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1)Suppose you purchase a zero coupon bond with a face value of ?$1,000?, maturing in 20 ?years, for ?$215
1)Suppose you purchase a zero coupon bond with a face value of ?$1,000?, maturing in 20 ?years, for ?$215.75. Zero coupon bonds pay the investor the face value on the maturity date.
What is the implicit interest in the first year of the? bond's life? ?(Round to the nearest? cent.)
2.What is the percentage change in price for a zero coupon bond if the yield changes from 7?% to 8.5?%? The bond has a face value of ?$1,000 and it matures in 10 years. Use the price determined from the first? yield, 7?%, as the base in the percentage calculation.
The percentage change in the bond price if the yield changes from 7?% to 8.5?% is ? ?(Round to two decimal? places.)
3.Beam Inc. bonds are trading today for a price of ?$626.64. The bond currently has 18 years until maturity and has a yield to maturity of 9.37?%. The bond pays annual coupons and the next coupon is due in one year.
What is the coupon rate of the? bond?? (Round to one decimal? place.)
4.Cyberdyne Systems is issuing a series of zero coupon bonds to raise? $500M to fund research and development at its Skynet division. Each bond will have a face value of ?$1,000 and will mature in 29 years. The yield on the bond is 5.5?%.
What is the fair price for one of? Cyberdyne's zero coupon? bonds? ?(Round to the nearest? cent.)
5.Beam Inc. bonds are trading today for a price of ?$934.06. The bond pays annual coupons with a coupon rate of 3?% and the next coupon is due in one year. The bond has a yield to maturity of 3.69?%.
How many years are there until the bond? matures? (Round to the nearest whole? number.)
Expert Solution
1) Computation of Implicit Interest in the first Year of Bond's Life:
Zero coupon bond value = Face value/(1+Interest rate)^Time to maturity
215.75=1000/(1+Interest rate)^20
Hence
(1+Interest rate)^20=(1000/215.75)
1+Interest rate=(1000/215.45)^(1/20)
Hence,
Interest rate=(1000/215.75)^(1/20)-1 =7.97%
So,
Implicit interest in the first year of the? bond's life =$215.75*7.97% =$17.19(Approx).
2) Computation of the percentage change in the bond price if the yield changes from 7% to 8.5%:
Bond price when yield is 7% = $ 1,000 / ( 1.07)^10 = $508.35
Bond price when yield changes to 8.5% = $ 1,000 / ( 1.085)^10 = $442.29
Percentage change in price = $ ( 442.29 - 508.35) / $508.35 * 100 = - 13.00%
3) Computation of Coupon Payment using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Coupon Payment = ?
Rate =9.37%
Nper = 18 years
PV = $626.64
FV =$1,000
Substituting the values in formula:
=pmt(9.37%,18,-626.64,1000)
PMT or Coupon Payment = $50
Coupon Rate = Annual Coupon Payment / Face Value = $50/$1,000 = 5%
4) Computation of Fair Price of Bond using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Current Bond Price = ?
Rate = 5.5%
Nper = 29 years
PMT = 0
FV = $1,000
Substituting the values in formula:
=-pv(5.5%,29,0,1000)
PV or Fair Price of Bond = $211.68
5) Computation of Number of Years to Maturity using NPER Function in Excel:
=nper(rate,pmt,-pv,fv)
Here,
Nper = Number of Years to Maturity = ?
Rate = 3.69%
PMT = $1,000*3% = $30
PV= $934.06
FV = $1,0000
Substituting the values in formula:
=nper(3.69%,30,-934.06,1000)
NPER or Number of Years to Maturity = 12 years
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