1. A 30-year 6% semi-annual coupon bond has a tenor of 18 years and a yield to m
ID: 2816278 • Letter: 1
Question
1. A 30-year 6% semi-annual coupon bond has a tenor of 18 years and a yield to maturity of 7.2%. If the PAR value of the bond is $1000, what is the price of the bond today? 2. A 30-year 6% semi-annual coupon bond has a yield to maturity of 8.1% and a PAR value of $1000. If the current price is 84.0723% of PAR, what must be the tenor, in years? 3. A 30-year 6% semi-annual coupon bond has a PAR value of $1000 and a current price of 103.2121% of PAR. If the tenor of the bond is 14 years, what must the yield to maturity be?
Please Show Work.
Explanation / Answer
1)
time to maturity = t = 18 years
coupon rate , c = 6% = 0.06
par value of bond , m = $1000
coupon value, x = c*m = 0.06*1000 = 60
semi-annual coupon value , C = x/2 = 60/2 = 30
no. of semi-annual periods , n = 2*t = 2*18 = 36
yield to maturity , y = 7.2%
semi-annual yield to maturity , r = y/2 = 7.2/2 = 3.6% = 0.036
price of bond today , p = (present value(PV) of coupon amounts) + (PV of maturity amount )
present value(PV) of coupon amounts = C*PVIFA(3.6%,36 )
where PVIFA = present value interest rate factor of annuity
PVIFA(3.6%,36 ) =[ (1+r)n -1]/((1+r)n *r)
= [ (1.036)36 -1]/((1.036)36 *0.036) = 20.00195588
present value(PV) of coupon amounts = 30*20.00195588 = 600.0586765
PV of maturity amount = par value/((1+r)n ) = 1000/((1.036)36 ) = 279.9295882
price of bond today , p = (present value(PV) of coupon amounts) + (PV of maturity amount )
p = 600.0586765 + 279.9295882 = 879.9882647 or $879.99 ( rounding off to 2 decimal places)
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