Expected Default and CoD

How to Calculate Expected Default Loss on a Bond?

The cost of debt is often confused with the yield to maturity (YTM) of a bond/loan.

The promised return is equal to the cost of debt when there is no risk of default. However, because there is a real risk of default, we must discount the expected cash flows instead of the promised coupons and principal amounts.

The expected cash flows depend on both the probability of default and the recovery rate in the event of default. The table below shows the recovery rates for senior unsecured bonds according to Moody’s ratings, based on the number of years since the rating was assigned, within 30 days after default.

For example, if a bond defaults within three years after being rated A, its price drops to an average of 45%.

Therefore, if we know the bond’s price, the probability of default, and the recovery rate in the event of default, we can calculate the cost of debt.

P[0] = ECF[1]/(1+CoD) + ECF[2]/(1+CoD) + … + ECF[t]/(1+CoD)

This is calculated in the same way as yield to maturity, but using expected cash flows in the denominator.

The difference between CoD and YTM is called the expected default loss (EDL).

E(DL) = YTM-CoD

*Corporate Valuation Theory, Evidence and Practice
Mark E. Zmijewski; Robert W. Holthausen
Second Edition