Given;
Bond Valuation;
The value of a bond is calculated using the formula;
Bond value V=PV of future interest payments+PV of maturity value
V=C×1-(1+r)-nrd+M(1+rd)n
Where PV is the present value and
C is the annual interest
For both bond A and B; Annual interest = 0.1×1000 = $100
Bond A Valuation
At 12% market rate;
V=100×1-(1+0.12)-120.12+1000(1+0.12)12=$876.12
At 6% market rate;
V=100×1-(1+0.06)-120.06+1000(1+0.06)12=$1335.35
At 2% market rate;
V=100×1-(1+0.02)-120.02+1000(1+0.02)12=$1846.02
Bond B Valuation
At 12% market rate;
V=100×1-(1+0.12)-20.12+1000(1+0.12)2=$966.20
At 6% market rate;
V=100×1-(1+0.06)-20.06+1000(1+0.06)2=$1073.34
At 2% market rate;
V=100×1-(1+0.02)-20.02+1000(1+0.02)2=$1155.32
The value at maturity of both bonds is $1000. The present value of the bonds at various market rates are as shown above. There are differences in prices due differences in coupon rates, the value of bond and the yield . A coupon rate higher than the yield results in a bond value worth more than the value at maturity i.e. the bond is sold at a premium. Whereas, a coupon rate lower than the yield is sold at a discount as the valuation is less than the value at maturity (Fabozzi & Peterson, 2003, P.230).
Works Cited
Fabozzi, Frank, and Pamela Peterson. "THE FUNDAMENTALS OF VALUATION." Financial Management and Analysis. Second ed. Hoboken, New Jersey: John Wiley & Sons, 2003. 226-230. Print.
