$6.$ Unicorn Inc. is considering issuing a $20-$year bond for its expansion project. In order to estimate the YTM of the new bond, the company has the following information for reference: First, the company currently has a bond issue outstanding, which pays a $10\%$ annual coupon, currently traded at $1114\mathrm{.}93($with $$1000$ face value$),$ and will mature in $8$ years. Secondly, the relevant yield curve indicates that the YTM for a $20-$year bond is higher than an $8$ year$-$bond with the same bond rating by $1\mathrm{.}2\%.(20$ marks$)$ a$.$ For Unicorn$$s currently outstanding bond, find which one of the following is its YTM: $7\%,8\%,9\%,10\%,11\%,12\%.$ Show calculations by formula. $(5$ marks$)$ b$.$ Suppose the new bond is also to pay $10\%$ annual coupon, calculate the issue price of the bond $($with $$1000$ face value$).(5$ marks$)$ c$.$ Assume the market interest rate will remain unchanged. What will be the current yield and the capital gains yield of the new bond for its first year? $(5$ marks$)$ d$.$ Explain why the yield of a $20-$year bond should be higher than that of a bond of the same company with $8$ years to maturity, supposing no change in the rate of inflation is expected for the foreseeable future.