An investor holds $$20$ million of three$-$year investment grade bonds issued by DuraCorp. The bonds carry a coupon of $4\%,$ paid annually. The investor is considering buying a three$-$year credit default swap $($CDS$)$ written on the DuraCorp bonds.$($a$)$Why is the investor considering the purchase of a CDS on DuraCorp bonds?$($b$)$What is the "fair" upfront premium if the annual probability of default of DuraCorp is assessed at $1\mathrm{.}3\%,$ the recovery rate is $70\%,$ the treasury bond yield curve is flat at $3\mathrm{.}0\%,$ CDS premiums are paid annually in advance, default by DuraCorp only occurs at year$-$end and the annual premiums paid by the CDS buyer on CDS written on DuraCorp bonds is $1\%$ of the par value? Show all working.