R & D

CORPORATE , STANDARD STRATEGIES AND THE VALUE OF TAX SAVINGS IN TEXTBOOK VALUATION FORMULAS

by

B. SCHWETZLER*

2000/46/FIN

* Professor, Chair of Financial Management, Leipzig Graduate School of Management (HHL), Jahnalle 59, D-04109 Leipzig, FRG Visiting Scholar, INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France.

A working paper in the INSEAD Working Paper Series is intended as a means whereby a faculty researcher’s thoughts and findings may be communicated to interested readers. The paper should be considered preliminary in nature and may require revision.

Printed at INSEAD, Fontainebleau, France.

Corporate Valuation, Standard Recapitalization Strategies and the Value of Tax Savings in Textbook Valuation Formulas

Bernhard Schwetzler*

* Professor, Chair of Financial Management, Leipzig Graduate School of Management (HHL), Jahnalle 59, D-04109 Leipzig, FRG Visting Scholar, INSEAD, Boulevard de Constance, 77305 Fontainebleau, CEDEX e-Mail: [email protected];

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Abstract

Typically, in finance and valuation textbooks three different formulas, known as the weighted average (WACC)-, the adjusted present value (APV)- and the flow to equity (FTE)- approach are proposed to calculate the present value of a levered firm. Recent results in research suggest that these formulas imply different types of recapitalization strategies, predetermining either absolute future debt levels or capital structures in future periods (D-strategy and L- strategy) leading to different tax shields and firm values if future firm values are uncertain. This paper will show that one of these two strategies attributed with riskless tax savings (the D-strategy) is not admissible in the expectations adaption regime necessary to apply risk adjusted CAPM-based rates of return on multiperiod uncertain cash flows. In contrast, the recapitalization strategy leading to riskier tax savings (L-strategy) is admissible. Standard valuation formulas that imply riskless tax savings thus overstate the tax benefits of debt financing. This result adds another possible explanation to the phenomenon that the effects of tax considerations upon decisions to be observed empirically are substantially smaller than suggested by standard formulas.

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1. Introduction

Since the pathbreaking work of Modigliani and Miller (1963) financial researchers have been puzzled by the effects of debt-related tax savings upon optimal capital structure and firm value. Recent findings by Inselbag and Kaufold (1997) and Kruschwitz and Löffler (1998), building on earlier work of Miles and Ezzel (1981), suggest that the tax advantage attributed to debt financing depends on the debt policy, more precisely: on the recapitalization strategy of the firm, if future firm values are uncertain. - If companies predetermine absolute levels of outstanding debt for every future period the absolute amount of debt, interest payments and tax savings attributed to these savings are known with certainty. I will refer to this policy as the „D-policy“ henceforth. - Companies following an „L-Policy“ predetermine their capital structure (leverage) L (to be measured in market values) as debt-to-firm-value for every future period. Whenever future firm values are uncertain, future debt levels are uncertain too. The tax benefits attributed to debt under the L-policy are more risky and hence less valuable to investors than those under the D-policy.1 Since Fama (1977) and Myers and Turnbull (1977) it is well known that using a single period CAPM-based risk adjusted rate of return for multiperiod capital budgeting and valuation, as proposed in valuation and finance textbooks, requires a particular expectations adaption process. Market participants are assumed to adjust their expectations of future operating cash flows of the firm relatively to the deviation of the currently realized cash flow to its expected value. This revision of expectations puts future market values of the firm under the same risk as its operating cash flows. Using standard textbook formulas for valuation purposes implies risky future market values of the firm and thus makes the distinction between the two different debt policies an important issue in corporate valuation. In this paper the implications of the expectations adaption process for the two different policies outlined above are analyzed. It will be shown that the D-policy collides with the assumptions of the multiperiod revised expectations model. As expectations revisions may drive future firm values down and debtholders may face risk of default, their reaction will prevent the firm from maintaining a predetermined debt level under all circumstances. Debtholders may force the firm to repurchase debt or may charge higher rates of return. Future (expected) interest payments and the risk attributed to these payments thus cannot remain unchanged. Riskless interest payments and therefore riskless tax savings are not achievable under the expectations adaption regime assumed by standard valuation formulas. The L-policy does not collide with the revised expectations model, if debtholders choose the amount of debt in order to avoid default risk. As debt levels are assumed to be permanently

1 Note that it is the uncertainty about the level of debt outstanding that puts risk upon the tax benefits. The debt itself may still be riskless. 4 adjusted in accordance to changes in total firm value, debtholders may not face a change of default risk over time. As the amount of outstanding debt and the interest payments are certain only for the next period, the tax savings will be certain only for the next period, too. The expectations adaption process under the L-policy puts future debt levels following the next period under the same risk as the operating cash flows. Miles and Ezzel (1981) have shown that the risk adjusted rate of return for the unlevered firm is the correct rate for further discounting and for determining the present value of the tax benefit. For the purpose of corporate valuation disadvantages of debt financing (costs of , agency costs of debt) are rarely explicitly taken into account. The reason for this may be that financial theory offered only little guidance to practitioners in order to accurately quantify these effects. The possible differentiation between the two strategies imposes a considerable degree of uncertainty on corporate valuations in practice: The D-policy will lead to higher tax benefits and hence higher firm values, but is not admissible under the asssumend expectations adaption regime. The L-policy fits into the expectations adaption model but leads to lower firm values. As it is just the announcement of the future recapitalization policy that accounts for the difference in value, the differentiation between the two strategies may be expected to become a major issue of debate in price negotiations. The results of this paper add another argument to the discussion about the magnitude of tax effects upon optimal capital structure. If capital market participants recognize that a D-policy is not achievable within the expectations adaption framework markets use for valuation purposes they may not give too much credit on the announcement and promise of a company to follow this strategy. Capital markets might then perceive the L-strategy as more credible and thus will attribute less value to future tax benefits than implied by the standard valuation models that assume the D-policy to hold. If the announcement of different recapitalization strategies (as D- and L-policy) is assumed to be the only difference between a D- and an L- company under analysis, marginal and average disadvantages of debt financing as costs of financial distress and agency costs may, at best, only slightly differ for the two strategies. If bankruptcy costs and other disadvantages of debt are assumend to be independent from the announced debt recapitalization strategy, the L-policy leads to substantially lower optimal debt levels D* than the D-strategy (if perceived to be achievable): lower marginal tax benefits have to outweigh unchanged marginal disadvantages of debt. Maximum firm value at optimal debt level is higher for the D-firm than for the L-firm. If capital markets attribute lower values to future tax savings than the D-model implies, the standard valuation formulas used in finance theory overstate the value of the . Optimal debt levels based on the assumptions of riskless tax savings thus appear to be too high. The differentiation between the two recapitalization strategies and the non- achieveability of riskless tax savings implied by the standard valuation formulas thus might add another explanation to the phenomenon that empirically observed amounts of debt and leverage ratios are significantly lower than predicted by standard valuation models. 5

Related work concentrating on the risk of future debt and the magnitude of tax effects upon firm value in a multiperiod setting has been done by Lewellen and Emery (1986), Lewis (1990) and Berens and Cuny (1995). The model developed by Berens and Cuny optimizes corporate debt by outweighing marginal tax advantages of uncertain tax savings on corporate level against the marginal disadvantage of additional riskless tax payments on bondholder level. As they assume risk neutral investors and independent identically distributed future cash flows (pp. 1193) they ignore the expectations adaption process implied by the standard valuation formulas. Lewis develops a state-preference model with state-contingent prices for every future state and period to arrive at an optimal, dynamic state-dependent recapitalization strategy (pp. 25). In this paper I want to analyze the effects of the two „standard recapitalization strategies“ stated above which are implied by using the standard textbook valuation formulas for corporate valuation. Lewellen and Emery investigate the effects of the two different recapitalization strategies, obtaining different firm values for each strategy (pp. 418). They conclude that the L-policy „seems ....to be the most logical characterization“ while a D-policy would be „difficult to envision“ (p. 423). Restricting their analysis to the difference in valuation they do not further analyze the feasibility of the two strategies or possible restrictions. The focus of this paper is to analyze such possible restrictions caused by the assumptions of the standard valuation model and to discuss some problems arising from the difference in firm value. Finally this paper is to be couched into work on optimal recapitalization rules and optimal capital structure. A line of research following Fischer, Heinkel and Zechner (1989) and Leland (1994; 1998) develops optimal recapitalization rules based on inventory control models: Taking uncertain future firm values into account, recapitalization takes place whenever firm value hits upper or lower boundaries. Again, the scope of this paper is to look at the standard strategies linked to the basic textbook valuation formulas. Both standard recapitalization strategies can be viewed as special cases of general recapitalization policies. The rest of the paper is organized as follows: section 2 will review the literature on different recapitalization strategies and relate it to the standard textbook valuation formulas. Section 3 shows the expectations adaption regime necessary to apply these valuation formulas. Problems with the valuation formulas under this regime will be discussed in section 4; it will be shown that the D-strategy is not admissible. Implications of the analysis for valuation and capital structure are discussed in section 5. Section 6 concludes the paper.

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2. Textbook Formulas and Implied Recapitalization Strategies

2.1. D-Strategy and Adjusted Present Value Formulas I start with a valuation model that is known as „adjusted present value“ (APV) dating back to Myers (1974). APV calculates the value of a levered firm VL as its value as an all equity financed or unlevered firm VU plus the value of the tax benefits caused by debt financing.

n n L = ()~ ()− ()+ − t + ()+ − t V0 ∑ E CFt 1 t C 1 k ∑ rf Dt −1t C 1 rf (1) t =1 t =1

()~ whereas E CFt : expected operating cash flow before interest and taxes

tC: corporate tax rate

Dt-1 debt outstanding at beginning of period t k: risk adjusted rate of return of the unlevered firm

rf riskless rate of return.

(1) is the special case of the general Miller-model, where the personal tax rate on equity income equals the personal tax rate on interest income (Miller (1977) pp. 267).

Discounting the tax benefits using the riskless rate rf (1) implies that there is no uncertainty regarding the tax savings in any future period t, tC ⋅ Dt-1 ⋅ rf. The firm will always be able to obtain these tax benefits by having taxable income that exceeds interest payments and a tax rate tC that is constant over time (Modigliani and Miller (1963) pp. 435). In addition, for the tax benefits to be riskless, the amount of debt outstanding in period t, Dt-1 must be known with certainty (Inselbag and Kaufold (1997) pp. 117; Kruschwitz and Löffler (1998) p. 5). The debt policy of the firm according to (1) is that the absolute amount or market value of debt is to be exogenously predetermined by the schedule of the debt service. This is why this policy is called the D-policy: management predetermines debt in absolute amounts for every future period.2 For the case of a perpetual stream of cash flows one gets the well-known APV formula

~ E (CF )()1− t VL = t C + t D (2) 0 k C 0 Once again by calculating the tax shield via = t C rf D0 t C D0 rf

2 In some articles D- and L-strategy are referred to a passive and active debt management. See e.g. Clubb and Doran (1995) p 682. 7 it is implied that the amount of debt currently outstanding will be predetermined and held constant to infinity.

The impact of a D-strategy upon financial leverage risk and cost of equity depends on the degree of uncertainty regarding future values of the firm and its equity. If there is no U L uncertainty about future firm values Vt , Vt and equity values Et, then corporate leverage in future periods t as defined by

D L = t t + E t D t is certain. If the firm chooses a D-strategy, Dt is known with certainty for every future period.

In the case of a perpetual payment stream Dt = D0 ∀ t has to hold. ~ L ~ If future firm and equity value are random variables Vt and E t with uncertain outcomes ˆ L ˆ Vt and E t then future leverage will be a random variable, too, as

~ D L = t . t ~ + Et Dt

Summing up, if future firm values are uncertain and the firm follows a D-strategy, future amounts of debt outstanding are certain, but capital structure in market values are random.3 Generally for both debt policies the cost of equity formula can be written as (Inselbag and Kaufold (1997) p. 118)

− T = + ()− Dt Vt kE,t k k rf (3) Et

T whereas Vt denotes the tax benefits outstanding in period t. In the case of perpetuity the D-policy will lead to the well known MM-formula for the cost of T equity by substituting tC D0 for Vt into (3)

= + ()()− − D0 kE k k rf 1 tC (4) E0

2.2. L-Strategy and the WACC-Formula Another frequently used approach for corporate valuation is the weighted average cost of capital (WACC) – formula. The value of a levered firm is calculated by

3 The different types of uncertainty necessary to support formulas (1) and (2) are discussed below. 8

n L = ()~ ()− ()+ −t V0 ∑E CFt 1 tC 1 rWACC,t (5) t =1 with

D E r = r ()1− t t + k t WACC,t f C L E,t L Vt Vt as the weighted average cost of capital.4

To apply (5) to the case of a perpetual stream of cash flows with a constant rate rWACC it is known that the firm has to keep its debt-equity ratio and its leverage ratio L constant over time (e.g. Miles and Ezzell (1981) p. 720). The standard valuation formula is then

( ~)()− L = E CF 1 tC V0 (6) rWACC

Löffler (1988) has recently shown that a modified version of (5) or (6) may be applied to changing, but predetermined debt-equity and leverage ratios over time (Löffler (1998) pp. 3). The debt policy implied by (5) and (6) is different from the one discussed above: the firm plans its future debt by predetermining a fixed ratio of debt to firm value (again to be measured in market values) instead of predetermining fixed amounts of debt. This is why this model is called L-model.5 ~ L If future firm values Vt are random and leverage ratios Lt are predetermined and certain then by ~ = Dt Lt ~ L Vt the future amount of debt also must be a random variable. As ~ L ~ ~ ~ D = t E and D = L VL , t − t t t t 1 L t ~ ~ ~ L Dt is directly related to the uncertain future values of E t and Vt . For the special case of a constant leverage ratio over time (that is Lt = L ∀ t) this implies that every change in market ~ L ~ L value Vt is to be balanced by an according change of the amount of debt outstanding. If Vt ~ L rises, the firm has to raise additional debt, if Vt is to decline the firm has to repay debt by repurchasing some of its loans outstanding. As a result, the amount of future debt outstanding must be a random variable, if future firm values are uncertain and the firm follows an L- policy (Miles and Ezzel (1981) p. 721; Kruschwitz and Löffler (1998) p. 7).

4 The weights of the two components are to be measured in market values. 5 Clubb and Doran (1995) develop an „intermediate“ recapitalization strategy that combines the D- and the L-case. A chosen level of debt is to remain unchanged for a certain span of time over several periods. After that span of time debt level is adjusted according to an L-policy. I will restrict the analysis on the two polar cases. 9

The uncertainty of the future amount of debt outstanding has an impact upon the value of the tax benefits of debt: Even if the firm always issues riskless debt the future tax savings are uncertain because the level of debt outstanding is uncertain. If a firm follows an L-strategy with L being constant, as implied by the WACC-Formula, the value of tax benefits is to be calculated by (Miles and Ezzell (1981) p. 725)

n T = ()~ ()()+ −1 + −t+1 Vt ∑ rf t C E D t−1 1 rf 1 k (7) t=1

As the debt outstanding at the beginning of t is known with certainty and the debt itself is 6 riskless, the tax savings of the period ahead rf tC Dt-1 are riskless. The appropriate one-period ~ L discount rate is the riskless rate. As the level of debt is directly related to firm value Vt and ~ U ~ ~ U Vt , random variable Dt has the same risk properties as total firm value Vt . This is the reason for using the risk adjusted rate k for discounting the tax benefits to the current point in time: the tax savings value in t+1 has the same risk as the value of the unlevered firm.7 Applying (7) to the perpetuity case the tax shield formula becomes (Inselbag and Kaufold (1997) p. 118)

r ()1+ k VT = t D f (8) 0 C 0 ()+ k 1 rf

The impact of the tax benefits upon the cost of equity for an L-strategy is determined only by the tax savings known with certainty:

t r VT = D C f (8a) t t + 1 rf

The value of the tax shield is substantially lower as in the case of the D-policy: the tax savings generated by debt financing are riskier because there is some uncertainty about the amount of debt outstanding. Total firm value of a levered firm in the perpetuity case can be written as ~ E(CF)()1− t r ()1+ k VL = C + t D f (9) 0 C 0 ()+ k k 1 rf

(9) indicates that the APV-formula can be adjusted for the case of the L-strategy and hence may be applied for both types of recapitalization strategies discussed above. It also makes clear that the WACC – model in (5) and the standard APV-Model in (1) imply different

6 In order to concentrate on the impact upon the standard valuation formulas I will assume riskless debt henceforth. 7 In the following section of this paper I will be more precise on the admissible types of risk to the formulas above. 10 strategies and must lead to different firm values (Inselbag and Kaufold (1997) p. 120; Kruschwitz and Löffler (1998) p. 2). One obtains the cost of equity for an L-strategy by substituting (8a) into the general cost of equity formula (3) (Inselbag and Kaufold (1997) p. 121)

D  r t  k = k + ()k − r 0 1− f C  (10) E f + E 0  1 rf 

Because of

r t f C < t + C 1 rf the cost of equity of a firm applying an L-strategy in (10) are always higher than those of a firm applying a D-policy in (4), all other things equal. The risk reduction generated by D − VT „riskless“ additional tax savings, which is expressed in the factor 0 0 in the general E0 cost of equity formula, is higher for a firm applying a D-policy.

3. Admissible Types of Uncertainty and Recapitalization Strategies

The impact of the two different debt strategies upon firm value depends on the type and ~ U ~ degree of uncertainty attributed to future firm values Vt and equity values E t respectively. If future firm values are certain there would be no difference between the two debt policies.

This most simple case would occur if all future cash flows of the firm CFt would be known with certainty. ~ Usually it is assumed that future cash flows ( CFt ) are random with a given probability distribution. The degree of uncertainty of future firm values depends on the interrelation between the cash flow distributions of two succeeding periods. Two different types of interrelation will be discussed: the independence and the martingale model. If future cash flow distributions are identically and independently distributed then future firm values are known with certainty for every future period t. This is shown by using the ~ U multiperiod valuation equation based on the CAPM. The unlevered firm value Vt can be calculated as

U = []()~ ()− + ~ U − λ ()~ ()− + ~ U ~ ()+ −1 Vt E CFt+1 1 t C Vt+1 cov CFt+1 1 t C Vt+1; rM,t+1 1 rf (11)

~ U whereas Vt+1 is the uncertain unlevered firm value in period t+1. The term in square brackets is the certainty equivalent of the uncertain total value of the firm (cash flow and firm value) one period ahead. (11) can be rewritten as 11

U ~ ~ ~ −1 V = []E()CF + ()1− t − λ cov()CF + ()1− t ; r ()1+ r t t 1 C t 1 C M f (12) + []()~ U − λ (~ U ~ )()+ −1 E Vt+1 cov Vt+1; rM 1 rf ~ As the distribution of the random variable CFt+1 is independent from the realized outcome in U ( U ~ ) t, CFt, Vt+1 is not a random variable. cov Vt+1; rM is zero and the discount rate to be applied (~ U ) to E Vt+1 is the riskless rate rf (Fama (1977) p. 8). (12) can be rewritten as

U = ()~ ()− ()+ −1 + ()~ U ()+ −1 Vt E CFt+1 1 t C 1 k s E Vt+1 1 rf

In the case of perpetual cash flows the valuation equation for the unlevered firm value is ~ E()CF ()1− t ()1+ r V U = C f (13) 0 ()+ rf 1 k

U L With Vt+1 being not random, the future value of the levered firm Vt+1 and the equity value 8 Et+1 are also known with certainty for all future periods. As neither Lt nor Dt are uncertain in the case of independently and identically distributed cash flows D- and L-policy lead to identical firm and equity values. Usually textbooks on corporate finance and valuation propose using a single-period CAPM- based risk adjusted rate of return as discount rate on a multiperiod stream of cash flows. (e.g. Brealey and Myers (2000), pp. 242; Copeland, Koller and Murrin (1994) pp. 239). As shown by Fama (1977 pp. 3) and Myers and Turnbull (1977 pp 326 ) this requires a particular process of expectations adjustment by investors.9 This process imposes the same type and ~ U ~ degree of risk on future firm values Vt+1 as on future cash flows CFt+1 . Let ~ε be a random variable that governs the realization of the cash flow in next next period ~ CFt+1 by

~ = ()~ Φ ()+ ~ε CFt+1 E CFt+1 t 1 (14)

()~ Φ ~ whereas E CFt+1 t is the expected value of the random variable CFt+1 based upon the ~ information available at t, Φt. ε represents the deviation between the realized cash flow and ~ U its expected value in t. In order to put the same risk on the future firm value Vt+1 as on the cash flows the necessary assumption is that capital market participants revise their

8 Note that independence requires that the risk adjusted rate is to be used as a discount rate for just one period. 9 The CAPM has come under criticism since the early 90´s. The main reason for this was the model´s lacking power to explain empirical returns. See e.g. Fama and French (1992), pp. 427 and Fama and French (1995), pp. 131. It is important to note that the expectations adaption model described below is not a prerequisite of the multiperiod CAPM. It has also to hold if risk adjusted returns derived by certainty equivalents using expected utilities are applied to multiperiod payment streams. See e.g. Schwetzler (1998), pp. 12. 12 expectations about future cash flows and its present value depending on the cash flow realized in period t+1 (See Fama (1977) pp. 7; Myers and Turnbull (1977), pp. 325).

~()~ Φ = ()~ Φ ()+ ~ε E CFt+2 t E CFt+1 t 1 t+1 (15)

Expectations about future cash flows evolve as a martingale: the expected value of the distribution one period ahead is equal to the cash flow realized in period t. The total ~ distribution over CFt+1 is obtained by using (14) on the basis of the revised expected value ()~ Φ E CFt+1 t . ~ U This adaptive expectations model puts future unlevered firm values Vt+1 at the same level of ~ risk as future cash flows in the succeeding period CFt+1 . Therefore k is the appropriate risk ()~ Φ (~ U Φ ) adjusted rate of return for E CFt+1 t and for E Vt+1 t . As Eq. (2) and (9) show for each ~ L ~ U recapitalization strategy Vt+1 and Vt+1 differ only by a constant scale factor and thus are perfectly correlated. As for both strategies the value of current debt outstanding is known with ~ U ~ certainty, Vt+1 is also perfectly correlated with the equity value E t+1 . The standard case of perpetual cash flows requires for ~ε to be identically independent distributed with E()~ε = 0. It is important to note that the adaptive expectations model above puts uncertainty on future firm and equity values even in the standard perpetuity model. Any ()~ realization of a cash flow departing from the expected value E CFt+1 will lead to a revision of the expected cash flows in the succeeding period.10 As a result the expectations adaption regime required to use standard valuation formulas ~ U ~ implies random future firm and equity values Vt+1 and E t+1 . Under these conditions the difference between D- and L-policy becomes important.

4. Adaptive Expectations Model and Debt Recapitalization Strategies

4.1. D-policy and the expectations adaption process How do the two recapitalization strategies fit into the framework of the adaptive expectations model outlined above? At first I will look at the D-strategy: A policy with predetermined amounts of debt outstanding for every future period collides with the assumptions of the adaptive expectations model. As the revision of expectations is always relative to the deviation between realized and expected cash flows there is always a positive probability that debt currently issued as riskless will face risk of default at some future date t.

10 Thus the standard perpetuity model of valuation does not imply that the cash flow distribution of the first ~ period CF1 remains unchanged. Unconditional distributions of cash flows beyond period 1 observed currently in period 0 are obtained by ~ = ~ ()+ ~ε t−1 . The notion „identically distributed“ may apply 0 CFt CF1 1 only upon the expected future distribution. 13

This is demonstrated by using a simple example with discrete probability distributions for ~ε with

Sj pj εj 1 0,3 0,25 2 0,4 0 3 0,3 -0,25 ()~ The expected value of period one cash flow E CF1 is $ 100 m; the distribution of the cash flows in the first period then is

~ ~ ~ ~ pj () ε CF = E()CF ()1 + ε E CF1 j 1 1 0,3 100 0,25 125 0,4 100 0 100 0,3 100 -0,25 75

Assuming a perpetuity valuation model a careful lender looking at the cash flow distribution in period 1 might decide to give $ 200 m debt at the riskless market rate rf at 7%. At period 1 interest coverage ratio even in the worst case will be more than 500 per cent. Suppose now, that according to the D-strategy the amount of debt outstanding is predetermined to stay constant to infinity. Given a tax rate tC of 35 per cent the D-policy is assumed to generate an infinite stream of riskless tax savings of $ 4,9 m. Using formula (2) for valuation, the present value of the tax benefits is calculated to be $ 70 m. But, in contradiction to the assumption, outstanding debt will not be able to generate riskless savings as calculated above to infinity. The expectations adaption process may put risk of default upon the debtholders and their reaction will change the amount or the risk characteristics of future interest payments. Assume that the negative realization of ~ε with a negative deviation of minus 25 per cent will occur six times in a row (which, of course, is at the worst case possible, as ~ε is independent and identically distributed).The realized operating cash flow in period 6 will then be 100 (1- 6 ()~ 0,25) = $ 17.8 m. After adjusting their expectations to E CFt+1 = $ 17.8 m the distribution of cash flows in the following period 7 will be 14

~ ~ ~ ~ pj () ε CF = E()CF ()1+ ε E CFt+1 j t+1 1+1 0,3 17.8 0,25 22.25 0,4 17.8 0 17.8 0,3 17.8 -0,25 13.35

With outstanding debt of $ 200 m and interest payments of $ 14 m at the end of period 6 the lender will face risk of default: In the worst case the interest charge of the next period will not be covered by the operating cash flow. And, even worse, due to the expectations adjustment the firm value will drop substantially below the face value of debt outstanding, if that state is to occur. No matter how debtholders react upon the increase of default risk, their reaction will always lead to a collision with the debt policy assumed under the D-strategy: - Debtholders could force the firm to repurchase some of the debt outstanding in order for the remaining interest liability to be covered by minimum operating cash flows again.11 By doing so the firm has to leave its debt strategy of predetermining permanent debt at the amount of $ 200 m. Reducing outstanding debt causes interest payments and the tax savings attributed to it to decline. The assumption of permanent riskless tax savings of $ 4.9 m per period as implied by the D-strategy and its valuation formulas does no longer hold. - Instead of forcing the firm to repurchase debt, debtholders could keep the amount of debt constant and adjust the rate of return. After the risk adjustment future interest payments will be uncertain and thus the tax savings tied to this payments will be uncertain, too.12 The expected value of tax savings and the appropriate rate of return have to be changed. This is also in contradiction with the assumption of permanent and riskless tax savings as implied by the D-strategy. As a result, the D-policy will not be feasible under the expectations adaption regime necessary to apply risk adjusted rates upon multiperiod payment streams.

4.2. L-Policy and expectations adaption process

If the firm chooses an L-policy, the debt-to-firm-value ratio Lt measured in market values is predetermined and fixed for every future period. With Lt being constant the firm has to adjust U the absolute amount of debt outstanding whenever Vt+1 is departing from its expected value (~ U ) E Vt+1 by repurchasing outstanding debt or issuing new debt.

11 This reaction of debtholders is assumed in the dynamic capital structure model of Fischer, Heinkel and Zechner (1989). Debtholders permanently monitor the firm value and force equity holders to recapitalize by repurchasing debt, if debt becomes risky. See Fischer, Heinkel and Zechner (1989), pp. 27. 12 This ignores the problems caused by offering a contingent claim liability and asking for tax deductions. Usually tax agencies will try to prevent equity-like securities from getting tax deductions. 15

As

~ L ~ D = t E t − t 1 L t the change in debt is always proportional to the change in equity value. How does the L-strategy fit into the expectations adaption model outlined above? Like the D- strategy, the L-strategy may also put some risk of default upon the debtholders if the adjustment of expectations drives firm value and equity value down. Depending on the ~ ~ U operating risk of the firm in CFt+1 and Vt+1 , and on the leverage ratio Lt+1 chosen by the ~ L shareholders, face value of debt outstanding Ft might exceed total firm value Vt+1 so that debtholders face risk of default. Under the L-strategy, face value of debt outstanding at the end of period t after adjustment is = ⋅ L Ft Lt Vt . To keep things simple it is assumed that debt is always issued and repurchased at par. After adjusting the debt level according to the revised expectations, face value of outstanding debt equals market value. As levered and unlevered firm value are perfectly correlated

~ L = L ()+ ~ε Vt+1 Vt 1 is also to hold for the future value of the levered firm. The probability of default is

(~ L < ) P Vt+1 Ft

~ L By substituting for Ft and Vt+1 one gets

()~ε < − P L t 1

By noting that ~ ~ CFt+1 ε = ()~ − 1 E CFt+1

the probability of default can be expressed as a function of the leverage Lt chosen by the ~ CFt+1 shareholders and the operating risk of the company ()~ : E CFt+1 ~  CF  P  t+1 < L  (16)  ()~ t   E CFt+1 

Using (16) debt holders can always force the firm to adopt an L-policy that leads to (~ L < ) P Vt+1 Ft = 0 by restricting the amount of debt and the leverage ratio Lt to 16

CF + CF + L* = Min,t 1 and F* = Min,t 1 V L (17) t ()~ t ()~ t E CFt+1 E CFt+1

respectively, if debt is still assumed to stay riskless, whereas CFMin,t+1 denotes the positive minimum of the cash flow distribution in t+1. Debtholders will not face default risk if they restrict the amount of debt issued by the firm as in (17). Even in the worst case realized operating cash flows not only cover interest payments but also the market value of the firm still exceeds face value of debt outstanding after a downwards revision of expectations. If debtholders restrict the amount of debt according to (17), the L-strategy will not get into conflict with the expectations adaption regime necessary to work with the standard textbook formulas.13 Permanent monitoring should enable the debtholders to react upon every change in firm value and thus to enforce the maintenance of the leverage ratio Lt predetermined in period 0, in case the shareholders were reluctant to change the level of debt outstanding. This would ensure interest payments and tax savings tied to it in the succeeding period always being riskless. The adaption of the level of outstanding debt according to the expectations adaption process directly yields the correct valuation formula for the L-strategy in (9).

4.3. A comparison between the two recapitalization strategies Neither the D- nor the L-policy are dynamic optimization strategies. Both policies predetermine future actions of the shareholders by fixing either the absolute levels of debt or the leverage ratio for every future period. The D-policy implies that future action of the shareholders does not depend on any changes in firm value.14 The L-policy implies that future recapitalization decisions depend on changes in firm value; whenever the firm value increases or decreases the firm has to raise or to repurchase debt. Though, this action is dependent on future events (the change in firm value). It is not a dynamic optimization; the way the firm reacts upon changing circumstances is predetermined. Debt has to be changed proportional to the change in firm value. For an L-policy to be a dynamic optimization strategy the optimal leverage L* currently chosen by the management must not change over time. Thus marginal benefits and costs of debt may not depend on the absolute size of the firm value. While this may be true for marginal tax benefits (while tC being a proportional tax rate), doubts may arise on the marginal disadvantages of debt financing as costs of financial distress or agency costs of debt. In the case of indirect bankruptcy costs, one might argue for example that customers and suppliers are more trustful, that the company under financial distress will be able to maintain its operations and meet its

13 Any possible deviation from the predetermined leverage ratio Lt enforced by debtholders as a reaction on default risk will change the expected tax savings and the risk attributed to it and thus will distort the value of the tax shield in comparison to the value implied by formula (8). 14 Of course a firm following that strategy may change its outstanding debt in any future period. But it has to predetermine that change in the current period so that the change will be independent from the conditions then prevailing. 17 obligations the higher the absolute operating cash flows and firm values for a given interest coverage ratio and debt-to-firm value ratio are. Indirect bankruptcy costs might be inversely related to absolute firm value.15 The firm thus may have a higher optimal leverage ratio as U Vt+1 increases. L* based on the current situation may not necessarily be the optimal leverage ratio when firm value changes. As the L-policy assumes that every change in firm value is to be followed by a proportional change in outstanding debt, it ignores transaction costs. By changing the level of outstanding debt the firm faces transaction costs when issuing or repurchasing debt. (e.g. Fischer, Heinkel and Zechner (1989), pp. 24). Taking transaction costs into account the permanent adjustment implied by the L-policy could be replaced by a policy that changes the level of outstanding ~ L debt whenever some optimal prespecified intervention values of Vt+1 are touched. Fischer, Heinkel and Zechner developed an „inventory control model“ of capital structure choice where this is the case.16 (See Fischer, Heinkel and Zechner (1989) pp. 21) As long as firm value stays between the upper and lower boundary („region of no recapitalization“) debt is not changed. Such models of dynamic recapitalization have not become standard for valuation purposes yet.

5. Implications

5.1. Implications for Corporate Valuation As the theory of finance does not offer simple methods to quantify the costs of financial distress and agency costs of debt, usually these costs are not taken explicitly into account when determining the value of a corporation. Thus when discussing the implications of the two different recapitalization policies on valuation models, I concentrate on their impact upon the value of tax benefits from debt. As both policies imply different levels of risk of future tax savings they lead to different tax shields and, other things equal, to different firm values. If both policies were perceived as feasible the choice would be simple: As it leads to higher firm values shareholders and their managers always would prefer the D-policy and potential investors valuing the company would do so, too. Unfortunately under the expectations adaption regime discussed above the D-policy is not admissible: Even a moderate level of debt will face a non-zero probalility of default over a longer period of time. Arguing with a D-policy overstates the advantage of the tax savings. This will put recapitalization strategies as a point of debate into transaction negotiations: The party interested in a higher price for the company (presumably the sellers or their advisers) will argue for a D-policy to be assumed for valuation purposes. The party interested in a lower price will prefer an L-policy by pointing out the problems of D-policies

15 For empirical evidence see e.g. Warner (1977), pp. 337. 16 This intervention bounds are also to be predetermined in the current period. 18

in the expectatins adaption regime discussed above. Making things worse, no party has yet to prove that it will really try to follow this policy; the impact on value occurs just by announcing this policy.17 Whenever tax savings are to be a substantial part of the firm and equity value, such a debate might arise. In the perpetuity model the difference in value caused by the two policies may be substantial. It is

r ()1+ k ∆ V = t D − t D f = D ∆VT (18) 0 C 0 C 0 ()+ 0 0 k 1 rf

t ()k − r wheras ∆ VT = C f is the relative difference between the two values in per cent of 0 ()+ k 1 rf market value of current debt outstanding, which is of course the same for both policies. As formula (18) shows, the difference in value is sensitive to the risk premium of the

unlevered company over the riskless market rate rf: the higher the difference between k and rf, ∆ T the higher is Vt . This is intuitively appealing: The higher the operating risk of the company, the higher the risk that an L-strategy puts on future outstanding debt. The figure ∆ T below shows the relation between k and Vt for given values of rf and tC.

recapitalization strategies and difference in firm value

0,45

0,4

0,35

0,3 For k

0,25 tax rate = 55% tax rate = 45% 0,2 tax rate = 35%

0,15 = 15 relative difference in firm value firm in difference relative

%, tC = 0,1 35%

0,05 and rf = 7% 0 12345678910111213141516171819202122232425 the

cost of equity k difference will be 17.4 per cent of the amount of outstanding debt.

17 I will argue on the credibility of such an announcement later in this section. 19

Under the expectations adaption regime outlined above, assuming an L-policy for valuation purposes seems more reasonable: Though ignoring transaction costs it accounts for the risk of the tax savings linked to that policy under the expectations adaption rule. If debtholders choose the debt level according to (17) in order to avoid risk of default,18 the assumption that interest payments and tax savings in the succeeding period will be riskless, may hold for all future periods. The announcement of shareholders and management to follow a D-policy and to maintain a given and prespecified level of debt for all future periods is not credible under the expectation adaptions regime. How could shareholders achieve a higher credibility of the more favourable D-strategy of recapitalization? One way to send credible signals about future debt policy could be to choose a certain maturity structure of debt. If the firm issues long-term debt then future debt levels, future interest payments and tax savings might be perceived less risky than in the case of short-term revolving debt.19 This argument would contradict the findings of Lewis (1990) who shows that for tax purposes the maturity structure of debt is irrelevant (Lewis (1990), p. 26): Unless there is no difference in the tax treatment, the tax savings associated with debt are independent from its maturity structure. In the argument outlined above maturity structure might not become relevant because the risk associated with the interest payments may be different, but because the amount of debt outstanding may have different degrees of risk over different maturities.20 According to this argument, firms with a higher average maturity of debt would be able to achieve higher market values because debt levels and tax savings associated with their debt are perceived as less risky. Whether this argument holds will depend on the covenants embedded in the long-term debt contract under consideration. Whenever the debt contract has a clause giving the debtholders the right to reinforce the repurchase of debt by the shareholders in the case of default risk, then there might be no difference between the credibility of planned tax savings of a long-term debt and of a revolving short-term debt contract. Whenever revision of expectations should drive firm value down to a level where long-term debt holders may face a probability of default greater than zero, they will force the company to repurchase some of its outstanding debt. Thus the firm will find itself in the same situation as if short-term debtholders adjusted their level of debt downwards at a rollover date. On the other hand, under realistic assumptions, the effects and costs of incurring a call of long term debt might not equal the effects and costs of renewing short-term debt. Thus the impact of different maturity structures upon the tax benefits associated with debt may still considered to be an open question.

18 This is the standard assumption of the textbook valuation formulas. 19 For other factors that affect the choice of debt maturity see e. g. Barclay and Smith (1995), pp. 609. 20 As Lewis does not use one of the two standard recapitalization strategies outlined above, but develops a dynamic recapitalization strategy optimizing the capital structure in every future period (pp. 27), the problem discussed here is not part of his analysis. Using a state-contingent framework building on unconditioned probability distributions over every future period, the complexity of such a presentation in a multiperiod setting would exceed the limitations for valuation purposes. 20

5.2. Implications for capital structure optimization

According to corporate finance text books at the firms optimal amount of debt D* marginal tax benefits of debt should equal marginal disadvantages of debt (costs of financial distress, agency costs of debt). As the marginal tax advantage of debt is substantially lower for a firm following an L-strategy, differentiation between the two recapitalization strategies may also have some important implications for the optimization of the capital structure. Whether there are differences in the optimal level of debt D*, the maximum firm value D* VL (D* ) and the leverage ratio L* = at optimal debt level depends on whether the VL ()D* disadvantages of debt are the same for the D-firm and the L-firm or not. In order to analyze this question, I will look at four different cases: 1. The disadvantages of debt are identical for the L- and for the D-firm. 2. The disadvantages of debt are lower for L-firm than for D-firm and a) L-firm and D-firm have identical optimal debt levels D*, b) L-firm and D-firm have identical maximum firm values VL (D* ) c) L-firm and D-firm have identical leverage ratios L* I will start the analysis with case (1), assuming that marginal and absolute disadvantages of debt are unrelated to the recapitalization strategy chosen by the firm. The function of these disadvantages C (D), henceforth referred to as the cost function of debt, has the standard properties C´(D) > 0 and C´´(D) > 0. Figure II shows the determination of the optimal debt level for the two firms; for simplicity the first assumption is C´ (D) being a quadratic function. 21

marginal benefits/ C ’(D) costs

BC tC

⋅∆ DE tC t

A * * DL DD debt

Figure II

Marginal tax benefits for the D-firm are tC. For the L-firm marginal tax benefits are tC ⋅ ∆t r ()1+ k where ∆t = f . As ∆t < 1, marginal advantages of debt are lower for the L-firm. At ()+ k 1 rf unchanged marginal costs of debt thus the optimal debt level D* has to be lower for the L- firm than for the D-firm. This holds for any chosen cost function with the properties stated above. Figure II also shows that maximum firm value at optimal debt level VL (D* ) has to be lower for the L-firm: the area marked by the triangle ABC denotes the net advantages of debt * at the optimal debt level for the D-firm DD ; net advantages for the L-Firm are given by the * area of the triangle ADE at optimal debt level DL . For the quadratic cost function assumed in figure II maximum firm value declines by ∆t per cent when switching from a D- to an L- L ( * ) L ( * ) policy. Of course the result VL DL < VD DD has to hold for any given cost function valid for both firms with the properties stated above. As both D* and VL (D* ) are lower for the L-firm, the impact of different recapitalization strategies upon optimal capital structure is not straightforward; it depends on the shape of the cost function of debt. Figure III shows the standard case: 22

firm value

L * VD (D )

L * VL (D ) VU

D* D* L D debt

Figure III * L ( * ) Optimal debt level DD leads to a maximum firm value of VD DD for the D-firm. The solid line in figure III is to show the combinations of VL (D* ) and D* with the same leverage ratio D* as the D-firm at optimal debt level. As in the case of figure III the ratio L of the L-firm L ()* VL DL is left of this line, the optimal leverage ratio is higher than for the D-firm. Whether * * ∆ LL exceeds LD or not depends on the particular cost function assumed, the factor t and the value of the unlevered firm VU. There may also be some combinations of these factors that lead to situations where the decrease in firm value VL (D* ) exceeds the decrease in optimal debt level D* so that L* is also decreasing for a firm shifting from a D- to an L-policy. As an important result maximum firm value VL (D* ) will always be higher for the D-firm than for the L-firm. Thus with costs of financial distress taken into account management will still prefer to follow the D-strategy (or at least to announce it) if it wants to maximize market value. Inselbag and Kaufold (1997)argue that it is not clear whether the D-strategy might be superior to the L-strategy when the possibility of higher marginal disadvantages of debt is taken into account. (Inselbag and Kaufold (1997), p. 120, footnote 12).21 The results above suggest that the costs of financial distress have to be substantially lower for the L-firm in order to arrive at the same (or at an even higher) maximum firm value than for the D-policy. Continuing the analysis by assuming lower costs for the L-firm it is asked how big the differences of these costs have to be in order to arrive at

21 Inselbag and Kaufold (1997) assume that both strategies are admissible in the multiperiod CAPM- framework. 23

- identical optimal debt levels D* (case (2a)), - identical maximum firm values VL (D* ) (case (2b)) and - identical optimal capital structures L* (case (2c)) for the two firms. As a special case the conditions that have to prevail for all three factors to be identical simultaneously will be analyzed.

Case (2a): lower disadvantages of debt for the L-firm; identical optimal debt level D* In the first step of my analysis I examine the conditions necessary for the optimal debt level D* to be the same for the D- and the L-firm at different disadvantages of debt. Figure IV shows the determination of the optimal debt level for the two firms:

marginal benefits/ ’ costs CD,I ’ ’ CD,II CL,I B C tC ’ CL,II

⋅∆ F G tC t

E A * D debt

Figure IV First, concentrating on the simple case of quadratic cost functions for both firms, Figure IV ´ shows that the marginal costs for the L-firm denoted by CL,I have to be significantly lower ´ than for the D-firm denoted by CD,I , in order to arrive at the same optimal debt level D* for the two policies. Figure IV indicates also that for the simple case of quadratic cost functions maximum firm value for the L-firm always will be lower than maximum firm value for the D- firm: as the net advantage of debt for the D-policy is still the area marked by the triangle ABC, the net advantage of the L-policy is the area of the triangle AFG. With ABC being 0,5 ⋅ ABCE and AFG being 0,5 ⋅ AFGE it is clear, that maximum firm value has to decrease ∆ ∆ ⋅ ∆ L ( * ) L ( * ) proportional in t: AFGE = t ABCE. As 0 < t < 1 the relation VL DL < VD DD generally holds for the case of a quadratic cost function. Are there conditions leading to identical maximum firm values for the two firms given identical optimal debt levels D*? To answer this question one has to look at the marginal 24 disadvantages for the two different firms in figure IV: Under the general assumption of C´(D) > 0 and C´´(D) > 0 any quadratic cost function with C´´´(D) = 0 will lead to the lowest possible net advantage given the amount of debt D*. Area ABC thus reflects the minimum net advantage of debt for a D-firm. For any cost function C (D) with C´´´(D) > 0 net advantages of debt at given debt level D* have to be higher; for instance with the marginal cost function ´ denoted by CD,II in figure IV the net benefits for the D-firm at debt level D* are given by the ´ area marked by ABC and the bented line of the marginal cost function CD,II and exceed the net benefits at the quadratic cost function.22 Thus the area of the triangle ABC marks the minimum net benefits of debt for the D-firm. What are the maximum net benefits of debt for an L-firm? Clearly the maximum advantage of debt would be achieved if there were no disadvantages at all for the L-firm at debt level D*. In this case the net effect would be the gross tax benefit marked by the area AFGE in Figure IV. Now combining maximum possible net advantages of the L-firm with minimum possible net advantages of the D-firm and accounting for ABC = 0,5 ⋅ tC ⋅ D* and AFGE = ∆t ⋅ tC ⋅ D* one gets the condition for higher or equal maximum firm values of the L-firm with

⋅ ∆ ⋅ * ≥ ⋅ ⋅ * tC t D 0,5 tC D

Even if one allows for the maximum possible differences between the two cost functions within the framework of general assumptions the additional requirement for the possibility of an L-firm value exceeding the D-firm value is ∆t ≥ 0,5. This condition is still understating the requirement because is assumes zero costs of financial distress for the L-firm. A cost function to fulfill the requirement should be as close as possible along the line AEG in Figure IV and ´ have the property C´´(D) > 0 for all D. In figure IV the line denoted by CL,II is such a cost function. The net advantage of debt will be lower in this case compared to the zero cost case; it is the area marked by the line AFG on the one and by the bented line of the marginal cost ´ function CL,II on the other side. As a result, under extreme conditions, it is at least possible that maximum firm value of the L-firm is equal or even higher than maximum firm value of the D-firm. But, as Figure IV clearly indicates, even in the general framework of assumptions for the disadvantages of debt with C´(D) > 0 and C´´(D) > 0 one has to take the two extremes of admissible cost functions to arrive at the desired result: For the D-firm the most unfavourable cost function with the minimum possible net benefit of debt has to be chosen, while for the L-firm the most favourable cost function leading to the maximum possible net benefits of debt has to hold. Clearly, as the only difference between the two firms should be the recapitalization strategy, L ( * ) L ( * ) * * beside the desire to arrive at the result VL DL = VD DD and DD = DL there is no evidence

22 Note that under the standard assumption C´(D) > 0 and C´´(D) > 0 the cost function will have no turning point. Thus cost functions with C´´´(D) < 0 and decreasing marginal costs are not admissible. 25 for the two cost functions to have such extreme differences. Thus the case that optimal debt level D*, maximum firm value VL(D*) and therefore optimal capital structure L* all are unrelated to the recapitalization stragey chosen by the firm is extremely unlikely. Figure V shows the absolute effects upon firm value in such an extreme case:

firm value

V L (D* )

VU

* D debt

Figure V L ( * ) In the following part of the paper I will concentrate on the reasonable case VL DL < L ( * ) VD DD . The effect of changing the recapitalization policy in case (2a) here is shown by figure VI:

firm value L * VD (D ) L * VL (D )

VU

* D debt

Figure VI 26

As maximum firm value decreases and optimal debt level is identical for both firms the * * optimal leverage ratio L* for the L-firm has to exceed the one of the D-firm: LL > LD .

Case (2b): lower disadvantages of debt for the L-firm; identical maximum firm value VL (D* )

Now the conditions that have to hold for the maximum firm value to remain unchanged for a L ( * ) L ( * ) firm switching from a D-policy to an L-policy are to be analysed: VL DL = VD DD Excluding the extreme case, where the maximum firm value and the optimal debt level are simultaneously identical, it is clear that the difference between the disadvantages of the two firms’ debt still has to be substantial in order to get the equality stated above. Figure VII shows marginal benefits and costs of debt for the L- and the D-firm in this case:

marginal benefits/ costs ’ ’ ’ CD,II CL,II CD,I B C tC

’ CL,I ⋅∆ F G tC t

E H A * D* D* D D L,II L debt

Figure VII

Starting with the simpliest case of both cost functions being quadratic with marginal costs of ´ ´ financial distress of CD,I and CL,I for the D-firm and the L-firm respectively, Figure VII indicates that in order to arrive at identical maximum firm values the net advantages of debt marked by the area of triangle ABC and the area of triangle AFG have to be equal. As ABC = * * ∆ 0,5 DD tC and AFG = 0,5 DL tC t the equation

1 D* = D* (19) L ∆t D has to hold. As (19) with 0 < ∆t < 1 and Figure VII indicate the optimal level of debt for the L-firm has to be substantially higher than for the D-firm to arrive at identical maximum firm 27 values under these conditions. If one allows for different types of cost functions for the two ´ firms and assumes a function with C´´´> 0 for the L-firm as shown by CL,II in Figure VII, the * necessary increase in D* will be lower (for instance to DL,II ) but, beside the extreme case * * being ruled out above, DL will exceed DD . By comparing the marginal cost functions for the two firms Figure VII highlights that the difference in the disadvantages of debt required to arrive at identical firm values for both firms is still extremely high. Figure VIII shows the determination of the maximum firm value in absolute numbers for the special case under analysis here.

firm value

L * = L * VL (D ) VD (D )

VU

* * DD DL debt

Figure VIII L ( * ) L ( * ) * * As VL DL = VD DD and DD < DL it follows that the optimal leverage for the L-firm has * * to be higher than for the D-firm: LD < LL

Case (2c): lower disadvantages of debt for the L-firm; identical optimal leverage ratio L*

The last special case to be analyzed here is different costs of financial distress leading to identical optimal leverage ratios for the D- and the L-firm. Again ruling out the extreme case L ( * ) L ( * ) * * of VL DL = VD DD and DD = DL it is clear that the maximum firm value and the optimal debt level have to decline at the same rate when L as the ratio of the two values is to be unchanged for a firm shifting from a D- towards an L-policy. 28

Figure IX shows this special case:

firm value

L * VD (D )

L * VL (D )

D* D* L D debt

Figure IX

If capital structure at optimal debt levels is to remain unchanged the optimal leverage ratios have to to be located on the solid line connecting the leverage ratio of the D-firm and the zero point in figure IX. The following table sums up the results of the analysis above, again restricting our attention () () on reasonable differences between CD D and CL D :

Optimal debt Maximum firm value Optimal Disadvantages of level D* VL (D* ) leverage debt ratio * * L ( * ) L ( * ) * Ø * () () Case (1) DD < DL VD DD > VL DL LD LL CD D = CL D * * L ( * ) L ( * ) * * () () Case (2a) DD = DL VD DD > VL DL LD < LL CD D > CL D * * L ( * ) L ( * ) * * () () Case (2b) DD < DL VD DD = VL DL LD < LL CD D >> CL D * * L ( * ) L ( * ) * * () () Case (2c) DD > DL VD DD > VL DL LD = LL CD D > CL D

The interpretation of these findings depends on how realistic one perceives the necessary differences in the disadvantages of debt between the D- and the L-firm. What can be said about possible differences in marginal and in absolute disadvantages of debt financing between the two strategies at this stage? Perhaps one should start by noting once again that besides the planned recapitalization strategy the D- and the L-firm are virtually identical in their assets in place, future prospects and operating risk. The only difference up to this point is the announcement that they intend to have different recapitalization strategies and adjustment 29 rules for outstanding debt when future firm values will change. Will the D- and the L- company have different probabilities of default? This, as stated above, depends on whether debtholders treat the two companies differently just on the announcement of different debt adjustment strategies. One might argue that default risk of debtholders will not depend on the promised adjustment strategy by the shareholders but on the relation between future uncertain ~ operating cash flows CFt and payments promised to the debtholders. Thus even when shareholders announce following a D-strategy, debtholders may act in the same way as in the case of a promised L-strategy, whenever revised expectations drive future firm value down to a level where they are facing risk of default. With the maturity of debt and the monitoring effort by the debtholders being the same for the two strategies23 the probability of default might not be different. Even when allowing for different maturities with a D-firm having a higher average time to maturity differences in default risk may not necessarily occur: long-term debtholders will force clauses and covenants into their contracts that enable them to reinforce recapitalization whenever they face risk of default. Only if long-term debtholders of the D-firm were lowering their monitoring efforts compared to the short-term debtholders of the L-firm differences in default probabilities could be possible. Once default has occured, the costs of reorganization and recapitalization should not depend on whether a firm followed a D- or an L-strategy before the default. The priority and the treatment of the debtholders in default are also assumed to be the same for both policies.24 As a result there seems to be no evidence for a difference between the two costs of financial distress big enough to keep optimal debt level, maximum firm value and optimal leverage unchanged for a firm switching from a D-policy towards an L-policy of recapitalization. This would mean putting very high disadvantages of debt upon the D-firm while leaving the L-firm almost without any disadvantages. Even the differences necessary to arrive at identical maximum firm values while allowing for different optimal debt levels seem unreasonably high. I argue here, that there are good reasons to assume maximum firm values of the D-firm to exceed maximum firm values of the L-firm, when allowing, at best, for moderately different disadvantages of debt.

23 The L-strategy could be established using long-term debt by giving the firm the right to repurchase debt at par according to changes in firm value. 24 Again a difference in the costs of reorganization could only occur if long-term debtholders of the D-firm lower their monitoring efforts on the announcement of a D-policy and enable the company to suffer substantial losses in firm value without reaction. In this case the value of assets still in place may be lower after the default becomes public, such increasing losses to the debtholders. 30

Figure X is designed to give an impression on the necessary differences in disadvantages of debt to arrive at the three desired relations in the cases (2a) to (2c): it shows the shape of the () () required cost functions assuming CD D and CL D both being quadratic functions.

Cost of Debt for D- and L-Firms

140

120

100

80 Cost of Debt D-Firm Case (2a):Cost of Debt L-Firm Case (2b): Cost of Debt D-Firm 60 Case (2c): Cost of Debt D-Firm

Cost of Debt (absolute Amount) 40

20

0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 Amount of Debt

Figure X

The bold line in Figure X marks a given quadratic function of disadvantages of debt (costs of debt) for the D-firm. The three lines below indicate the cost functions necessary to get the desired results stated in the three cases (2a) to (2c). The dottet line shows the costs of financial distress for the L-firm necessary to arrive at the same maximum firm value than the D-firm. Figure X indicates that the required differences in costs of financial distress are extremely high.

As a result, the situation is similar as in the section above: If market participants perceive the D-policy as admissable and feasible, it pays for the shareholders and their managers to adopt or, at least to announce, a D-strategy. On the other hand, the announcement of a D-policy may not be credible, if capital market participants value their using the expectations adaption process outlined above. Capital markets might perceive the L-strategy as more credible. As long as there are no empirical studies on the impact of different announced recapitalization strategies on firm values, this is also still an open question. In any case, the value attributed to tax savings at given debt levels for L-firms might be substantially lower than proposed by the standard valuation formulas in finance textbooks. This result adds another possible explanation to the puzzle of tax saving effects on capital 31 structure choice and on why „tax advantages of debt financing must be substantially lower than conventional wisdom suggests“ (Miller (1977) p. 266).25

6. Conclusions

This papers has shown that the D-strategy usually assumed in textbook valuation formulas is not admissible under the expectations adaption regime necessary to use CAPM-based, risk- adjusted rates of return in a multiperiod framework. On the contrary, the alternative L-strategy fits into this framework. For valuation purposes costs of financial distress and other disadvantages of debt are rarely taken explicitely into account. For corporate valuation the L-policy leading to lower tax benefits will result in lower firm values. As differences in value between the two recapitalization strategies may be substantial the recapitalization strategy assumed for valuation is expected to become a major point of debate in price negotiations. The static trade off theory of optimal capital structure relates tax benefits to costs of financial distress and other disadvantages of debt. In this paper, I argue that due to the lower tax benefits optimal level of debt and maximum firm value of the L-firm has to be substantial lower than for the D-firm (assumed this strategy is to hold). Differences in costs of financial distress and disadvantages of debt between the two strategies necessary to arrive at equal optimal debt or even at equal maximum firm values at optimal debt are by far to high to be justified simply by the announcement of different recapitalization strategies.

References

Barclay, M. and Smith, C. 1995, The maturity structure of corporate debt, Journal of Finance 50, 609-631 Berens, J. and Cuny, Ch. 1995, The capital structure puzzle revisited, Review of Financial Studies 8, 1185-1208 Brealey, R. and Myers, S. 2000, Principles of corporate finance, 6th ed. Clubb, C. and Doran, P. 1995, Capital budgeting, debt management and the apv-criterion, Journal of Business Finance and Accounting 22, 681-694 Copeland, Th., Koller, T. and Murrin, J. 1994, Valuation, 2nd ed., Wiley & Sons Inc. Cornell, B. 1993, Corporate valuation, Irwin Damodaran, A. 1994, Damodaran on valuation, New York DeAngelo, H. and Masulis, R. 1980, Optimal capital structure under corporate and personal taxation, Journal of Financial Economics 8, 3-29

25 For other possible explanations to that puzzle see e.g. DeAngelo and Masulis 1980 pp. 3; Berens and Cuny pp. 1185. 32

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