Tax-adjusted discount rates

This paper develops models for discount rates that are adjusted for the interest tax shields of an infra-marginal firm in a general tax equilibrium where there is cross-sectional variation in corporate tax rates. Under the assumption that the firm optimally maintains a predetermined debt ratio, a tax-adjusted riskless discount rate model is given for valuing certainty-equivalents and a tax-and-risk-adjusted discount rate model is given for valuing expected cash flows. For the latter case, the asset, equity, debt and tax-shield betas are derived and a weighted average cost of capital interpretation is given. The tax-adjusted CAPM/APT security market lines for expected returns in stock and bond markets both have the same slope but different intercepts. A formula is also provided for the present value of the interest tax shield when the firm optimally maintains a predetermined debt level. The analysis here also differs from the existing literature in the following respects: It allows for cross-sectional variation in corporate tax rates and personal tax rates. It shows that the market values of risky and riskless interests tax shield differ only to the extend that tax laws provide for nonlinear taxation of gains and losses. It also shows that interest tax shields should be discounted at a tax-adjusted discount rate that reflects the fact that they accrue to equity investors, rather than debt investors. Continuous-time simplifications of the formulas in this paper and the previous literature are also given.