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Spartans outstanding bonds have a $1,000 par value and they mature in 20 years
Spartans outstanding bonds have a $1,000 par value and they mature in 20 years. Their nominal yield to maturity is 9% and they pay interest semiannually. The bond sell at a price of $975.
a) What is the bond's coupon rate?
b) Next year the same bond with the coupon rate that you calculated in part a is selling for a nominal yield to maturitty of 8.50%.What is the price of that bond next year?
Expert Solution
a) We can calculate the semiannual coupon payment by using the following formula in excel:-
=pmt(rate,nper,-pv,fv)
Here,
Pmt = Semiannual coupon payment
Rate = 9%/2 = 4.5% (semiannual)
Nper = 20*2 = 40 periods (semiannual)
PV = $975
FV = $1,000
Substituting the values in formula:
= pmt(4.5%,40,-975,1000)
= $43.64
Coupon rate = Annual coupon payment / Face value
= $43.64 * 2 / $1,000
= 8.73%
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 = 8.50%/2 = 4.25% (semiannual)
Nper = (20-1)*2 = 38 periods (semiannual)
Pmt = Coupon payment = $43.64
FV = $1,000
Substituting the values in formula:
= -pv(4.25%,38,43.64,1000)
= $1,021.33
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