Environ Systems is a firm that specializes in cleaning environmental damage $($waste disposal$)$ and specialty chemicals. As part of its expansionary plans, it has made a large issuance of $10-$year corporate bonds, with a face value of $$1000$ each and an annual coupon rate of $12\%.$

$($a$)$ Assuming a discount rate of $7\%,$ calculate the value of the bond.

$($b$)$ Environ got into deep financial troubles and defaulted on $($ie: stopped paying$)$ its bonds in year $6.$ During that year, Environ negotiated with bondholders on a debt restructuring deal which included extending the maturity of the bond $2$ extra years $($ie: from $10$ years previously to $12$ years$),$ a full relief from coupon payments in years $7$ and $8,$ a payment of coupons at a reduced rate of $3\%$ per annum from years $9$ to year $12,$ and a repayment of $70\%$ of the face value in year $12.$ Under such conditions and assuming a discount rate of $7\%,$ what would the value of the bond be$?$ What would the bondholder's profit$/$loss be relative to the face value of the bond?