# Tax-adjusted discount rates: a general formula under constant leverage ratios tax-adjusted discount rates

Molnár, Peter; Nyborg, Kjell G (2013). Tax-adjusted discount rates: a general formula under constant leverage ratios tax-adjusted discount rates. European Financial Management, 19(3):419-428.

## Abstract

Cooper and Nyborg (2008) derive a tax-adjusted discount rate formula under a constant proportion leverage policy, investor taxes and risky debt. However, their analysis assumes zero recovery in default. We extend their framework to allow for positive recovery rates. We also allow for differences in bankruptcy codes with respect to the order of priority of interest payments versus repayment of principal in default, which may have tax consequences. The general formula we derive differs from that of Cooper and Nyborg when recovery rates in default are anticipated to be positive. However, under continuous rebalancing, the formula collapses to that of Cooper and Nyborg. We provide an explanation for why the effect of the anticipated recovery rate is not directly visible in the general continuous rebalancing formula, even though this formula is derived under the assumption of partial default. The errors from using the continuous approximation formula are sensitive to the anticipated recovery in default, yet small. The ‘cost of debt’ in the tax adjusted discount rate formula is the debt’s yield rather than its expected rate of return.

## Abstract

Cooper and Nyborg (2008) derive a tax-adjusted discount rate formula under a constant proportion leverage policy, investor taxes and risky debt. However, their analysis assumes zero recovery in default. We extend their framework to allow for positive recovery rates. We also allow for differences in bankruptcy codes with respect to the order of priority of interest payments versus repayment of principal in default, which may have tax consequences. The general formula we derive differs from that of Cooper and Nyborg when recovery rates in default are anticipated to be positive. However, under continuous rebalancing, the formula collapses to that of Cooper and Nyborg. We provide an explanation for why the effect of the anticipated recovery rate is not directly visible in the general continuous rebalancing formula, even though this formula is derived under the assumption of partial default. The errors from using the continuous approximation formula are sensitive to the anticipated recovery in default, yet small. The ‘cost of debt’ in the tax adjusted discount rate formula is the debt’s yield rather than its expected rate of return.

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