18. Capital Structure: Trade-Off Theory and Market Timing

As discussed in Chapter 2, classical trade-off theory says there are benefits and costs of debt (higher leverage). This section is empirical evidence on the tax benefit of debt.

18.1.1 Measuring the tax benefit of debt: Graham (2000). Graham (2000) measures the tax benefit by defining the kink of a firm's tax function, concluding that most firms are not even close to that kink.

• Define the kink: Graham (2000) models the income process as a random walk with drift,

$$\Delta\text{EBIT}_{it}=\mu_i+\xi_{it},\quad \mu_i\ge0 \tag{18.1}$$

where \(\text{EBIT}_{it}\) is "earnings before interest and taxes" of firm \(i\) in period \(t\), close to operating income; (18.1) assumes capital structure doesn't affect the operating process (an MM (1958) flavor). The tax shield is determined by:

$$\text{Operating Income}=\text{Revenue}-\text{COGS}-\text{SG\&A}-\text{Depreciation}$$

$$\text{Pre-tax Income}=\text{Operating Income}-\text{Interest Expense}$$

$$\text{Tax Shield}=\text{Interest Expense}\times\tau_c\quad(\text{if Pre-tax Income}>0)$$

\(\tau_c\) is the corporate tax rate. When pre-tax income \(\le0\), the tax benefit is through tax-loss carryforwards, more complicated and generally marginally smaller than the constant marginal benefit in the pre-tax-income $>0$ region; for pre-tax income $>0$ the marginal benefit per dollar of interest is simply \(\tau_c\). Plotting "percent of actual interest deduction" (x) against "marginal tax benefit" (y), the tax function is flat then downward-sloped past a kink (future income-exhaustion states) — see Figure 18.1. The distance to the kink is determined by the current interest payment (higher → closer), operating income (lower → closer), and income volatility (higher → closer, due to uncertainty in future realization).

• Findings: most firms are far to the left of their kinks = lack of aggressiveness; levering to the kink would add 15.7% value for the average firm (7.3% computing DTS with personal taxes as in (2.1)), still surprisingly big.
• Comments: this only measures the benefit of debt, not its costs; costs are not well-known (Graham-Harvey 2001 survey 392 CFOs on factors affecting debt issuance, Figure 18.2); only tax benefit, not other benefits; only the marginal effect, possibly missing factors affecting the first-dollar decision. MacKie-Mason (1990) uses a probit (discrete choice) to show firms close to or already tax-exhausted (with TLCF) are less likely to finance with debt. Identification problem: evidence typically comes from phases of tax-rate changes, but those are accompanied by tax-base changes, complicating the estimate; Panier et al. (2015) gives cleaner estimates via the Belgium 2006 experiment.

In 2006 Belgium introduced an equity subsidy: firms could deduct \(rE\) from taxable income (\(r\) a fixed number, \(E\) the book value of equity), regardless of equity payout policy. Panier et al. (2015) exploit this to estimate the effect of the tax benefit on financing.

Key questions: (1) Did Belgian firms' capital structure respond? (2) Is the leverage change around 2006 the tax benefit or confounding? (3) Differences in Belgian firms' responses? (4) If leverage changes, what financing strategies do equity-tilting firms use?

Empirical design (DiD):

$$E_{it}=\alpha+\beta\text{TREAT}_i+\gamma\text{POST}_t+\delta\,\text{TREAT}_i\times\text{POST}_t+\boldsymbol\psi\cdot\mathbf X_{it}+\phi_i+\eta_t+\xi_{it}+\varepsilon_{it}$$

\(E_{it}\) = equity-to-asset ratio; \(\text{TREAT}_i=1\) if Belgium, \(0\) if a neighboring country; \(\text{POST}_t=1\) after 2006; \(\mathbf X_{it}\) controls; \(\phi_i\) country FE, \(\eta_t\) time FE, \(\xi_{it}\) country-time FE. Clean identification: country FE address the two groups being in different industries; a current tax-structure variable controls for concurrent tax reforms; the sample only includes firms within 100/250/500 km of the Belgian border for comparability; standard errors clustered at the country level (per (17.12)).

Results: the subsidy → higher equity-to-asset ratio of Belgian firms relative to controls within two years; both new and incumbent firms raise the ratio (incumbents rebalance toward equity after 2006, new firms rely heavily on equity after 2006); large and new firms respond more strongly; the higher ratio comes from new equity issuance and higher absolute equity, not from reducing non-equity liabilities or changing payout; the effect is strong for large standalone firms, not just MNC subsidiaries.

To understand the sensitivity of capital structure to tax incentives, we study MNC behaviors. MNC profit shifting from high-tax countries to tax havens is increasingly severe (Figure 18.3, Zucman 2014). Two types: physical (tangible capital/assets transferred abroad, involving local production and employment) and non-physical (no actual capital shifted, profits virtually shifted via legal/financial procedures, no local production/employment).

Desai et al. (2004): MNC subsidiaries use more debt, especially from the internal capital market, in foreign countries with underdeveloped financial markets. Using MNCs as "laboratories" (a single MNC in different tax environments cleanly illustrates the effect of local tax rates on subsidiary capital structure): a typical MNC has 10% higher local tax rates ↔ 2.8% higher debt/asset ratios; internal capital market borrowing (among subsidiaries) is sensitive to taxes; external financing is sensitive to local financial development (subsidiaries in underdeveloped markets less likely to use external debt; IV regression shows internal borrowing substitutes for 75% of reduced external borrowing of subsidiaries in underdeveloped countries).

Torslov et al. (2018): more tax-avoiding strategies are available beyond debt. Studying MNC profit shifting from a different perspective opens a new way of thinking about the benefits of debt — nowadays firms have strategies like profit shifting to avoid high taxes, so we must think more carefully about benefits of debt other than the tax shield (the tax shield is less important now, a new direction in capital structure research). Results: 40% of MNC profits shift to tax havens yearly; in tax-haven countries foreign subsidiaries are more profitable than local firms, while in non-tax-haven countries they are less profitable than local firms (high returns on capital from low tax rates drive the higher profitability of foreign firms in tax havens, Figure 18.4); for US MNCs, tax-haven subsidiaries are 5–7 times more profitable than non-tax-haven ones (Figure 18.5); high-tax tax authorities fail to combat this → persistence in profit shifting.

Trade-off theory says debt has costs = financial distress. This section gives empirical evidence. A dichotomy: direct (lawyer's fees and other bankruptcy-process costs) and indirect (costs of high leverage from operations, i.e. the debt overhang and asset substitution/risk shifting of §2.6; risk shifting is always on the off-equilibrium path with little empirical evidence, but introducing contracts/capital structure to prevent it is still important).

Identifying the financial-distress effect suffers the selection bias of (17.1), coming from the economic-distress effect. Let \(J_i=1\) if firm \(i\) suffers financial distress, \(J_i=0\) otherwise, with \(V_{1i}/V_{0i}\) the firm value with/without financial distress. The directly capturable effect \(\mathbb{E}[V_{1i}\mid J_i{=}1]-\mathbb{E}[V_{0i}\mid J_i{=}0]\) (18.2) suffers bias:

$$\mathbb{E}[V_{1i}\mid J_i{=}1]-\mathbb{E}[V_{0i}\mid J_i{=}0]=\underbrace{\mathbb{E}[V_{1i}\mid J_i{=}1]-\mathbb{E}[V_{0i}\mid J_i{=}1]}_{\kappa}+\underbrace{\mathbb{E}[V_{0i}\mid J_i{=}1]-\mathbb{E}[V_{0i}\mid J_i{=}0]}_{\text{selection bias}<0} \tag{18.3}$$

The bias is negative (distressed firms often have economic troubles, lower counterfactual \(V_{0i}\)), so (18.2) overestimates the negative effect. Challenge: separate financial from economic distress. Altman (1984) groups by Z-score: for each Z group, estimate expected profits (regression + analyst forecasts) using data three years before bankruptcy, then compute actual − expected; the low-Z group (high bankruptcy probability) averages \(0.98\)/share vs \(0.08\)/share for the high-Z group, so high-bankruptcy-probability firms tend to underperform. But Z is accounting-based and also subject to economic distress; grouping by Z doesn't tease out financial from economic distress (low-Z firms may underperform even at 100% equity), so Altman's (1984) estimates are not clean. The Z-score (Altman 1968):

$$Z=1.2A+1.4B+3.3C+0.6D+0.999E$$

\(A=\) working capital/total assets, \(B=\) retained earnings/total assets, \(C=\) EBIT/total assets, \(D=\) equity's market value/total assets, \(E=\) total sales/total assets.

Use highly leveraged transaction (HLT) data to isolate financial from economic distress, then estimate the effect of financial distress on performance.

Data: 136 HLTs (LBOs and MBOs); focus on the 31 that faced financial distress and defaulted. Separating financial from economic distress: these 31 are highly leveraged with severe financial distress — average coverage \(\text{EBITDA}/\text{Interest Expense}=0.97\), much lower than the industry median of 4, can hardly pay interest from operations, high default risk; but claimed not economically distressed (the crucial assumption) — average operating margin \(\text{EBITDA}/\text{Sales}=9.8\%\), good and above the industry median. So the authors attribute the subsequent performance effect entirely to financial distress.

Two analyses: (1) Overall HLT effect: value change from pre-HLT to post-distress-resolution, industry-adjusted mean return 12% (median 4%), market-adjusted mean 8% (median 5%) — HLTs create overall positive value. (2) Financial-distress effect: value change from the end of the year before distress (value at distress) to post-distress-resolution (value at resolution). The value at distress (HLTs not publicly traded then / bought out) is estimated as

$$\text{cash}+\big(\text{industry median multiple of }\tfrac{\text{Total Capital}}{\text{EBITDA}}\big)\times\text{EBITDA of HLTs}$$

and the value at resolution (mostly publicly traded again, robust excluding exceptions, interim payments to capital included). Median estimates: financial distress cost 20.7% industry-adjusted, 24.7% market-adjusted; mean estimates 9.7% and 9.8%.

Challenges: though smaller in magnitude than Altman (1984), it could still be overestimated (economic distress may not show up at the end of the year before distress, underestimating its contribution); PE firms in an LBO may inefficiently cut costs to push up the price to sell high, leading to long-term decline — the "financial distress effect" partly caused by such detrimental behaviors, nothing to do with capital structure; the data spans a boom-bust cycle, partly explaining the price changes, biasing the estimate. So this places an upper bound on the financial-distress effect, at most ~20% of firm value.

Hortacsu et al. (2013) (durable goods with warranty): logic — a durable-goods producer in financial distress → consumers worry the warranty won't be honored → stop buying → poor later performance (from lost consumer confidence). Data: used cars at wholesale auctions + manufacturer CDS (credit default swap; higher CDS spread → higher default probability). Specification:

$$p_{ijklt}=\beta\,\text{CDS}_{it}+\gamma\,Z_{ijklt}+\delta\,(\text{CDS}_{it}\times Z_{ijklt})+\boldsymbol\Gamma\cdot\mathbf X_{ijklt}+\alpha_{ijkT}+\varepsilon_{ijklt} \tag{18.4}$$

\(i\)=manufacturer, \(j\)=car model, \(k\)=auction region (8 US regions), \(l\)=specific auction, \(t\)=transaction day, \(T\)=week; \(p\)=auction price, \(\text{CDS}_{it}\)=manufacturer CDS spread, \(Z\)=car-specific measure of future service flows (warranty indicator, mileage quantile, condition), \(\alpha_{ijkT}\)=car-region-week FE. Use daily high-frequency variation to isolate the immediate effect, the interaction \(\text{CDS}\times Z\) to isolate the warranty channel, and saturate with controls. Results: a 1 bp rise in CDS spread → a 6.8 cent drop in used-car auction prices, stronger for cars with longer expected service life, robust. Challenge: doesn't rule out economic distress (CDS rises not only from financial distress), so it estimates "the effect of corporate distress on durable-good prices," not "financial distress."

Brown and Matsa (2016) (attractiveness to job applicants): intuition — candidates work at a non-distressed firm for a lower wage (implicit unemployment insurance, less likely fired from bankruptcy); a distressed firm needs a wage premium to attract young talent. Identification difficulty: separate the loss of attractiveness into supply side (applicants less attracted) and demand side (distressed firms may shrink scale and labor demand); employment/wage data cannot separate them (both affected by both). Strategy: use job-application data for each open position (supply side only, demand fixed); focus on 78 financial-service firms April 2008–Dec 2009 (volatile months provide variation); proprietary online-platform data (postings + applicants). Specification:

$$N_{itsj}=\alpha+\beta\,\text{CDS}_{it}+\phi_{itsj}+\varepsilon_{itsj}$$

\(i\)=firm, \(t\)=month, \(s\)=state, \(j\)=job title; \(N\)=number (or log) of applications, \(\text{CDS}_{it}\)=quantile indicators of CDS price (or CDS itself), \(\phi_{itsj}=\{\phi_i,\phi_t,\phi_s,\phi_j,\phi_{itsj}\}\) detailed FE. Results: firms attract significantly fewer applicants when distressed, a 1000 bp CDS rise → 20% fewer applicants per position; demand side ruled out (no evidence postings change target recipients or reduce posted wage). Challenge: CDS measures default probability (a good "corporate distress" measure, not necessarily "financial distress"), so it measures how "corporate distress" affects attractiveness.

18.3.1 Evidence against trade-off theory. Graham (2000) finds "large, liquid, profitable firms with low expected distress costs use debt conservatively," against trade-off theory (such firms should use debt aggressively). Rajan-Zingales (1995) find correlations the static trade-off theory can't justify: leverage rises in size, rises in fixed assets, falls in market-to-book and ROA. So alternatives arise: (1) the pecking order theory (Myers-Majluf 1984, §4.2) — under information asymmetry firms prefer debt to signal good quality, with a financing hierarchy (internal funds → debt → equity), reconciling the anomaly that profitable, liquid firms issue less debt; (2) market timing.

18.3.2 Current capital structure as a cumulative outcome of past timing: Baker and Wurgler (2002). Managers time the market — issue stock when the price is high relative to book and past market value; this aims to exploit temporary fluctuations in the cost of equity relative to other capital; so a firm's current capital structure is the cumulative outcome of past attempts to time the equity market. Data: all COMPUSTAT firms 1968–1999. Supporting evidence — decompose the leverage change:

$$\frac{D_t}{A_t}-\frac{D_{t-1}}{A_{t-1}}=-\underbrace{\frac{e_t}{A_t}}_{\text{Part 1}}-\underbrace{\frac{R_t}{A_t}}_{\text{Part 2}}-\underbrace{E_{t-1}\!\left(\frac1{A_t}-\frac1{A_{t-1}}\right)}_{\text{Part 3}} \tag{18.5}$$

\(D\)=debt, \(A\)=asset, \(E\)=equity, \(e_t\)=newly issued equity, \(R_t\)=retained earnings (all period \(t\)); Part 1 = equity-issuance channel, Part 2 = retained-earnings channel, Part 3 = residual channel. Regressing each part on market-to-book (and other variables): higher market-to-book → higher equity issue; retained earnings not significantly affected; asset growth positively related to market-to-book (so higher market-to-book → more negative \(\frac1{A_t}-\frac1{A_{t-1}}\) → higher leverage per (18.5)) — establishing that market-to-book affects leverage through equity issuance. They also document that market-to-book fluctuations have persistent effects on leverage (past market-to-book significantly affects current leverage even controlling for recent values). Conclusion: after fitting trade-off, pecking order, and market timing, market timing is the most reasonable theory for the persistent effect of market-to-book on leverage. But this is contested by non-behavioral follow-ups — market timing can still be generated by the dynamic trade-off theory (Hennessy-Whited 2005, §2.6.5) producing the negative correlations Baker-Wurgler document.