Valuation of Callable Bonds under Progressive Personal Taxes and Interest Rate Uncertainty
Mauer, David C., Barnea, Amir, Kim, Chang-Soo, Financial Management
* Several studies have offered tax-based rationales for the widespread practice of attaching call provisions to corporate bonds. Boyce and Kalotay  demonstrate that if there is a positive difference between the tax rates of the corporation (borrower) and the typical investor (lender), then there will be a net tax benefit from the call. Their argument is that since the interest schedule on a callable bond and its future refunding bond can never increase, but may decrease, the present value of the stream is higher for investors facing lower tax rates (higher after-tax discount rates) and lower for corporations (higher present value of interest tax shields). In a different vein, Yawitz and Anderson  and Marshall and Yawitz  considered the net tax benefit associated with the call premium paid when the bond is called.(1) Since the call premium is taxed as a capital gain to investor, but is deductible as an ordinary income expense to the firm, they concluded that the expected tax benefit for a callable bond will be higher than for an otherwise identical but noncallable bond. Recently, however, Brick and Wallingford  have argued that the call premium tax asymmetry may produce even greater tax benefits for noncallable debt repurchased at market prices because there will be an expanded set of profitable call opportunities. Thus, they argue that the call premium tax asymmetry probably cannot explain the widespread practice of attaching call provisions to bonds.
Although much has been learned from existing tax based analyses of callable bonds, the extant models suffer from both theoretical and practical deficiencies. First, most analyses do not consider the broader capital structure implications of their tax assumptions. For example, the assumption that the personal tax rate is below the corporate tax rate, which drives Boyce and Kalotay's conclusions, implies a corner leverage decision not-withstanding the call feature studied. To avoid such empirically unreasonable implications, the tax implications of particular bond characteristics should be studied under the benchmark conditions of Miller's  equilibrium analysis which leads to capital structure irrelevance.(2) Of course, the advantage of this approach is that it allows for the analysis of the tax effects of bond features (e.g., call provision) net of the tax gains from leverage. Second, the universally employed assumption that personal tax rates are fixed and equal across investors obscures the basic reality that future marginal personal tax rates are uncertain. This feature of the tax environment, which arises from the interaction between progressive personal taxation and uncertain future income (both wage and portfolio), induces a temporal association between future tax rates and interest rates, which may significantly affect the relative corporate aop personal valuation of the call.
The current analysis examines the value of the call under the realistic assumption that future marginal personal tax rates and interest rates are uncertain. Although the analysis does not depend on any particular covariance function between tax and interest rates, logic suggests that it is reasonable to assume that both variable are positively affected by the level of business conditions and therefore have a positive partial correlation. An upturn of the economy may be characterized by high marginal personal tax rates and interest rates, while a downturn may be associated with low tax interest rates. Indeed, inspection of the empirical record of nominal interest rates over the last three decades provides considerable evidence in support of a positive association between interest rates and economic activity. Short-term rates have generally been high during expansionary periods and low during recessions, while long-term rates have generally followed the same pattern (see, for example, Van Horne ).
While less direct evidence is available concerning the relationship between marginal personal tax rates and the state of the economy, a positive association is predicted by the recent capital structure models of Dammon  and Ross , and the subsequent multiperiod extension of those models, by Lewis . …