Black-Scholes Model question
For simplicity, numbers are in millions.

We assume that markets are efficient, and that the value of equity and liabilities equals that of assets. So debt + equity = 300. We want to solve for the value of the debt, and get equity as the residual.

The valuation debt $=\frac{200}{1.05}$ assumes no default. We model default by the probability of the value of the assets dropping below 200 (redemption value of debt) after one year.

We can value the default risk by nothing that it could be cancelled out by buying a put on the asset values, with a strike at 200. I leave to the reader the determination of this value. Buying the bond and the put creates a default risk free bond, which has the discounted value above.

The value of bond with default is therefore the value of the default free bond less the value of the put.