Consider a 10-year zero-coupon bond with face value \(\$ 100\). The interest rate is fixed at 5\%. The credit spread for the bond is estimated to be \(1 \%\) (except in part (a)). Calculate:

(a) The bond value if there is no possibility of default.

(b) The probability of default.

(c) The value if there is no recovery.

(d) The value if there is \(50 \%\) recovery at maturity.

(e) The value of \(\$ 100\) that is paid at default.

[For (a), \(\left.e^{-r T} F=\$ 6.65.\right]\)