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Suppose a? ten-year, $1,000 bond with an 8
Suppose a? ten-year, $1,000 bond with an 8.6% coupon rate and semiannual coupons is trading for $1,034.06.
a. What is the? bond's yield to maturity? (expressed as an APR with semiannual? compounding)?
b. If the? bond's yield to maturity changes to 9.8% ?APR, what will be the? bond's price?
Expert Solution
a). We can calculate the yield to maturity by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Yield to maturity (semiannual)
Nper = 10*2 = 20 periods (semiannual)
Pmt = Coupon payment = $1,000*8.6%/2 = $43
PV = $1,034.06
FV = $1,000
Substituting the values in formula:
= rate(20,43,-1034.06,1000)
= 4.05%
Yield to maturity = Rate * 2
= 4.05% * 2
= 8.10%
b). We can calculate the price of the bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of the bond
Rate = 9.8%/2 = 4.9% (semiannual)
Nper = 10*2 = 20 periods (semiannual)
Pmt = Coupon payment = $1000*8.6%/2 = $43
FV = $1,000
Substituting the values in formula:
= -pv(4.9%,20,43,1000)
= $924.59
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