Suppose a 10-year,
$1,000
bond with an
8.9 %
coupon rate and semi-annual coupons is trading for a price of
$1,034.97.
a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)?
b. If the bond's yield to maturity changes to
9.1 %
APR, what will the bond's price be?
a) | ||
Bond price =C*[1-(1+YTM)^-n / YTM] + [P/(1+YTM)^n] | ||
Where, | ||
C= Coupon amount | ||
YTM = Yield To maturity | ||
n = Number of periods | ||
P= Par value | ||
$1034.97=89 * [1 - (1 + YTM)^-10 / YTM] + [1000 / (1 + YTM ) ^10] | ||
YTM = | 8.37% | |
b) | ||
Computation Of Bond Price | ||
a | Semi-annual Interest Amount | $ 44.50 |
($1000*8.9%/2) | ||
b | PV Annuity Factor for (20 Years,4.55%) | 12.951762 |
c | Present Value Of Annual Interest (a*b) | $ 576.35 |
d | Redemption Value | $ 1,000.00 |
e | PV Factor Of (20 Years,4.55%) | 0.41069 |
g | Present Value Of Redemption Amount (d*e) | $ 410.69 |
f | Intrinsic Value ( Price ) Of The Bond (c+g) | $ 987.05 |
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