Question

A corporate bond with a 3.95% coupon has 21 years left to maturity.   It has had a credit rating of BBB and a yield to maturity of 5.35%. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate for a bond with this level of credit risk and time to maturity is 6.55%.

What will be the net change in the bond’s price in dollars if this rating downgrade and associated new discount rate occurred today? (Assume interest payments are semiannual; round and display your answer to 2 decimal places i.e. 1.23)

Answer 1

Price of bond	Interest payment*(1-((1+r)^-n)/r) + Face value*(1/(1+r)^n)
where r represents yield to maturity and n represents number of years.
Assuming the par value of bond is $1,000.
Interest payment	$19.75	1000*(3.95%/2)
No of payments (n)	42	21*2
Semi-annual yield ( r)	2.68%	5.35%/2
Calculation of current price of bond
Price of bond	19.75*((1-(1.0268^-21))/0.0268)+1000*(1/1.0268^21)
Price of bond	19.75*15.90119 + 1000*0.573848
Price of bond	$887.90
Semi-annual yield ( r)	3.28%	6.55%/2
Calculation of price of bond if new discount rate occurred today
Price of bond	19.75*((1-(1.0328^-21))/0.0328)+1000*(1/1.0328^21)
Price of bond	19.75*15.00729 + 1000*0.507761
Price of bond	$804.15
Net change in bond's price	804.15-887.90
Net change in bond's price	-$83.74
Thus, price of bond would decrease by $83.74.