Assume you have a one-year investment horizon and are trying to choose among thr
ID: 2714285 • Letter: A
Question
Assume you have a one-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 9 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 9.0% coupon rate and pays the $90 coupon once per year. The third has a 11.0% coupon rate and pays the $110 coupon once per year.
If all three bonds are now priced to yield 9.0% to maturity, what are their prices? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
If you expect their yields to maturity to be 9.0% at the beginning of next year, what will their prices be then? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
What is your rate of return on each bond during the one-year holding period? (Do not round intermediate calculations.Round your answers to 2 decimal places.)
a.If all three bonds are now priced to yield 9.0% to maturity, what are their prices? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Explanation / Answer
a)
Zero Coupon Bond
Current prices = 1000/(1+9%)^9
Current prices = $ 460.43
9.0% Coupon
Since Coupon rate = YTM, Bond is trading at par
Current prices = $ 1000
11.0% Coupon
Current prices = pv(rate, nper,pmt,fv)
Nper (indicates the period) = 9
PV (indicates the price) = ?
PMT (indicate the annual payment) = 110
FV (indicates the face value) = 1000
Rate (indicates YTM) = 9%
Current prices = pv( 9%,9,110,1000)
Current prices = $ 1119.90
b-1)
Zero Coupon Bond
Price one year from now = 1000/(1+9%)^8
Price one year from now = $ 501.87
9.0% Coupon
Since Coupon rate = YTM, Bond is trading at par
Price one year from now = $ 1000
11.0% Coupon
Price one year from now = pv(rate, nper,pmt,fv)
Nper (indicates the period) = 8
PV (indicates the price) = ?
PMT (indicate the annual payment) = 110
FV (indicates the face value) = 1000
Rate (indicates YTM) = 9%
Price one year from now = pv( 9%,8,110,1000)
Price one year from now = $ 1110.70
b-2)
Zero Coupon Bond
Rate of return = ( Price one year from now-Current prices)Current prices
Rate of return = (501.87-460.43)/460.43
Rate of return = 9%
9.0% Coupon
Rate of return = ( Price one year from now-Current prices+ Coupon)Current prices
Rate of return = (1000-1000+90)/1000
Rate of return = 9%
11.0% Coupon
Rate of return = ( Price one year from now-Current prices+ Coupon)Current prices
Rate of return = (1110.70-1119.90+110)/1119.90
Rate of return = 9%
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