= Solution
{c}
At maturity debt receives the smaller of face value and firm assets:
$$
D_T=\min(F,V_T)=F-(F-V_T)_+.
$$
Thus it is equivalent to a zero-coupon payment $F$ minus a <European put option> on the firm value. Its time-$t$ price is
$$
\boxed{D_t=Fe^{-r(T-t)}-P^E(t,V_t;F).}
$$
Equity receives the residual $(V_T-F)_+$, hence is a <European call option>:
$$
\boxed{E_t=C^E(t,V_t;F).}
$$
<put-call parity> verifies $E_t+D_t=V_t$, consistent with the stated balance-sheet identity. As with the replication arguments elsewhere, the physical drift $\mu$ does not enter these option prices.
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