of capital ( ! ) whereby debt benefits are included in the discount rate: It has been demonstrated that the aggregate model leads to the same result as the disaggregate model when benefits from tax-shields are discounted at the unlevered cost of equity (Ruback 2002). Thus, adapting the traditional relation between weighted average cost of capital and unlevered cost of equity to the case of banking firms, the relation between ! and ! can be written as: Other things remaining equal, ! decreases when leverage increases more than proportionally according to the size of liquidity premium and taxes effect (Hanson et al. 2011;Kashyap et al. 2010). Our model is also consistent with an equity-side model. In this case the value of a bank can be measured as: where ! is the cost of equity. Combining (12) with the traditional weighted average cost of capital formula (14): we obtain the cost of equity ! consistent with the valuation approach proposed: Equation (15) is the second proposition of MM. As in the case of non-financial firms, when bank debt benefits are discounted using the cost of unlevered firm, the cost of equity is not directly dependent on the tax rate and liquidity premium. As in the case of MM (1963) and in line with the original adjusted present value approach of Myers (1974), debt benefits are both discounted at the risk-free rate (the cost of debt) and therefore Equation (9) becomes: and the concise version of the valuation model (Equation 10) becomes: The weighted average cost of capital, and the cost of equity consistent with the use of cost of debt to discount tax benefits and liquidity premium, are respectively: where Equation (19) is the reinterpretation of MM's work with taxes integrated with the liquidity premium. All other things remaining equal, the larger the difference between the risk-free rate and the pricing of deposits, the flatter the effect of leverage on cost of equity.

The steady growth valuation model
In the case of growth too, we can assess banks' debt benefits by discounting either using the unlevered cost of equity (Dempsey 2013) or the cost of debt (Massari et al. 2007). Thus, considering a constant growth rate both for asset and debt, following Dempsey (2013), (9) becomes: and (10) becomes: Also in the steady growth scenario, the model must be consistent with both the aggregate model and with the equity-side approach. In the case of the aggregate model, bank value is equal to: The weighted average cost of capital making equal the value obtained through (21) with that obtained through (22) is reached using the same formula as the steady state framework (Miles and Ezzell 1980;Dempsey 2013): Thus when debt benefits are discounted at the unlevered cost of capital, growth does not affect the weighted average cost of capital. For the equity-side approach too, we can assess the value of equity discounting the expected free cash flow to equity at the difference between the cost of equity and the growth rate: As we noted, the cost of equity in a growth scenario is calculated as by MM in their second proposition without taxes: Conversely, following Massari et al. (2007), our model becomes: Accordingly, the weighted average cost of capital (18) and cost of equity (19) must be restated for the growth scenario. Combining (26) with (22), we find the relation between the weighted average cost of capital and the unlevered cost of capital: and combining (27) with (23), we restate the cost of equity as: Unlike the previous version of the model, in this version the weighted average cost of capital and the cost of equity are affected by taxes, liquidity premium and growth rate.

Choosing the appropriate discount rate for debt benefits
The debt benefits stand-alone valuation requires the choice of the appropriate discount rate for tax-shields and liquidity premium. In the case of fiscal benefits arising from debt, the literature on industrial firms recommends using cost of debt in the steady state hypothesis (MM 1963;Myers 1974) and, conversely, the unlevered cost of capital in the steady growth hypothesis (Dempsey 2013). In the first case, when debt is kept fixed over time, MM (1963) justify the use of the cost of debt rather than the unlevered cost of capital, claiming the risk profiles for firms' operating and tax-shield cash flows are different. The operating cash flow is uncertain and dependent on the risk associated to assets, while the tax-shield cash flow is the result of a determined stock of debt. In the second case, when the dynamic of debt is in line with that of the free cash flow from operations (and with the same expected growth rate), the literature discounts the tax benefits using the unlevered cost of capital (Cooper and Nyborg 2006;Dempsey 2013;Harris and Pringle 1985;Miles and Ezzell 1980;Ruback 2002). However, the choice depends on the assumption about future debt policy. If it is assumed that debt value will remain stable in the forecast period, the discount rate should be equal to the cost of debt. Alternatively, assuming a constant debt-tovalue ratio in the case of steady growth, the appropriate discount rate should be equal to that of asset cash flows. With regards to banks, although there are no explicit references in the literature to standalone valuation of debt benefits, empirical models used to investigate the effect of capital requirements on systematic risk implicitly take the cost of unlevered capital as the discount rate for debt benefits (Baker andWurgler 2015, Miles et al 2013). This is because it is assumed that additional cash flows due to debt undergo the same risk as operating assets. This perspective is widely endorsed by the literature, which considers bank debt to be operational rather than financial in nature (among others Massari et al. 2014). However, these different views on bank debt should not lead to treating it as working capital. Rather, it should maintain its function as a stable source of funding even when it holds benefits in terms of value creation.

Comparing asset and equity cash flow method: the capital structure effect
Empirical evidence suggests a positive correlation between leverage and bank cost of equity, in both systematic and specific risk frameworks. Among others, Kashyap et al. (2010) highlight a negative relation between book equity to asset ratio and equity beta, while Miles et al. (2013) confirm the same results finding a similar relation using the inverse of price earning ratio as a measure of cost of equity. Moreover, the relation is still valid using beta or equity standard deviation and both book and market leverage ratios (Rosenberg and Perry 1978).
Given the empirical evidence that leverage has a significant effect on banks' cost of equity, the valuation approach needs to consider the dynamics of debt and equity in order to assess how the financial structure affects value in the absence of distress costs. The choice in terms of leverage is not negligible in banking, because as well as affecting the cost of capital, leverage is closely monitored by the Basel framework which sets specific limitations on the bank's ability to take on debt. Although capital requirements and leverage are regulated, banks can choose to operate with different financial structures and may opt to set their requirements above regulation levels or near to minimum requirements. But such relative small differences can have substantial effects in terms of valuation.
The asset cash flow method we introduce in this paper offers a potential solution to the problem of the hypothesis of constant debt to value ratio proper of DCF equity side metrics almost universally applied in banking valuation. In an infinite time horizon (with a terminal value) the assumption might be a reliable estimation, but in an explicit forecast period, the capital structure can no longer be constant (Tagart 1991). The same problem arises if we implement an aggregate asset side valuation (WACC approach) since the discount rate is affected by the leverage ratio due to the presence of taxes and liquidity premium.
The cost of equity and weighted average cost of capital redetermination process requires a basic market leverage-cost of capital theory for banking firms, which we introduced in Section 3. Alternatively, the problem can be resolved applying directly the disaggregate asset cash flow method, because it does not require the market leverage ratio as an input and is more appropriate when target leverage ratios are linked to regulatory measures. Thus, precise assumptions can be made about the dynamic of bank debt in the analytic forecast period (Inselbag and Kaufold 1997). More generally, if a leverage-consistent valuation for banks is required, our model allows us to move from an asset to equity side approach, still considering the effects of changes in financial structure on cost of capital and value.

Conclusions
This paper presents a theoretical framework for bank valuation, reconciling asset and equity side approaches while explicitly taking into account the financial structure and the unique benefits banks obtain from liquidity premium. It formalizes a DCF disaggregate asset-side model showing the contribution of assets and debt to enterprise value. Consistent with the original assumptions of MM's propositions, the segmented markets model is used as in DeAngelo and Stulz (2015), but it differs in three main aspects. First, using MM's original arbitrage proof, it is shown how to determine the equity value of a bank using an indirect approach to valuation (Hanson et al. 2015). Unlike most applied valuation metrics, this makes it possible to split value creation between assets and liabilities. Second, the presence of risky assets, rather than just hedged assets, is considered, in order to take into account the riskiness of cash flows from assets, which is a realistic assumption in a context of valuation. Third, the cost of capital implications when the liquidity premium and taxes come into play is derived. This shows how the mark-down spread mitigates the effect of increasing leverage on the cost of equity.
On this basis, it might be concluded that MM's irrelevance principle is not valid for banks owing to the liquidity premium banks gain on marked-down financial instruments, which make the choices on financial structure relevant in terms of value. According to MM's first proposition with taxes, total bank value is the sum of the stand-alone asset value and debt advantages (Miller 1995). In addition, the cost of capital implications are in line with MM's partial off-set, which can be highlighted empirically. These conclusions lay the foundation for a theory of leverage-bank cost of capital and for a bank-specific valuation scheme based on asset and debt cash flows in which the total value is a function of the present value of cash flows from asset, tax benefits and the liquidity premium, similarly to the Adjusted Present Value of Myers (1974) and the Capital Cash Flows of Ruback (2002) applied in the valuation of industrial firms. Additionally, we contribute to the literature by highlighting the application of the model in a steady state and steady growth scenario, providing a reconciliation equation that equates the results of the aggregate asset-side model and the equity DCF methods.
The model is helpful in seeking to analyse how macroeconomic conditions affect bank value through interest rates. Lower interest rates reduce the value created by mark-down and fiscal benefits on debt. The closer the liquidity premium moves to zero and the more neutral the fiscal effect, in the absence of distress costs, the more irrelevant the choice between equity and debt. However, in the presence of distress costs, increasing regulatory capital in the form of equity becomes the most appropriate source of funding for reducing such costs (Allen et al. 2015;Admati and Hellwig 2013). Equity can generate value because the decrease in debt benefits is more than compensated for by the decrease in the present value of distress costs. Empirical evidence highlights a positive correlation between bank value and equity capital, owing to the lower probability of being closed (Mehran and Thakor 2011).
The theoretical framework presented in this paper has useful applications in bank valuation. First, compared to the currently applied DCF equity-side models, the disaggregate perspective to valuation reveals more clearly where between assets and liabilities the value of a bank is generated. Other equity-side methods lack such useful information, providing only a synthetic view of value creation. More specifically, the minimum regulatory requirements that banks must comply with do not negate the need to analyse the effects of financial structure on value, as banks can create value not only by choosing between equity and debt, but also by choosing between the several types of debt financial instruments available for each special category of firm, on which depends the size of the liquidity premium. Second, the disaggregate model does not require the assumptions typical of the DCF equity side methods, namely the distribution of the excess capital, the adjustments for such capital distribution, a stable capital structure in the forecast period and the assumption on the level of distributable earnings.
The main limitation of the model is that it does not take into account the present value of distress costs. Future research is called for to introduce this effect into the bank valuation scheme, formalizing a trade-off between debt advantages (liquidity premium and taxshields) and disadvantages in term of distress costs.

Appendix A -Systematic risk and leverage: determining the cost of unlevered bank
A separate determination of bank unlevered value requires the use of the unlevered cost of equity ( ! ) to discount the asset cash flows. The cost of equity for the unlevered firm is generally unobservable due to the presence of levered firms in the financial market. Assuming a perfectly diversified investor, we can express ! through the CAPM relation: where ! is the beta of the unlevered bank, and where ! is the return of the market portfolio. Allowing the CAPM, the problem shifts to the calculation of the unlevered beta. Hamada (1972) introduced a model to determine an unlevered (or asset) beta combining MM's second proposition and the CAPM. Assuming that the beta of debt is zero (in line with prior studies analysing the effect of leverage on bank overall cost of capital) and debt benefits are discounted using at the unlevered cost of capital, we can establish the relation between levered and unlevered beta as: Alternatively, when debt is fixed and debt benefits are discounted at the cost of debt (risk free rate), Equation (30) becomes: Independently of whether debt benefits are discounted at the cost of unlevered capital, the Hamada equation is the same of the case of non-financial firms. In contrast, equity betas are affected by taxes and by the difference between the risk-free rate and the cost of core deposits. Inverting the two relations, we reach the unlevered beta in the two different basic assumptions, respectively:

Appendix B -A comparison between the asset cash flow method and flow to equity model
The following example provides a comparison in terms of application of the asset cash flow method and flow to equity model. The example aims to demonstrate that if the cost of equity is not consistently determined over time, significant mistakes in valuation can occur. We assume the absence of taxes and growth in the terminal value and require an increasing level of capital requirement (Tier 1) covered by equity.

Table B1
Balance sheet and financial market data Book value, expected return on asset and risk weighted assets are fixed. After Period 4 a steady state scenario is adopted. The main hypotheses is a progressive replacement of debt with equity, according to an expected growth of Tier 1 ratio from 12% to 15%. As a consequence, some repayments of debt through shareholder capital are expected. FCFA are free cash flows from assets.
in € 1 2 3 4 oo Account value of assets (t) 1,000,000,000 1,000,000,000 1,000,000,000 1,000,000,000 1,000,000,000 Risk weighted assets density (t) 50% 50% 50% 50% 50% Applying the asset cash flow method, the bank unlevered value is: 29,500 1 + 3.42% + 29,500 1 + 3.42% ! + 29,500 1 + 3.42% ! + 29,500 1 + 3.42% ! + 29,500 3.42% The present value of debt benefits (in this case represented by a liquidity premium since we are assuming the absence of taxes) is:  Moving toward a flow to equity method, we calculate first the cost of equity and then the equity value. ! = ! + ! − ! ! ! = 3.42% + 3.42% − 3% 940,000 58,017 = 10.22% In order to directly reach the value of equity, we need to know the free cash flow to equity. In Table 2 we provide a summary of a cash flow statement. In the absence of taxes, the free cash flow to equity is given by netting free cash flow from assets of interest expenses and debt repayments. Interest expenses are calculated on the debt at the beginning of the year using the cost of debt.
The equity value is determined as: 6,000 1 + 10.22% + 1,000 1 + 10.22% ! + As we noted above, unless the cost of equity is stated consistent with leverage changes, the result of the flow to equity model is misleading. In Table B3, we report the dynamics of leverage ratio and the consistent changes in cost of equity. Table B3 Leverage and cost of equity dynamic The present value of debt benefits is calculated using the liquidity premium applied to debt at the beginning of the year and discounted at the expected return of assets.