Bond X is a premium bond making semiannual payments. The bond pays a 8 percent c
ID: 2651365 • Letter: B
Question
Bond X is a premium bond making semiannual payments. The bond pays a 8 percent coupon, has a YTM of 6 percent, and has 20 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 20 years to maturity.
What is the price of each bond today? (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 six years? In twelve years? In 17 years? In 20 years? (Round your answers to 2 decimal places. (e.g., 32.16))
Bond X is a premium bond making semiannual payments. The bond pays a 8 percent coupon, has a YTM of 6 percent, and has 20 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 20 years to maturity.
Explanation / Answer
What is the price of each bond today? (Round your answers to 2 decimal places. (e.g., 32.16))
Today
Price of bond X = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 20*2 = 40
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 6%*1/2 = 3%
Price of bond X = pv(3%,40,40,1000)
Price of bond X = $1231.15
Price of bond Y = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 20*2 = 40
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*6%*1/2 = 30
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 8%*1/2 = 4%
Price of bond Y = pv(4%,40,30,1000)
Price of bond Y = $ 802.07
If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In six years? In twelve years? In 17 years? In 20 years? (Round your answers to 2 decimal places. (e.g., 32.16))
Answer
Working
one year from now
Price of bond X = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 19*2 = 38
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 6%*1/2 = 3%
Price of bond X = pv(3%,38,40,1000)
Price of bond X = $1224.92
Price of bond Y = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 19*2 = 38
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*6%*1/2 = 30
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 8%*1/2 = 4%
Price of bond Y = pv(4%,38,30,1000)
Price of bond Y = $ 806.32
Six year from now
Price of bond X = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 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 yearly YTM) = 6%*1/2 = 3%
Price of bond X = pv(3%,28,40,1000)
Price of bond X = $1187.64
Price of bond Y = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 14*2 = 28
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*6%*1/2 = 30
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 8%*1/2 = 4%
Price of bond Y = pv(4%,28,30,1000)
Price of bond Y = $ 833.37
Twelve year from now
Price of bond X = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 8*2 = 16
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 6%*1/2 = 3%
Price of bond X = pv(3%,16,40,1000)
Price of bond X = $1125.61
Price of bond Y = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 8*2 = 16
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*6%*1/2 = 30
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 8%*1/2 = 4%
Price of bond Y = pv(4%,16,30,1000)
Price of bond Y = $ 883.48
17 year from now
Price of bond X = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 3*2 = 6
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 6%*1/2 = 3%
Price of bond X = pv(3%,6,40,1000)
Price of bond X = $1054.17
Price of bond Y = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 3*2 = 6
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*6%*1/2 = 30
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 8%*1/2 = 4%
Price of bond Y = pv(4%,6,30,1000)
Price of bond Y = $ 947.58
20 year from now
Price of bond X = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 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 yearly YTM) = 6%*1/2 = 3%
Price of bond X = pv(3%,0,40,1000)
Price of bond X = $1000
Price of bond Y = pv(rate,nper,pmt,pv,fv)
Nper (indicates the semi annual period left to maturity) = 0
PV (indicates the price) = ?
PMT (indicate the semi annual payment) = 1000*6%*1/2 = 30
FV (indicates the face value) = 1000
Rate (indicates half yearly YTM) = 8%*1/2 = 4%
Price of bond Y = pv(4%,0,30,1000)
Price of bond Y = $ 1000
Price of Bond Bond X Bond Y One year 1,224.92 806.32 Six years 1,187.64 833.37 Twelve years 1,125.61 883.48 17 years 1,054.17 947.58 20 years 1,000.00 1,000.00