Firm XYZ has three zero$-$coupon bonds outstanding. Bond A has a maturity of $1$ year and a yield of $3\mathrm{.}7\%.$ Bond B has a maturity of $2$ years and a yield of $4\mathrm{.}8\%.$ Bond C has a maturity of $3$ years and a yield of $5\mathrm{.}4\%.$ Zero$-$coupon Treasury securities with maturities of $1,2,$ and $3$ years have yields of $3\mathrm{.}2\%,3\mathrm{.}8\%,$ and $4\mathrm{.}0\%$ respectively. Assume that if firm XYZ defaults, bondholders of A$,$ B$,$ and C will recover nothing.

a$.$ Calculate firm XYZ$$s annual marginal default probabilities for years $1,2,$ and $3.(2$ pts$.)$

b$.$ Calculate firm XYZ$$s cumulative default probabilities for years $1,2,$ and $3.(0\mathrm{.}5$ pts$.)$

c$.$ Calculate bond C$$s yield spread. $(0\mathrm{.}5$ pts$.)$

d$.$ Assume that firm XYZ is about to issue a senior secured bond that pays no coupons and matures in $1$ year. The expected recovery rate on this bond is $$0\mathrm{.}35$ on the dollar. Bases on the implied default probability you calculated earlier, what should be the required yield on this new bond? $(1$ pt$.)$