Assume an $8-$year corporate bond with a $7\%$ annual coupon and a par value of $100.$ This bond has a current market price of $106\mathrm{.}17$ and a yield to maturity $($YTM$)$ of $6\%.$ Show the calculation for the current market price of $106\mathrm{.}17$ and calculate a revised price for the bond, assuming a YTM of $8\%.$ What is the general relationship that the change in the bond$$s market price illustrates? $(5$ marks$)$

b$)$ The equity shares of Jade Plc have a beta value of $0\mathrm{.}90.$ The risk$-$free rate of return is $5\%$ and the market risk premium is $3\%.$ Corporation tax is $19\%.$ Determine the required rate of return on the shares of Jade Plc and explain the impact of beta on the shares of the company. $(4$ marks$)$

c$)$ Identify and discuss two advantages and two disadvantages to a company issuing convertible bonds. $(8$ marks$)$

d$)$ Suppose there is a general expectation that prices will increase by $3\%$ over the course of the year. The one$-$year nominal interest rate is $4\%.$ What is the real interest rate? $(3$ marks$)$

e$)$ Estimate the YTM on a zero$-$coupon bond issued at $40$ repayable at par value $(100),$ in $5$ years$$ time, using discount tables. $(5$ marks$)$