Bond X is a premium bond making semiannual payments. The bond pays a coupon rate
ID: 2771867 • Letter: B
Question
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 10 percent, has a YTM of 8 percent, and has 14 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 8 percent, has a YTM of 10 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 four years? In nine years? In 13 years? In 14 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 10 percent, has a YTM of 8 percent, and has 14 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 8 percent, has a YTM of 10 percent, and also has 14 years to maturity. The bonds have a $1,000 par value.
Explanation / Answer
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 10 percent, has a YTM of 8 percent, and has 14 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 8 percent, has a YTM of 10 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.)
Bond X
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 14*2 = 28
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*10%*1/2 = 50
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 8%*1/2 = 4%
Bond Value = pv( 4%,28,50,1000)
Bond Value = $ 1166.63
Bond Y
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 14*2 = 28
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,28,40,1000)
Bond Value = $ 851.02
If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In four years? In nine years? In 13 years? In 14 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)
One Year
Bond X
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 13*2 = 26
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*10%*1/2 = 50
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 8%*1/2 = 4%
Bond Value = pv( 4%,26,50,1000)
Bond Value = $ 1159.83
Bond Y
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 13*2 = 26
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,26,40,1000)
Bond Value = $ 856.25
Four Year
Bond X
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 10*2 = 20
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*10%*1/2 = 50
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 8%*1/2 = 4%
Bond Value = pv( 4%,20,50,1000)
Bond Value = $ 1135.90
Bond Y
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 10*2 = 20
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,20,40,1000)
Bond Value = $ 875.38
Nine Year
Bond X
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 5*2 = 10
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*10%*1/2 = 50
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 8%*1/2 = 4%
Bond Value = pv( 4%,10,50,1000)
Bond Value = $ 1081.11
Bond Y
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 5*2 = 10
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,10,40,1000)
Bond Value = $ 922.78
13 Years
Bond X
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) =1*2 = 2
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*10%*1/2 = 50
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 8%*1/2 = 4%
Bond Value = pv( 4%,2,50,1000)
Bond Value = $ 1018.86
Bond Y
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 1*2 = 2
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,2,40,1000)
Bond Value = $ 981.41
14 Years
Bond X
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) =0*2 = 0
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*10%*1/2 = 50
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 8%*1/2 = 4%
Bond Value = pv( 4%,0,50,1000)
Bond Value = $ 1000
Bond Y
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 0*2 = 0
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates Half year YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,0,40,1000)
Bond Value = $ 1000
Answer
Price of bond Bond X Bond Y One year 1,159.83 856.25 Four years 1,135.90 875.38 Nine years 1,081.11 922.78 13 years 1,018.86 981.41 14 years 1,000.00 1,000.00