## John R. Graham, The Journal of Finance, Volume LV, No. 5 Oct 2000 pp 1901-1941

## Introduction

The question being asked here is “How do tax incentives affect firm value?” We know from our previous readings that there is a tax advantage to issuing debt rather than equity, because interest payments are deductible from taxable earnings. We would think that because of this, firms would lean much more heavily towards debt. What is the quantification of this benefit?

So what is the contribution of this paper? Graham states them directly: 1) quantifying the tax benefit by determining a tax function and then integrating to come up with the area under it, 2) use the tax function to determine how aggressive firms are in their use of debt, and 3) estimate how much firms could add to their value by increasing their debt level.

The third point is clearly the key contribution of the paper. To give away the end of the story in advance, Graham determines that firms are leaving a lot of money on the table. The typical firm could add 15.7% to its value by increasing its debt load (without adding any significant risk of distress).

## The Costs and Benefits of Debt

#### Estimating the Tax Costs and Benefits of Debt

The traditional way of calculating the net benefit of directing a dollar to investors as interest rather than equity is:

$(1-\tau _{\rm P})-(1-\tau _{\rm C})(1-\tau _{\rm E})$ Where

$\tau _{\rm P}$ = Personal Income Tax Rate

$\tau _{\rm C}$ = Corporate Tax Rate

$\tau _{\rm E}$ = Personal Capital Gains Tax Rate

Estimating marginal tax rate (MTR) for different levels of hypothetical debt levels as a % of the firms’ actual debt levels: 0%, 20%, 40%, 60%, 80%, 100% (actual debt), 120%, 160%, 200%, 300%, 400%, 500%, 600%, 700%, and 800%. To forecast earnings, Graham uses his 1996 model that states that earnings follow a pseudo-random walk with drift:

$\Delta EBIT_{\rm it}= \mu _{\rm i}+ \epsilon _{\rm it}$

Where $\mu _{\rm i}$ = the maximum of $\Delta EBIT_{\rm i}$ and zero and $\epsilon _{\rm it}$ is a normally dist. error with mean of zero and same variance as $\Delta EBIT$

To forecast earning for years t+1 through t+18, Graham draws 18 random values for ε and plugs them into the above equation. The tax bill is calculated using the standard corporate tax table for that year. Then $10,000 is added to earnings and the tax bill is recalculated. Then the difference between the two tax bills is divided by $10,000 yielding the marginal tax rate (MTR) for an additional dollar of earnings. This is done 50 times and then averaged for each firm, for each year of the study, in order to incorporate earnings uncertainty.

Graham estimates present value benefit at EOY1 for a firm by using historical data through year 1 to derive an interest deduction benefit function for EOY2 and integrates to find area under the curve (the benefit). Still using data through EOY1, projects the function for an additional year (through EOY3), and integrates to find the benefit. Integrate, rinse and repeat through 15 years.

#### Nontax Explanations of Debt Policy (Here are some of his variables)

Expected Costs of Financial Distress – Trade-off theory that firms are averse to debt when the expected costs of financial distress are high. Ex ante probability of distress measured by:

(EBIT + Sales + RE + Working Capital) / Total Assets

Investment Opportunities - Measured by Tobin’s q and approximated by:

(Preferred and Common Stock + LTD + Net Short-term Liabilities) / Total Assets

Cash Flows and Liquidity – Measured by quick ratio and current ratio.

Managerial Entrenchment and Private Benefits – uses 6 variables to measure

% of common shares owned by CEO

Vested options held by CEO as a % of common shares

Log of number of years as CEO

Log of number of directors

% of outside directors

% of common shares held by non-CEO board members

Product Market and Industry Effects

Industry concentration

Product uniqueness – uses SIC codes to identify industries with unique products (codes in range 340-400, i.e. chemical, computer, or aircraft)

Cash flow volatility – industry with cyclical cash flows

Other Factors that Affect Debt Policy

Financial flexibility – looks at acquisitions and capital expenditures

Informational asymmetry – do they pay dividends (non-dividend firms subject to large asymmetries.

Size – market value of firm and natural log of real sales

Asset collateral – PPE-to-assets

## Data and Measurement Issues – Data Source is COMPUSTAT

### Tax Variables

$\tau _{\rm E}$ = [d+(1-d)g$\alpha$]$\tau _{\rm P}$ (note: sample mean is 12%)

Where:

d=dividend payout ratio

g=proportion of long term capital gains that are taxable

∝ =benefit of deferring capital gains

$\tau _{\rm P}$ = (R$_{\rm taxable}$ - R$_{\rm taxfree}$)/R$_{\rm taxable}$

### Using the Kink in the Benefit Function to Infer How Aggressively Firms Use Debt

Table II (not included) – Relation Between the Kink in a Firm’s Tax Benefit Function and Standardized Kink. The mean value of the kink is 2.36, which indicates that the average firm could more than double their debt before hitting the downward sloping part of the tax benefit function. However this mean value has declined over time. In 1980, the average value of the kink is 3.1, compared to only 1.9 in the 90’s. This means that firms have become less conservative with regard to their debt policy over the sample time period.

## Empirical Evidence on the Tax-Reducing Benefit of Interest Deductions

### Firm-By-Firm Analysis of the Tax Benefits of Debt

Tobit Analysis to determine what types of firms have the largest tax benefits to debt. Large, liquid, profitable, collateralized firms with low expected distress costs and small research expenses.

## Using Benefit Curves to Examine the Cost of Debt

### Relating Benefit Curves to Measures of the Cost of Debt

Table V (not included) – Relation between the Kink in a Firm’s Tax Benefit Function and Firm Characteristics

Table VI – Tobit Regressions Using the Kink in the Benefit Function as Dependent Variable. Firms are conservative when they pay dividends, have owner’s equity, have large ROA, low expect distress costs, and no NOL (net operating loss). Ironically, these are also the firms with the lowest costs of debt. Regarding entrenchment, when he uses the full set of control variables, only the % of outside directors is significant (-0.351). So the evidence is weak that there is any effect of managerial entrenchment on debt conservatism.

### Persistence, the Peso Problem, and the Pecking Order of Possible Explanations of Debt Conservatism

Graham shows that debt conservatism is very persistent. Companies that start out as conservative in the study tend to remain conservative.

Peso Problem – Possibly firms are more cautious than necessary in order to prevent some huge disaster with very low probability.

Pecking Order – firms that are debt conservative should be even more conservative about issuing equity. The results of this analysis show the opposite. The higher the kink, the higher the relative use of equity, which is inconsistent with pecking order.

## Is Money Left on the Table?

Yes. Gross tax benefit from levering up to the kink is between 28% (1980) and 8% (1993) of the total value of the firm, with a mean of 15.7%. When personal tax penalty is netted out, we are left with 10% and 4.5%, respectively (with a mean of 7.5%). This is a highly significant amount of potential value that is being discarded.

## Conclusions

Firms are leaving money on the table, an average of 15.7% of their firm value. They could lever up safely to their kink without significantly increasing risk. Most could easily double their debt with no adverse effects. Either the incremental costs of debt are very large, or the firms must be using debt too conservatively. The most conservative firms are growth firms that produce unique products, as well as firms that are large, profitable and liquid.