In: Finance
XYZ Inc. has issued a 30-year bond with a coupon rate of 8%, the future value of $1000, and a market rate of 9%. What is the current market price for the bond?
Current Market Price of bond | $ 897.26 | |||||||||||
Working: | ||||||||||||
Current Market Price of bond is the present value of cash flow from bond throughout its life. | ||||||||||||
Present Value of annuity of $ 1 | = | (1-(1+i)^-n)/i | Where, | |||||||||
= | (1-(1+0.09)^-30)/0.09 | i | 9% | |||||||||
= | 10.2737 | n | 30 | |||||||||
Present Value of $ 1 to be received in 30 years | = | (1+i)^-n | Where, | |||||||||
= | (1+0.09)^-30 | i | 9% | |||||||||
= | 0.0754 | n | 30 | |||||||||
Annual coupon payment | = | Par Value x Coupon rate | ||||||||||
= | 1000 x 8% | |||||||||||
= | $ 80.00 | |||||||||||
Present Value of coupon | = | Coupon Payment x Present Value of annuit of $ 1 | ||||||||||
= | $ 80.00 | x | 10.2737 | |||||||||
= | $ 821.89 | |||||||||||
Present Value of Par Value | = | Par Value x Discount factor | ||||||||||
= | $ 1,000.00 | x | 0.0754 | |||||||||
= | $ 75.37 | |||||||||||
Present Value of cash flow from bond | = | Present Value of coupon | + | Present Value of Par Value | ||||||||
= | $ 821.89 | + | $ 75.37 | |||||||||
= | $ 897.26 | |||||||||||