I have a problem interpreting the following excerpt from “How big are the tax benefits of debt” by J. Graham. “A firm’s tax function is defined by a series of marginal tax rates, with each rate corresponding to a specific level of interest deductions. (Each marginal tax rate incorporates the effects of non-debt tax shields, tax-loss carrybacks, carryforwards, tax credits, the alternative minimum tax, and the probability that interest tax shields will be used in a given year, based on the methodology of Graham (1996a)). The tax function is generally flat for small interest deductions but, because tax rates fall as interest expense increases, eventually becomes downward sloping as interest increases. This occurs because interest deductions reduce taxable income, which decreases the probability that a firm will be fully taxable in all current and future states, which in turn reduces the tax benefit from the incremental deductions.” Okay, I understand the second part where he shows why the curve will become downward-sloping but the expression that the tax function is defined by “a series of marginal tax rate” is not clear to me. So he essentially compares marginal benefit of debt versus the interest deductions. I don’t clearly see the connection between the marginal tax rate and the marginal benefits of debt or at least I can’t understand how he derives that marginal benefit from “the series of marginal tax rates”. Anyone willing to discuss this interesting piece from the paper ?