Answer:
= 846.6576207
Explanation:
The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.
These cash flows include interest payment and redemption value
The price of the bond can be calculated as follows:
Step 1
PV of interest payment
Semi-annual coupon rate = 6%/2 = 3%
Semi-annual Interest payment =( 3%×$1000)= $30
Semi annual yield = 9%/2 = 4.5%
PV of interest payment
= A ×(1- (1+r)^(-n))/r
Note that the the bond was issued 3 years ago, therefore the time to maturity = 10 -3 = 7 years
A- interest payment, r- yield - 4.5%, n- no of periods- 2 × 7 = 14 periods
= 30× (1-(1.045)^(-7×2))/0.045)
= 30× 10.22282528
=$ 306.6847585
Step 2
PV of redemption value (RV)
PV = RV × (1+r)^(-n)
RV - redemption value- $1000, n- 7, r- 4.5%
= 1,000 × (1+0.045)^(-2×7)
= 539.97
Step 3
Price of bond = PV of interest payment + PV of RV
$ 306.68 + 539.97
= $846.6576207
Answer:
Price to get if the bond is sold $846.66
Explanation:
Face value of the bond $1000
Cr = 6%
r = 9%
n = 10 but the bond was issued 3 years ago so it has 7 years remaining to maturity semiannual = 7*2 = 14
Coupons payments are made semi annualy
C = 6%*1000/2 = $30
r = 9%/2 = 4.5%
BV = C* 1-(1+r)^-n/r + FV/ (1+r)^n
=30* 1-(1+0.045)^-17/0.045 +1000/(1+0.045)^14
=306.6848+ 539.9729
=$846.66
The bond wil trade below par since coupon rate is lower than market rate
