CORPORATE FINANCE II: TAXES AND FINANCIAL DISTRESS

OUTLINE

• VALUATION OF THE DEBT TAX SHIELD
• FINANCIAL DISTRESS
• TRADEOFF THEORY
• THEORY AND REALITY
• SUMMARY

VALUE OF UNLEVERED FIRM

• As you learned in Financial Management
• The value of any asset equals its expected cash flows discounted at a risk adjusted rate that reflects the riskiness of the cash flows
• Thus, $V_{0}^{U}$ the value of an unlevered firm at date 0, equals

$$ V_{0}^{U}=\sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{CF}_{t}^{U}]}{(1+r_{U})^{t}} $$

• where
  • $r_U$ is the required return on the unlevered firm, and
  • $\tilde{CF}_{t}^{U}$ is the random future cash flows of the unlevered firm

PROBLEM

• As discussed in the previous lecture, conceptually accounting for the effects of tax shield on value is simple: $V^{L}$, the value of the levered firm at date 0 equals

$$ V_{0}^{L}=V_{0}^{U}+PV \text{ of debt tax shield} $$

• Like all assets, the present value of the tax shield equals the sum of discounted expected future cash flows, so

$$ \text{PV of debt tax shield} = \sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{TS}_{t}]}{(1+r_{TS})^{t}} $$

where $\tilde{TS}_t$ is the random cash flow produced by the interest tax shield at date t, and $r_{TS}$ is the appropriate discount rate for the cash flows produced by the tax shield.

THE PROBLEM

• However, we face a practical problem: what is $r_{TS}$?
• Answer to this question is not obvious
• It requires making assumptions about firms' capital structure policies
• In practice, two policies are considered: the constant ratio policy and the constant level policy
  • Constant ratio policy: keep the ratio $L=D/V$ constant
  • Constant level policy: keep the debt level D constant

DISCOUNT RATES FOR TAX SHIELDS: CONSTANT RATIO POLICY

• In any given period, the tax shield equals $\tau r_D D$ where $r_D$ is the required return on debt, $\tau$ is the corporate tax rate, and D is the market value of debt
• Suppose that $r_D$ and $\tau$ are constant (i.e., not random)
• Constant ratio policy: Adjust the level of debt, D, to maintain a constant debt-to-value ratio, L, between levered firm value $V^L$ and debt value.
• so $D_t = L V_t^L$ at every date t
• because $V_t^L$ is random, the firm at date 0 does not know how large its tax shield will be at date $t > 0$

EXAMPLE

• The tax shield is risky even if the debt is risk free because the amount of debt outstanding is random, it depends on the random evolution of firm value.
• If firm value at date t, $V_t^L$, is say £2 mn, then the tax shield at date t will equal $\tau r_D D_t = \tau r_D L V_t^L = 2 \tau r_D L$
• But if firm value at date t, $V_t^L$ is say £4 mn, the tax shield at date t will equal $4 \tau r_D L$
• At date 0, the firm does not know what its value will be at date t
• So, it does not know how large its tax shield will be
• How should this risk be reflected in the discount rate applied to the tax shield?

DISCOUNT RATE UNDER CONSTANT RATIO POLICY

• Because, under the constant ratio policy (and only under the constant ratio policy), cash flows from the tax shield are proportional to firm value
• And firm value is proportional to cash flows
• the discount rate for the tax shield equals the required return for unlevered cash flows
• In other words $r_{TS} = r_U$

COST OF CAPITAL FOR LEVERED FIRMS UNDER THE CONSTANT RATIO POLICY

• By definition, $r_U$ is the appropriate discount rate for unlevered cash flows
• Under the constant level policy, $r_U$ is the appropriate discount rate for the tax shields
• All of the levered firms cash flows are either unlevered cash flows or debt tax shield cash flows
• Thus, under the constant ratio policy, the firms' levered cost of capital, $r_L$, equals its unlevered cost of capital.
• $r_L = r_U$
• By definition (regardless of capital structure policy), the levered cost of capital is the weighted average of the debt, $r_D$, and equity, costs of capital, $r_L = (1-L)r_E + L r_D$.
• Hence, if the firm follows the constant ratio policy, $r_U = (1-L)r_E + L r_D$

CONSTANT RATIO POLICY: CCF APPROACH

• Under the constant ratio policy $r_{TS} = r_U$

$$ \text{PV of debt tax shield} = \sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{TS}_{t}]}{(1+r_{U})^{t}} $$

And the value of the levered firm equals

$$ V_{0}^{L} = V_{0}^{U} + \text{PV of debt tax shield} = \sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{CF}_{t}^{U}+\tilde{TS}_{t}]}{(1+r_{U})^{t}} \quad \text{(CCF-Valuation)} $$

• This approach is called the capital cash flow (CCF) approach (Ruback, 2002)

CONSTANT RATIO POLICY: WACC APPROACH

• In practice, CCF is rarely used to value firms or projects (except in Harvard Business school cases)
• The CCF valuation formula is conceptually simple and transparently displays the effect of the constant ratio policy on tax-shield valuation
• However, an approach equivalent to CCF valuation is widely used.

WACC FORMULA (CONT)

• CCF valuation of all cash flows is equivalent to discounting unlevered cash flows using the weighted average cost of capital (WACC), $r_{WACC}$,

$$ V_{0}^{L}=\sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{CF}_{t}]}{(1+r_{WACC})^{t}} $$

where $r_{WACC} = r_E (1-L) + (1 - \tau)r_D L \quad \text{(WACC-Valuation)}$

• The WACC approach is simple: rather than value the tax-shield cash flows explicitly, adjust the the discount rate
• WACC is not the required return of the firm itself (even if the firm follows the constant ratio policy)

SUMMARY: CONSTANT RATIO POLICY

• Under constant ratio policy, projects can be valued either by
  • CCF Approach: Discount all cash flows including the cash flows generated by tax shields (CF and TS) at the firm's unlevered cost of capital, $r_U$
  • WACC Approach: Discount only unlevered cash flows (ignoring tax shield cash flows) at the firm's weighted average cost of capital (WACC), $r_{WACC} = r_E(1-L) + (1-\tau)r_D L$
• The WACC approach is simpler to apply because it does not require estimating the cash flows generated by the tax shield explicitly
• The WACC is just a short cut that permits the valuation of levered firms without explicitly computing the cash flows generated by tax shields.
• $r_{WACC}$ has no economic meaning for firms that do not follow the constant ratio policy.

THE ALTERNATIVE: CONSTANT LEVEL POLICY

• Constant level policy: firm keeps the market value of its debt constant and equal to D
• When the value of debt falls (e.g. because a bond issue is redeemed) the firm immediately issues new debt
• When the market value of debt increases (e.g. interest rates fall), the firm immediately buys back or retires some of its debt
• In this case, as long as the firm is solvent, its debt level is fixed

CONSTANT LEVEL: VALUING THE DEBT TAX SHIELD

• Thus, the required return of the debt tax shield should be well approximated by the required return of debt
• So

$$ \text{PV of debt tax shield} = \sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{TS}_{t}]}{(1+r_{D})^{t}} $$

And the value of the levered firm equals

$$ V_{0}^{L} = \sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{CF}_{t}^{U}]}{(1+r_{U})^{t}} + \sum_{t=1}^{\infty}\frac{\mathbb{E}_{0}[\tilde{TS}_{t}]}{(1+r_{D})^{t}} $$

• The constant-level policy valuation of debt tax shields is an instance of the Adjusted Present Value (APV) approach to valuation:

APV VALUATION

• APV approach: when a project's cash flows stream can be segregated into different component streams (e.g., operating cash flow and tax shields)
• Find the present value of each stream by discounting each stream at its own required rate of return
• Then sum up the present values of the components to determine the present value of the project

CORPORATE TAX SHIELDS MATTER BUT ARE THEY THE ONLY IMPERFECTION THAT MATTERS?

• Research by John Graham (JF, 2000) estimates that the typical firm's tax shield accounts for 9.7 percent of its value
• Who reaps the benefits of the larger tax shield?
• Why don't companies take on a lot more debt?
• Using the standard WACC approach, at 100% debt the firms cost of capital would be $(1-\tau)r_D$
• Since, in this case, debt takes on all corporate risk, $r_D = r_U$
• So, at a 40% corporate tax rate the tax shield would be worth
  • 40% of unlevered firm value
  • $0.40 / (1+0.40) \approx 30\%$ of total firm value
• Are almost all corporations seriously underlevered?

FINANCIAL DISTRESS

• Maybe not, because of the cost of financial distress
• Financial distress occurs when shareholders are unwilling or unable to make contracted payments to debtholders
• When financial distress occurs, frequently, shareholders and debtholders enter into negotiations
• When negotiation fails, firms enter in to a formal legal process called bankruptcy (US term) or insolvency (UK term).

BANKRUPTCY

• What is bankruptcy for?
  • It is the law that governs the way that the company's assets are distributed in the wake of a failure to pay debt
• What are the costs of financial distress?

DIRECT COSTS OF BANKRUPTCY

• Direct costs are out-of-pocket expenses associated with bankruptcy proceedings
  • Filing, legal, and professional fees
• The 1979 US Bankruptcy code requires firms to list every fee that they pay in Chapter 11 bankruptcy proceedings
• Weiss (JFE 2000) surveys 37 New York and American Stock Exchange firms that filed for bankruptcy between Nov 1979 and Dec 1986
• Direct costs of bankruptcy average:
  • 3.1% of the MarketValue(equity) + BookValue(debt)
  • 2.8% of Book Value(assets)
• Is 3% a high cost of bankruptcy?
• Is this the full story?

INDIRECT COSTS OF FINANCIAL DISTRESS

• Financial distress might have indirect costs:
  • Loss of goodwill with customers
  • Private information of company revealed to courts
  • Firms forced to quickly sell assets without waiting for the highest bid (fire sales)
  • Delays in making decisions because of the need for court approval.
• How large are these costs?
• To what extent can these costs be attributed to capital structure?
  • Example: In the 1970s many companies making slide rules went bankrupt: these bankruptcies were not caused by high levels of debt but rather resulted that few people wanted to buy slide rules after the electronic calculator was invented.

EVIDENCE: DOES FINANCIAL DISTRESS HAVE SIGNIFICANT COSTS?

Andrade, G., & Kaplan, S. N. (1998). How costly is financial (not economic) distress? Evidence from highly leveraged transactions that became distressed. Journal of Finance, 53(5), 1443-1493.

An empirical paper that attempts to measure the effects of leverage on financial distress costs.

CAUSES OF DISTRESS

Results as a percentage of the total are as follows:

	Industry Performance	Firm Performance	Leverage	Short-Term Rate Changes
Median	0.03	-0.04	1.04	-0.02
Mean	0.06	0.02	0.95	-0.02
S.D.	0.36	0.96	0.91	0.07

EFFECT OF DISTRESS ON OPERATING PERFORMANCE

	Year 0	Change from year -1 to:
		Preresolution	Postresolution
EBITDA/Sales
Nominal Growth	-16.10%	-22.90%	-7.10%
Industry-Adjusted Growth	-17.00%	-16.90%	-12.30%
CAPX/Sales
Nominal Growth	-12.60%	-10.60%	2.90%
Industry-Adjusted Growth	-9.80%	-21.90%	11.00%
NCF/Sales
Nominal Growth	-9.00%	-17.00%	-44.70%
Industry-Adjusted Growth	-8.80%	-30.20%	-16.70%

• Add 3 percent direct costs. Chapter 11 costs 10-20 percent of asset value.
• What are we assuming?
  • Persistence of the effects above, so an x% fall in growth is not a temporary (1 year) drop but rather implies a permanent reduction in the growth rate by x%.

TRADEOFF THEORY: MOTIVATION

• If Andrade and Kaplan's (1998) analysis is correct and financial distress imposes significant costs on shareholders
• Debt financing has a cost, financial distress, and a benefit, capturing the debt tax shield
• This observation points to a simple potential explanation for cross-section variations in corporate leverage

THE TRADE-OFF THEORY

• Firms trade off the value of the tax shield against the increasing expected costs of bankruptcy until the two effects are the same at the margin
• If this theory is correct, firms with high distress costs should have lower leverage, e.g.,
  • Liquid second-hand markets for corporate assets (say, aircraft)
  • More tangible assets (for example, buildings)
  • Low market-to-book ratios, i.e., low stock price relative to the replacement cost of assets.
• firms with low distress costs should be more levered

TRADEOFF THEORY: PLAUSIBILITY

• The tradeoff theory seems plausible because at least one of its drivers, taxes, appears to have a profound influence on firms' leverage policies
• MacKie-Mason (1990) and Givoly, Hayn, Ofer, and Sarig (1992) show that aggregate corporate debt issuance is responsive to changes in tax law
• However, Graham, Leary, and Roberts (2015) argue that other macro economic factors offer explain much more of the time series variation in average corporate debt levels

BASIC SETTING FOR TRADEOFF MODELS

• Capital markets are perfect and complete except for corporate taxes and financial distress costs
• Firms' assets, and operating cash flows are exogenous and not affected by capital structure
• Capital structure changes involve swapping debt for equity or equity for debt
  • Example: issue debt and use the proceeds of the issue to pay dividends or repurchase shares
  • Example: repurchase debt and fund debt repurchase by issuing equity

OPTIMAL TRADE-OFF POLICY

• If the firm issues debt with value D, the wealth of the shareholders will equal the value of the levered firm, $V_L(D)$, less the value of the new debtholders' claim, D, plus the proceeds from the debt issue.
• By assumption, capital structure does not affect operating policy or assets
  • So, the value of the levered firm equals the value unlevered firm plus the value of the tax shields.

TRADE-OFF PERSPECTIVE

• Firm investment and real operating policy are unaffected by capital structure, so $V_U$ is not affected by D
• Thus, the objective of the owners is to maximize $TS(D) - BC(D)$ over D
• Unless the optimal debt level, $D^*=0$, maximisation requires

$$ TS'(D^*) = BC'(D^*) $$

• Trade off models of capital structure specify environments,
  • economic environment, e.g., cash flow distributions, asset pricing regimes
  • legal environment, e.g., tax and bankruptcy resolution systems
• Given the specified environment, they identify capital structure polices that maximize TS - BC over capital structure polices
• Ideally, a tradeoff model should produce result like this

OPTIMAL LEVERAGE WITH TAXES AND COSTS OF FINANCIAL DISTRESS

BUT ITS NOT SO EASY

• It might seem that it is fairly straightforward to develop trade-off theory models that account for firms' capital structure and produce reasonable optimal debt levels
• However, there are some difficulties to surmount
  • Only the interest component of debt repayment is tax deductible.
  • The more debt a firm issues the higher its default risk and thus higher nominal interest rates
  • Higher the nominal interest rate (YTM) imply more tax deductions generated by debt
  • Nominal interest rate affects value of debt and value of debt affects nominal interest rate, messy
  • This problem can be surmounted by assuming all debt repayments are interest repayments, i.e., perpetual debt
  • But perpetual debt requires an infinite time horizon
  • But, in a multi-period/infinite period context, it is not clear when firms will default
  • Shareholders might want want to reach into their own pockets (or issue equity) to cover debt payments.

LELAND (1994): MOST IMPORTANT TRADEOFF THEORY PAPER

Leland, H. E. (1994). Corporate debt value, bond covenants, and optimal capital structure. Journal of Finance, 49(4), 1213-1252.

Leland develops a very elegant continuous time tradeoff model with the same tools Black and Scholes used to develop option pricing models.

LELAND'S PROGRAMME

• Specify a Black/Scholes style economy (used in option pricing models)
• Show that no-arbitrage conditions in this economy imply that debt value satisfies a differential equation.
• Solve the differential equation for debt value
• Use the debt value to determine the value of tax shields and the cost of bankruptcy
• Characterize optimal capital structures

LELAND (1994): SPECIFICATION

• Continuous-time, infinite date economy, instantaneous risk-free rate of interest is constant and equal to r.
• firm whose unlevered value, V, is exogenous and random, changing through time.
$$ V_t = V_0 + \int_0^t \mu ds + \sigma \int_0^t V_s dW_s; \quad \sigma > 0 $$
• The value of the unlevered firm can also be expressed in this more intuitive if a bit more dodgy notation
$$ \frac{dV_t}{V_t} = \mu dt + \sigma dW_t $$

WHAT IS W?

• W represents a Weiner process (aka Brownian motion)
• A Weiner process has the following characterizing properties
  • $W_0 = 0$
  • $W_t - W_s$ is Normally distributed with mean 0 and variance $t-s$
  • The paths of the process are continuous
  • the changes in the process (increments) are independent
• In other words, past changes tell you nothing about future changes.

INTUITION

• at each instant the return on unlevered firm, $dV/V$ is the sum of a non-random component and a random component.
  • The non-random component: $\mu dt$, is called the drift term. The larger $\mu$ the larger the expected return.
  • The random component: $\sigma dW_t$, $\sigma$ is called the volatility term. The larger $\sigma$ the more uncertain the return.

LELAND (1994): ECONOMY

• V, or an asset perfectly correlated with V is traded in the financial market.
• Debt takes the form of perpetual bonds, continuously paying out cash flows to bondholders at the rate of C until bankruptcy occurs.
  • C is called the coupon rate.
• When bankruptcy occurs, debtholders receive $(1-\alpha)V$ and stockholders receive nothing.
• Debt is permanent-no new debt can be issued after time 0. This implies that, post-bankruptcy, firms cannot issue debt.

SOLUTION FOR THE VALUE OF DEBT

Solution: The value of debt is given by

$$ D(V, V_B) = \left(\frac{C}{r}\right) \times (1 - p_B(V, V_B)) + (1-\alpha)V_B \times p_B(V, V_B) $$ $$ p_B(V, V_B) = \left(\frac{V}{V_B}\right)^{-\frac{2r}{\sigma^2}} $$

INTERPRETATION

• V: the value of the firm
• D: the value of the firm's debt
• $V_B$ the value of the firm at which the equity holders will declare bankruptcy.
• $p_B$: $0 \le p_B \le 1$, $p_B$ represents the present value of a security that pays $1 when the firm goes bankrupt.
• $1-p_B$: represents the present value of is a security that makes continuous payment of rdt until the firm declares bankruptcy.

LELAND (1994): DETERMINING THE VALUE OF TAX SHIELDS AND BANKRUPTCY COSTS

• Tax shields of $\tau C$ are received as long as the firm is solvent, thus
$$ TS(V, V_B) = \tau(1 - p_B(V, V_B))\frac{C}{r} $$
• Bankruptcy costs occur the first time the firm enters bankruptcy. The realised costs of distress are $\alpha V$,
$$ BC(V, V_B) = \alpha V_B p_B(V, V_B) $$

VALUATION OF THE FIRM AND EQUITY

• Firm and equity are valued as residuals
  • Firm: $v(V, V_B) = V + TS(V) - BC(V)$
  • Equity: $E(V, V_B) = v(V, V_B) - D(V, V_B)$

LELAND (1994): $V_B$ - THE BANKRUPTCY POINT

• Shareholders must pay bondholders Cdt at every instant dt as long as the firm is not bankrupt
• At any point in time t, shareholders can declare bankruptcy
• If shareholder declare bankruptcy, ownership of the firm is transferred to the bondholders
• shareholders no longer make interest payments to bondholders
• Shareholders follow a rule: If at date t, firm value is greater than $V_B$, do not declare bankruptcy
• As soon as firm value reaches $V_B$, declare bankruptcy
• How do shareholders determine $V_B$? two possibilities, ex ante or ex post.

EX ANTE VS. EX POST

• Ex ante decision: You commit to following a rule. You will follow the rule even if at the time you have to apply the rule you do not want to follow the rule.
• Ex post decision: At each point in time to decide what you want to do. In general, it ex ante and ex post decision rules will be different.
• Assuming decisions are made ex post seems more reasonable.
• However, solving for the optimal ex post rule is frequently harder.

EX ANTE BANKRUPTCY DECISION

• Stockholders decide at date 0, the bankruptcy point, $V_B$
• Stockholders pick bankruptcy point to maximise the value of equity
• First-order condition: $\frac{\partial E}{\partial V_B}|_{V_B=V_B^*} = 0$
• Solution: $V_B^* = \frac{(1-\tau)C}{r + (1/2)\sigma^2}$

EX-POST BANKRUPTCY POINT

• The point at which shareholders will actually exercise the bankruptcy option if they have to make the decision in real time
• Leland shows that in his model the ex ante bankruptcy point is the same as the ex post bankruptcy point.

LELAND (1994): ENDOGENOUS BANKRUPTCY

• Endogenous means determined inside the model.
• Leland now substitutes in the optimal bankruptcy point, i.e., he sets

$$ V_B = V_B^* = \frac{(1-\tau)C}{r+(1/2)\sigma^2} $$

• This results in stared versions of $p_B$, called $p_B^*$

VALUATION WITH ENDOGENOUS BANKRUPTCY

$p_B^*$, $TS^*$, $BC^*$

$$ p_B^* = \left(\frac{(1-\tau)C}{V(r+(1/2)\sigma^2)}\right)^{\frac{2r}{\sigma^2}} $$ $$ TS^* = \tau(1-p_B^*)\frac{C}{r} $$ $$ BC^* = p_B^* \alpha V_B^* $$

• Now that Leland has expressions for the tax shield, TS, and the cost of bankruptcy, BC, he can find the optimal choice of the coupon rate, C, which we call $C^*$.

CHARACTERIZING OPTIMAL CAPITAL STRUCTURES, $C^*$

• The value of the firm v, as shown above, is given by $v=V+TS-BC$

• Unlevered firm value, V is not affected by C, so the optimal C is determined by the first order condition

$$ \frac{dTS}{dC} - \frac{dBC}{dC} = 0 $$

OPTIMAL CAPITAL STRUCTURE

• Pick the debt service level $C^*$ that equates the marginal costs and benefits of debt finance

• The first order condition is

$$ [\frac{\tau}{r}](1-p_B^*) - [\frac{2\tau}{\sigma^2} + \alpha \kappa(1+\frac{2r}{\sigma^2})] p_B^* = 0 $$

K is a constant defined in the paper.

LELAND (1994): OPTIMAL C

FIGURE: Firm value v and the coupon payment, C. In the figure $\tau=0.35$, $\sigma=0.50$, $\alpha=0$ and unlevered firm value $V=1$.

LELAND (1994): COMPARATIVE STATICS: DETERMINANTS OF CAPITAL STRUCTURE

Using the first-order condition, Leland can compute the optimal coupon for any choices of the parameters, V, $\tau$, $\sigma$, and $\alpha$. Plugging the optimal C, $C^*$, to the equations for the value of debt, D and the value of the firm v, Leland can compute the debt-to-value ratio, $D/v$. He finds that

• The debt-to-value ratio $D/v$ is decreasing in volatility $\sigma$
• The debt-to-value ratio is increasing in the corporate tax rate, $\tau$
• The debt-to-value ratio is decreasing in the cost of financial distress, $\alpha$
• The debt-to-value ratio is constant in unlevered firm value, V.

THEORY AND REALITY: EMPIRICAL RESEARCH

• To what extent do theories of capital structure explain actual firm capital structures?
• Most empirical research on this question has taken a "horse race approach"
• The two horses are the pecking order theory (Myers and Majluf) and the trade-off theory (Leland 1994 and others)
• However, empirical research has also lead to another hypothesis: the market timing theory (discussed below)

EMPIRICAL IMPLICATIONS OF TRADE-OFF THEORY

• Because issuing new securities entails significant issuance costs, firms will not immediately adjust their capital structure to the tax and bankruptcy cost optimal level, instead
  • They will keep the firm's debt ratio within a band around the optimal debt-to-value ratio.
  • The width of the band will depend on the transaction costs of issuing securities
  • When the actual ratio reaches the boundary of the band, firm will readjust to the optimal ratio
• The drivers of capital structure are the optimal debt ratio (determined by volatility, profitability, costs of financial distress and taxes) and the transactions costs from new issues

EMPIRICAL IMPLICATIONS OF PECKING ORDER THEORY

• Myers and Majluf argue that firms follow a pecking order when they choosing their capital structures:
  • Because of bankruptcy costs and other costs associated with financial distress firm will sometimes issue equity, but equity will be a last resort.
  • Firms will first use internal funds
  • Then finance with debt, and when debt finance becomes too expensive
  • Issue equity
• Capital structure is driven by a firm's real investment opportunities and desire to avoid external finance, especially equity finance
• A prime driver of the leverage ratio is the net financing deficit, the difference between the funds required to make real investments and the firm's financial slack

PROBLEM WITH TESTING THE THEORIES

• Market timing: Baker & Wurgler(2002) report that debt ratios are strongly negatively related to past market timing opportunities.
  • Market timing opportunities: high Market Value/Book (accounting) value ratios.
• Firms issue equity when the Market/Book ratio is relatively high
• So firms with high past stock prices relative to accounting valuations use less debt financing
• Welch (2004) shows that 40% of the change in firm debt ratio's can be explained by changes in stock prices; 60% by active adjustments by firms.
  • But the target-debt ratios explain only a small fraction of active adjustments

DEBT RATIOS AND THE TRADEOFF THEORY

• Welch's and Baker and Wergler's results show that the debt ratio is not entirely determined by the firm's capital structure policy
• The debt ratio also depends on
  • the current market price of the firm's stock, and
  • perhaps past stock prices because of attempts of the firm to time the equity market
• So, even if the trade-off theory is mostly correct, debt ratios may not be the best measure of firms' tradeoff-theory-motivated capital structure adjustment
  • Using actual debt or equity issuance/repurchase events would avoid Welch's and Baker and Wergler's critique

EMPIRICAL EVIDENCE: LEARY AND ROBERTS

Leary, M. T., and Roberts, M. R. (2005). Do firms rebalance their capital structures? Journal of Finance, 60(6), 2575-2619.

• Leary and Roberts attempt to test alternative theories of capital structure determination by examining what leads firms to make capital structure adjustments.
• They estimate a "hazard rate model" of capital structure adjustment
• Adjustments are substantial changes in the amount of debt and equity outstanding

HAZARD RATE MODEL

• What is a "hazard"? A 'hazard" is a change in capital structure

• In their empirical model, the likelihood of a hazard depends on
  • FIRM-SPECIFIC EFFECT: some firms may be more reluctant to make capital structure changes
  • TIME: the amount of time that has passed since the last adjustment
  • FACTORS: the variables that the pecking order, tradeoff, and market timing models have identified as being important

HOW DOES A HAZARD MODEL WORK? DATES AND SPELLS

Sample path for capital structure adjustments for firm i:

WHAT IS THE HAZARD RATE?

• The hazard rate - Let $\tilde{T}$ be the time between adjustments of the firm's capital structure, then the hazard rate associated with $\tilde{T}$ is defined by

$$ h(t) = \lim_{m\to 0} \frac{\mathbb{P}[\tilde{T} \in [t, t+m) | \tilde{T} > t]}{m} $$

• If the hazard rate is constant then, the time from last capital structure has no effect on the likelihood of the next adjustment
• If the hazard rate is increasing then the more "stale" the capital structure, the more likely the firm will make an adjustment
• If the hazard rate is decreasing then a "fresh" capital is more likely to be adjusted.

THE HAZARD RATE MODEL

• The estimation model used to determine the corporate hazard rate for capital structure adjustment is

$$ h_{ij}(t|\omega_i) = \omega_i h_0(t) \exp\{x_{ij}(t)'\beta\} $$

• In this estimation model
  • $h_{ij}(t|\omega_i)$ is the hazard rate for firm i over spell j
  • $x_{ij}(t)'\beta = \sum_{k=1}^K x_{ijk}(t)\beta_k$, where k indexes a set of factors that might effect capital structure and $\beta_k$ measure the effect of factor k.
  • $\omega_i$ is a firm-specific random factor
  • $h_0$ is the hazard-rate estimated by the model

ECONOMETRIC ASSUMPTIONS

• $h_0$ is common to all firms, estimated both as step function and cubic polynomial
• Firm specific eccentricity is captured by $\omega_i$, it acts like a firm dummy in that it captures firm specific fixed effects
• The effect of the factors, x, on capital structure measured by $\beta$ is constant across time and firms.
• The model is estimated using maximum likelihood
• Authors report the hazard impact HI of the factors, where HI is $(\exp[\beta]-1) \times 100$, measures the % shift in the hazard curve induced by one unit change in the factor.

HAZARD RATE ESTIMATES

IMPLICATIONS OF HAZARD RATES

• Estimated hazard rates are decreasing, thus the time from the last capital structure adjustment reduces the likelihood of a capital structure adjustment now.
• Inconsistent with optimising the debt ratio under fixed adjustment costs. Why?
  • Under a fixed target, firms would allow capital structure to drift until it reached a fixed divergence level and the push capital structure back to the target ratio
  • This would lead to an increasing hazard rate
• Actual data consistent with multiple partial adjustments clustered in time or no fixed target ratio.

DETERMINANTS OF LEVERAGE CHANGES

	Leverage Increase		Leverage Decrease
	Estimate	HI(%)	Estimate	HI(%)
Size	-0.0031**	-0.31	-0.0094**	-0.94
MA/BA	0.0379*	3.87	0.1868**	20.54
CapEx(t+1)	0.0804**	8.37	0.0021	0.21
Cash	-0.0278**	-2.74	-0.0152**	-1.51
DepAmort	-0.06**	-5.82	0.0417	4.26
Tangibility	-0.0034**	-0.34	-0.0116**	-1.16
Profitability	-0.0245**	-2.42	-0.0004	-0.04
Volatility	0.0072	0.72	0.0221**	2.24
Z-score	0.0000	0.00	-0.0008**	-0.08
Selling expense	0.0004	0.04	0.0013*	0.13
Equity return	0.0004	0.04	0.0023**	0.23
ΔLeverage	-0.0057**	-0.57	0.0057**	0.57
Leverage	-0.0076**	-0.76	0.0159**	1.60
LeverDown	0.3855**	47.03
LeverUp			0.5023**	65.26

IMPACT OF FACTORS

• Tradeoff theory Tax/Bankruptcy factors affect the intensity of capital structure adjustments
  • One anomalous coefficient: negative effect of profit on leverage increases seems inconsistent with tax/bnk. model
• But pecking order factors also matter, e.g.,
• Overall, leverage policy seems consistent with both the standard pecking order and bnk./tax considerations,
• Equity issuance is also strongly effected by the market/book ratio which may indicate either
  • market timing
  • increased investment in response to high market valuations (feedback from the market)
• Leverage and equity policy appear to respond to different factors, 1 more dollar of debt is not a perfect substitute for 1 less dollar of equity.

SUMMARY: TRADEOFF THEORY

• It is possible to formulate elegant dynamic tradeoff models of capital structure (Leland (1994) and its descendants)
• Variables identified in these model have explanatory power
• However, other factors like financing needs also explain much of the variation in leverage
• The evidence for firms systematically adjusting capital structure to maintain a fixed leverage ratio is rather weak

SUMMARY: PECKING ORDER THEORY

• It is possible to formulate elegant models of capital structure rooted in asymmetric information and real investment opportunities (Myers and Majluf (1984) and its descendants)
• Variables identified in the pecking order model, especially real investment opportunities, have explanatory power for corporate leverage changes
• However, other variables clearly related to taxation like depreciation/non debt tax shields also affect capital structures.
• Stock issuance when stock prices are high (market timing) seems inconsistent with firms always viewing equity financing as a last resort.