We propose that companies with high R&D costs have high risk premia. To test this hypothesis, we run monthly cross$-$sectional regressions where we regress stock excess returns on R&D intensity and other control variables. We then extract the monthly coefficients for R&D from these regressions and regress these coefficients on the Fama$-$French factors. If we obtain a significant alpha from this regression, it would suggest that there is a premium associated with R&D$.$

We now want to investigate why these companies pay a risk premium and what they are being compensated for. One potential reason could be default risk. We are exploring how to use each company's Altman Z$-$score to determine if the premium is due to compensation for default risk.

Could you help us understand how to incorporate the Altman Z$-$score into our analysis to test this hypothesis?