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You want to figure out how much money you will make by investing in bonds
You want to figure out how much money you will make by investing in bonds. In your portfolio, you have a premium bond from Pi Corporation that pays annual coupons at 8.7%. You also own a discount bond from Delta Inc. that pays 4.7% coupons annually.
Both bonds have twelve years to maturity and a par value of $1,000.
The market (YTM) for both bonds is 6.7%.
a) What is the current yield for Bond Pi? For Bond Delta?
(Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 12.34.)
b) If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond Pi? For Bond Delta?
(Hint: you will need to solve the price of each bond next year to find the capital gains yield. Each bond will have a maturity of 1 less year next year)
(A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Expert Solution
a) We can calculate the price of bond Pi now by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond Pi now
Rate = 6.7%
Nper = 12 periods
Pmt = Coupon payment = $1,000*8.7% = $87
FV = $1,000
Substituting the values in formula:
= -pv(6.7%,12,87,1000)
= $1,161.42
Computation of the current yield for bond Pi:-
Current yield = Annual coupon payment / Price of bond
= $1,000*8.7% / $1,161.42
= 7.49%
We can calculate the price of bond delta now by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond delta now
Rate = 6.7%
Nper = 12 periods
Pmt = Coupon payment = $1,000*4.7% = $47
FV = $1,000
Substituting the values in formula:
= -pv(6.7%,12,47,1000)
= $838.58
Computation of the current yield for bond delta:-
Current yield = Annual coupon payment / Price of bond
= $1,000*4.7% / $838.58
= 5.60%
b) We can calculate the price of bond Pi after 1 year by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond Pi after 1 year
Rate = 6.7%
Nper = 12-1 = 11 periods
Pmt = Coupon payment = $1,000*8.7% = $87
FV = $1,000
Substituting the values in formula:
= -pv(6.7%,11,87,1000)
= $1,152.24
We can calculate the price of bond delta after 1 year by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond delta after 1 year
Rate = 6.7%
Nper = 12-1 = 11 periods
Pmt = Coupon payment = $1,000*4.7% = $47
FV = $1,000
Substituting the values in formula:
= -pv(6.7%,11,47,1000)
= $847.76
Computation of the capital gains yield for bond Pi:-
Capital gains yield = ($1,152.24 - $1,161.42) / $1,161.42
= -$9.18 / $1,161.42
= -0.79%
Computation of the capital gains yield for bond delta:-
Capital gains yield = ($847.76 - $838.58) / $838.58
= $9.18 / $838.58
= 1.10%
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