Question

It is now October 2011. You are looking to price a bond that matures in April 2014.

The bond is $1,000 par value and it pays 5% coupon rate with semi-annual coupon payments.

The next coupon payment occurs in 6 months. You go to the Wall Street Journal to find the price of this bond and find that YTM of this bond is 4%.

Can you determine the price of this bond with this information?

If so, calculate the price of the bond. If not, explain why not.

Answer 1

Price of a bond is equal to the PV of cash flow expected from the bond discounted at YTM.

We have been provided with all the required information. So, Yes we can calculate price of the bond.

Par value =1000

Semi annual coupon = 1000 x 5% /2 = 25

Semi annual YTM = 4/2 = 2%

No. Of semi annual periods remaining = 5 ( Apr12,Oct 12,Apr13,Oct13,Apr14)

PV OF Coupon payments = Coupon amount x Annuity factor

= 25 x PVAF(2%,5)

= 25 x [1-(1+0.02)^-5]/0.02. [ Using Formula for calculating annuity payments i.e. [1-(1+r)^-n]/r. ]

= 25 x 4.7135

= 117.84

PV of maturity amount = Par Value /(1+r)^n

= 1000/(1+0.02)^5

= 905.73

PRICE OF BOND = 117.84 + 905.73 = 1023.57