While trying to arrive at equity value from EV, Should you reduce par value of a zero coupon debt or current market value as zero coupon debt trades below par always?
Example: let's say EV of a company is 100 with zero debt and zero cash resulting in equity value of 100. The company now decides to raise debt via zero coupon bond and ends up raising 80 debt whose face value is 100.
Assuming the company raised debt at market rates, and all other factors as constant, EV should remain unchanged and therefore equity value should also remain the same.
In the example above I am reducing market value of 80 and not par value. Should I be reducing Debt of 100 and end up with Equity of 80 instead?