Show how the value calculation changes if the recovery rate is $60\%.$

If the airline defaults in the middle of a year, the bondholder receives the recovery payment at the end of that year but gets no coupon payment for that year.

Update the cash flow and present value in the table to reflect the recovery. I believe the value of the bond with recovery is $$959\mathrm{.}87.$

$\backslash$table$[[,$Probability,Year $1,$Year $2,$Present$],[$Outcome $1($default middle of year $1),5\%,,$$$0,],[$Outcome $2($default in middle of year $2),4\mathrm{.}75\%,$$$30,,],[$Outcome $3($no default$),90\mathrm{.}25\%,$$$30,$$$1030,-]]$

You must show your calculations to receive credit.

$5.$ This question is about the credit triangle.

Bond

One$-$year zero coupon bond issued by a risky airline

Risk$-$free U$.$S$.$ treasury bond

Yield to maturity

$75\%$

$5\mathrm{.}0\%$

The credit triangle relationship implies the company has a $5\%$ chance of default, assuming a $50\%$ recovery rate.

Explain how I know this using the risky and risk$-$free bond yield. You must show your calculations to receive credit.