Question

A corporate bond with a 7.000 percent coupon has fifteen years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.7 percent. The firm has recently become more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.6 percent. What will be the change in the bond’s price in dollars? (Assume interest payments are semiannual.) (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Change in bond price $ What will be the change in the percentage terms? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

Old Price
Redemption value	1000
Time	15
coupon rate	7
YTM	8.70%
PV of redemption price	=1000/(1+8.7%)^15	286.1257
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
PV of coupon payments	=PMT x (((1-(1 + r) ^- n)) / i)
PV of coupon payments	=70* (((1-(1 + 8.7%) ^- 15)) / 8.7%)
PV of coupon payments	574.3816
Bond Price	=574.38+286.14
Bond Price	860.52
New Price
Redemption value	1000
Time	15
coupon rate	7
YTM	7.60%
PV of redemption price	=1000/(1+7.6%)^15	333.29
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
PV of coupon payments	=PMT x (((1-(1 + r) ^- n)) / i)
PV of coupon payments	=70* (((1-(1 + 7.6%) ^- 15)) / 7.6%)
PV of coupon payments	614.08
Bond Price	=614.08+333.29
Bond Price	947.37
Change in bond price	=947.37 - 860.52
Change in bond price	86.85
Change in bond price in %	86.85/860.52
Change in bond price in %	10.09%