Bond X is a premium bond making semiannual payments. The bond pays a coupon rate
ID: 2733272 • Letter: B
Question
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 8 percent, has a YTM of 6 percent, and has 14 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6 percent, has a YTM of 8 percent, and also has 14 years to maturity. The bonds have a $1,000 par value.
What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)
If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In five years? In ten years? In 12 years? In 14 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)
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What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)
Explanation / Answer
The price of a bond can be calculated with the use of Present Value (PV) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = YTM, Nper = Period, PMT = Coupon Payment and FV = Face Value of Bonds.
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1 Year
Bond X
Here, Rate = 6%/2 = 3%, Nper = (14 - 1)*2 = 26, PMT = 1,000*8%*1/2 = $40 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(3%,26,40,1000) = $1,178.77
____
Bond Y
Here, Rate = 8%/2 = 4%, Nper = (14 - 1)*2 = 26, PMT = 1,000*6%*1/2 = $30 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(4%,26,30,1000) = $840.17
________
5 Year
Bond X
Here, Rate = 6%/2 = 3%, Nper = (14 - 5)*2 = 18, PMT = 1,000*8%*1/2 = $40 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(3%,18,40,1000) = $1,137.54
____
Bond Y
Here, Rate = 8%/2 = 4%, Nper = (14 - 5)*2 = 18, PMT = 1,000*6%*1/2 = $30 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(4%,18,30,1000) = $873.41
________
10 Year
Bond X
Here, Rate = 6%/2 = 3%, Nper = (14 - 10)*2 = 8, PMT = 1,000*8%*1/2 = $40 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(3%,8,40,1000) = $1,070.20
____
Bond Y
Here, Rate = 8%/2 = 4%, Nper = (14 - 10)*2 = 8, PMT = 1,000*6%*1/2 = $30 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(4%,8,30,1000) = $932.67
________
12 Year
Bond X
Here, Rate = 6%/2 = 3%, Nper = (14 - 12)*2 = 4, PMT = 1,000*8%*1/2 = $40 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(3%,4,40,1000) = $1,037.17
____
Bond Y
Here, Rate = 8%/2 = 4%, Nper = (14 - 12)*2 = 4, PMT = 1,000*6%*1/2 = $30 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(4%,4,30,1000) = $963.70
________
14 Year
Bond X
Here, Rate = 6%/2 = 3%, Nper = (14 - 14)*2 = 0, PMT = 1,000*8%*1/2 = $40 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(3%,0,40,1000) = $1,000
____
Bond Y
Here, Rate = 8%/2 = 4%, Nper = (14 - 14)*2 = 0, PMT = 1,000*6%*1/2 = $30 and FV = 1,000
Using these values in the above formula for PV, we get
Price of Bond = PV(4%,0,30,1000) = $1,000
____________
Tabular Representation:
Price of bond Bond X Bond Y One Year $1,178.77 $840.17 Five Years $1,137.54 $873.41 Ten Years $1,070.20 $932.67 12 Years $1,037.17 $963.70 14 Years $1,000.00 $1,000.00