Question

a bond was issued 5 years ago at par with a maturity of 10 years, a yield-to-maturity of 6.50% compounded semiannually and semi annual coupons. what is the price of this bond today immediately after the receipt of today's coupon if the YTM has fallen to 5.50% compounded semi annually?

Answer 1

Sol:

Face value (FV) = $1000 (assumed)

Rate of interest = 5.5% (Semiannually) 5.50%/2 = 2.75%

Period = 5 years (Semiannually) = 5 x 2 = 10

Yield = 6.5% (Semiannually) = 6.5%/2 = 3.25%

PMT = 1000 x 3.25% = $32.5

Price of bond today is the present value of future cash flows.

Present value (PV) = (PMT x (1-(1+r)^-n)/r) + (FV/(1+r)^n)

PV = (32.5 x (1-(1+2.75%)^-10)/2.75%) + (1000/(1+2.75%)^10

PV = (32.5 x (1-(1+ 0.0275)^-10)/0.0275) + (1000/(1+0.0275)^10

PV = (32.5 x 8.6401 + 762.3979

PV = 280.8033 + 762.39789

PV = $1043.20

Therefore present value of this bond today will be $1043.20