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1) If the nominal rate of interest is 12
1) If the nominal rate of interest is 12.37% and the real rate of interest is 8.48%?, what is the expected rate of? inflation?
2) What is the price of a 6?-year, 8.1% coupon? rate, $1,000 face value bond that pays interest annually if the yield to maturity on similar bonds is 7.1%?? The price of the bond is ?$ . ? (Round to the nearest? cent.)
3) With celebrity? bonds, celebrities raise money by issuing bonds to investors. The royalties from sales of the music are used to pay interest and principal on the bonds. In April of? 2009, EMI announced that it intended to securitize its back catalogue with the help of the Bank of Scotland. The bond was issued with a coupon rate of 6.5?% and will mature on this day 39 years from now. The yield on the bond issue is currently 6.15?%. At what price should this bond trade? today, assuming a face value of ?$1,000 and annual? coupons?
The price of the bond today should be ?$ . ?(Round to the nearest? cent.)
4) What is the percentage change in price for a zero coupon bond if the yield changes from 9?% to 6?%? The bond has a face value of ?$1,000 and it matures in 6 years. Use the price determined from the first? yield, 9?%, as the base in the percentage calculation.
The percentage change in the bond price if the yield changes from 9?% to 6?% is ?%. ?(Round to two decimal? places.)
Expert Solution
1) Computation of the expected rate of inflation:-
(1+Nominal rate of interest) = (1+Real rate of interest)*(1+Inflation rate)
(1+12.37%) = (1+8.48%)*(1+Inflation rate)
(1+Inflation rate) = (1+12.37%)/(1+8.48%)
Inflation rate = 1.0359 - 1
= 3.59%
2) We can calculate the price of bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond
Rate = 7.1%
Nper = 6 periods
Pmt = Coupon payment = $1,000*8.1% = $81
FV = $1,000
Substituting the values in formula:
= -pv(7.1%,6,81,1000)
= $1,047.52
3) We can calculate the price of bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond
Rate = 6.5%
Nper = 39 periods
Pmt = Coupon payment = $1,000*6.15% = $61.5
FV = $1,000
Substituting the values in formula:
= -pv(6.5%,39,61.5,1000)
= $950.77
4) We can calculate the price of bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond
Rate = 9%
Nper = 6 periods
Pmt = 0
FV = $1,000
Substituting the values in formula:
= -pv(9%,6,0,1000)
= $596.27
We can calculate the price of bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond
Rate = 6%
Nper = 6 periods
Pmt = 0
FV = $1,000
Substituting the values in formula:
= -pv(6%,6,0,1000)
= $704.96
Computation of the percentage change in price:-
% change in price = ($704.96 - $596.27) / $596.27
= $108.69 / $596.27
= 18.23%
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