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?A(n) 10
?A(n) 10.0?%, ?25-year bond has a par value of? $1,000 and a call price of ?$1,100. ?(The bond's first call date is in 5? years.) Coupon payments are made semiannually? (so use semiannual compounding where? appropriate).
a. Find the current? yield, YTM, and YTC on this? issue, given that it is currently being priced in the market at $1,225. Which of these 3 yields is the? highest? Which is the? lowest? Which yield would you use to value this? bond?
b. Repeat the 3 calculations? above, given that the bond is being priced at ?$875. Now which yield is the? highest? Which is the? lowest? Which yield would you use to value this? bond?
Expert Solution
a). Computation of the current yield:-
Current yield = Annual coupon payment / Current price of the bond
= $1,000 * 10% / $1,225
= 8.16%
We can calculate the yield to maturity (YTM) by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = YTM (semiannual)
Nper = 25*2 = 50 periods (semiannual)
Pmt = Coupon payment = $1,000*10%/2 = $50
PV = $1,225
FV = $1,000
Substituting the values in formula:
= rate(50,50,-1225,1000)
= 3.96%
YTM = Rate * 2
= 3.96% * 2
= 7.92%
We can calculate the yield to call (YTC) by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = YTC (semiannual)
Nper = 5*2 = 10 periods (semiannual)
Pmt = Coupon payment = $1,000*10%/2 = $50
PV = $1,225
FV = $1,100
Substituting the values in formula:
= rate(10,50,-1225,1100)
= 3.20%
YTC = Rate * 2
= 3.20% * 2
= 6.40%
Current yield is highest.
YTC is lowest.
The yield to call (YTC) will be used to value of the bond because the convention is to use the lower more conservative measure of yield.
b). Computation of the current yield:-
Current yield = Annual coupon payment / Current price of the bond
= $1,000 * 10% / $875
= 11.43%
We can calculate the yield to maturity (YTM) by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = YTM (semiannual)
Nper = 25*2 = 50 periods (semiannual)
Pmt = Coupon payment = $1,000*10%/2 = $50
PV = $875
FV = $1,000
Substituting the values in formula:
= rate(50,50,-875,1000)
= 5.77%
YTM = Rate * 2
= 5.77% * 2
= 11.53%
We can calculate the yield to call (YTC) by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = YTC (semiannual)
Nper = 5*2 = 10 periods (semiannual)
Pmt = Coupon payment = $1,000*10%/2 = $50
PV = $875
FV = $1,100
Substituting the values in formula:
= rate(10,50,-875,1100)
= 7.53%
YTC = Rate * 2
= 7.53% * 2
= 15.06%
YTC is highest.
Current yield is lowest.
The yield to maturity (YTM) will be used to value the bond because the convention is to use the lower of YTM or YTC for discount bonds
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