Homework SourseBond A Bond B Bond C Face Value 1000 1000 1000 Coupon rate 1
Bond A
Bond B
Bond C
Face Value
1000
1000
1000
Coupon rate
12
15
8
Yield to Maturity
11%
11%
11%
Years left to Maturity
15
10
9
Annual or Semi-Annual
Annual
Annual
Annual
You have been hired as a financial analyst. Your client has the choice between buying one of the bonds listed in the table above. You are required to create a detailed report to aid your client to reach a decision.
Compute the price of each bond. Why are the bonds’ prices different?
Compute the duration for each bond. What is the meaning of the duration result for each bond?
Analysts have predicted that in 3 months real interest rates will be 4% and that expected inflation will be 6.5%. Use the duration for each bond to help you to compute the expected percentage change in each price due to the change in the prevailing market interest rates in 3 months. Which bond will be more sensitive to the change in interest rates?
| Bond A | Bond B | Bond C | |
| Face Value | 1000 | 1000 | 1000 |
| Coupon rate | 12 | 15 | 8 |
| Yield to Maturity | 11% | 11% | 11% |
| Years left to Maturity | 15 | 10 | 9 |
| Annual or Semi-Annual | Annual | Annual | Annual |
Solution
Bond A Bond B Bond C Face Value (F) 1000 1000 1000 Coupon Rate (\'r) 12 15 8 Yield to maturity (i) 11 11 11 Years to maturity (n) 15 10 9 Annual or semiannual Annual Annual Annual Price of Bond = C*(1-(1/(1+i)^n))/i + F/(1+i)^n = (120*(1-(1/((1+0.11)^15)))/0.11+1000/((1+0.11)^15)) (150*(1-(1/((1+0.11)^10)))/0.11+1000/((1+0.11)^10)) (80*(1-(1/((1+0.11)^9)))/0.11+1000/((1+0.11)^9)) = 1,071.91 1,235.57 833.89 Bond prices are different because each bond ahas a different coupon rate and a different period for maturity Bond A Period Coupon Par Value Present Value Factor PV of Coupon PV/Price i.e. 1071.91 Duration A B C D= B*C E F= E*A -1 120 0.90 108.11 0.10 - 0.10 -2 120 0.81 97.39 0.09 - 0.18 -3 120 0.73 87.74 0.08 - 0.25 -4 120 0.66 79.05 0.07 - 0.29 -5 120 0.59 71.21 0.07 - 0.33 -6 120 0.53 64.16 0.06 - 0.36 -7 120 0.48 57.80 0.05 - 0.38 -8 120 0.43 52.07 0.05 - 0.39 -9 120 0.39 46.91 0.04 - 0.39 -10 120 0.35 42.26 0.04 - 0.39 -11 120 0.32 38.07 0.04 - 0.39 -12 120 0.29 34.30 0.03 - 0.38 -13 120 0.26 30.90 0.03 - 0.37 -14 120 0.23 27.84 0.03 - 0.36 -15 120 1000 0.21 234.08 0.22 - 3.28 Duration = - 7.86 years Bond B Period Coupon Par Value Present Value Factor PV of Coupon PV/Price i.e. 1235.57 Duration A B C D= B*C E F= E*A -1 150 0.90 135.14 0.11 - 0.11 -2 150 0.81 121.74 0.10 - 0.20 -3 150 0.73 109.68 0.09 - 0.27 -4 150 0.66 98.81 0.08 - 0.32 -5 150 0.59 89.02 0.07 - 0.36 -6 150 0.53 80.20 0.06 - 0.39 -7 150 0.48 72.25 0.06 - 0.41 -8 150 0.43 65.09 0.05 - 0.42 -9 150 0.39 58.64 0.05 - 0.43 -10 150 1000 0.35 405.01 0.33 - 3.28 Duration - 6.18 years Bond B Period Coupon Par Value Present Value Factor PV of Coupon PV/Price i.e. 1071.91 Duration A B C D= B*C E F= E*A -1 80 0.90 72.07 0.09 - 0.09 -2 80 0.81 64.93 0.08 - 0.16 -3 80 0.73 58.50 0.07 - 0.21 -4 80 0.66 52.70 0.06 - 0.25 -5 80 0.59 47.48 0.06 - 0.28 -6 80 0.53 42.77 0.05 - 0.31 -7 80 0.48 38.53 0.05 - 0.32 -8 80 0.43 34.71 0.04 - 0.33 -9 80 1000 0.39 422.20 0.51 - 4.56 Duration - 6.51 years Higher is the duration of the bond, greater is the sensitivity of the bond to price changes. From duration calculated we can say that, Bond A is more sensitive to price changes as compared to Bond B and C Bond C is more sensitivie than Bond B Bond B is the least sensitive bond to price changes amongst the 3 bonds. Real Interest Rate 4% Expected Inflation Rate 6.50% Expected Interest Rate 10.50% There is 50 point change in bond yield Approximate Percent Price change = - duration x change in yield x 100 Bond A Bond B Bond C -DURATION -7.86 -6.18 -6.51 Change in yield 0.005 0.005 0.005 Approximate Percent Price change - 3.93 - 3.09 - 3.26 Bond A is more sensitive to price changes
