Consider a 10-year bond that pays a 5 percent coupon semi-annually with a face v

Question

Consider a 10-year bond that pays a 5 percent coupon semi-annually with a face value of $1000.

a. What is the price of this bond if the annualized yield to maturity of 4 percent (i.e., the stated rate is .04 compounded semi-annually)?

b. What is the price of this bond if the annualized yield to maturity of 5 percent (i.e., the stated rate is .05 compounded semi-annually)?

c. What is the price of this bond if the annualized yield to maturity of 6 percent (i.e., the stated rate is .06 compounded semi-annually)?

d. What is the price of this bond if the annualized effective rate is 5 percent?

Explanation / Answer

we have FV = 1000, Coupon = 5% Semi = 5%*1000/2 = 25 nper = 10*2 period = 20 a. YTM = 4%. So HY YTM = 4%/2 = 2% SO Price of bond = PV(Rate,nper,PMT,FV) = PV(2%,20,25,1000) = $1,081.76 b. YTM = 5%. So HY YTM = 5%/2 = 2.5% SO Price of bond = PV(Rate,nper,PMT,FV) = PV(2.5%,20,25,1000) = $1,000.00 c. YTM = 6%. So HY YTM = 6%/2 = 3% SO Price of bond = PV(Rate,nper,PMT,FV) = PV(3%,20,25,1000) = $925.61 d. annualized effective rate is 5 % ie EAR = (1+i/2)^2 -1 = 5% Solving for i, we get i = 4.94% YTM = 4.94%. So HY YTM = 4.94%/2 = 2.47% SO Price of bond = PV(Rate,nper,PMT,FV) = PV(2.47%,20,25,1000) = $1,004.69

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