The following data are available for three bonds A, B and C. These bonds are used by a bond portfolio manager to fund an outflow scheduled in 6 year…

CA Final · Advanced Financial Management · RTP · September 2025
The following data are available for three bonds A, B and C. These bonds are used by a bond portfolio manager to fund an outflow scheduled in 6 year Current yield is 9%. All bonds have face value of 100 each and will be redeemed at par. Interest is payable annually. Bond Maturity (Years) Coupon rate A 10 10% B 8 11% C 5 9% (i) Calculate the duration of each bond. (ii) The bond portfolio manager has been asked to keep 45% of the portfolio money in Bond A. Calculate the percentage amount to be invested in bonds B and C that need to be purchased to immunise the portfolio. (iii) After the portfolio has been formulated, an interest rate change occurs, increasing the yield to 11%. The new duration of these bonds are: Bond A = 7.15 Years, Bond B = 6.03 Years and Bond C = 4.27 years. Is the portfolio still immunized? Why or why not? (iv) Determine the new percentage of B and C bonds that are needed to immunize the portfolio. Bond A remaining at 45% of the portfolio. Present values be used as follows : Present Values t1 t2 t3 t4 t5 PVIF 0.09,t 0.917 0.842 0.772 0.708 0.650 Present Values t6 t7 t8 t9 t10 PVIF 0.09,t 0.596 0.547 0.502 0.460 0.422

Suggested Answer and Working Notes:

4. (i) Calculation of Bond Duration Bond A Year Cash flow P.V. @ 9% (1) x (4) (1) (2) (3) (4) 1 10 0.917 9.17 9.17 2 10 0.842 8.42 16.84 3 10 0.772 7.72 23.16 4 10 0.708 7.08 28.32 5 10 0.650 6.50 32.50 6 10 0.596 5.96 35.76 7 10 0.547 5.47 38.29 8 10 0.502 5.02 40.16 9 10 0.460 4.60 41.40 10 110 0.422 46.42 464.20 106.36 729.80 Duration of the bond A is = 729.80 / 106.36 = 6.862 years or 6.86 year Bond B Year Cash flow P.V. @ 9% (1) x (4) (1) (2) (3) (4) 1 11 0.917 10.09 10.09 2 11 0.842 9.26 18.52 3 11 0.772 8.49 25.47 4 11 0.708 7.79 31.16 5 11 0.650 7.15 35.75 6 11 0.596 6.56 39.36 7 11 0.547 6.02 42.14 8 111 0.502 55.77 445.76 111.13 648.25 Duration of the bond B is = 648.25 / 111.13 = 5.833 years or 5.83 years Bond C Year Cash flow P.V. @ 9% (1) x (4) (1) (2) (3) (4) 1 9 0.917 8.25 8.25 2 9 0.842 7.58 15.16 3 9 0.772 6.95 20.85 4 9 0.708 6.37 25.48 5 109 0.650 70.85 354.25 100.00 423.99 Duration of the bond C is = 423.99 / 100 = 4.24 years (ii) Amount of Investment required in Bond B and C Period required to be immunized 6.000 Years Less: Period covered from Bond A (45% of 6.86) 3.087 Years To be immunized from B and C 2.913 Years Let proportion of investment in Bond B and C is b and c respectively then. b + c = 0.55 (1) 5.84b + 4.24c=2.913 (2) On solving these equations, the value of b and c comes 0.3631 and 0.1869 respectively and accordingly, the % of investment of B and C is 36.31% and 18.69% respectively. (iii) With revised yield the Revised Duration of Bond stands 0.45 x 7.15 + 0.3631 x 6.03 + 0.1869 x 4.27 = 6.21 year No portfolio is not immunized as the duration of the portfolio has been increased from 6 years to 6.21 years. (iv) New percentage of B and C bonds that are needed to immunize the portfolio. Period required to be immunized 6.000 Year Less: Period covered from Bond A (7.15 x 45%) 3.218 Year To be immunized from B and C 2.782 Year Let proportion of investment in Bond B and C is b and c respectively, then b + c = 0.55 6.03b + 4.27c = 2.782 b = 0.2466 On solving these equations, the value of b and c comes 0.2463 and 0.3037 respectively and accordingly, the % of investment of B and C is 24.63% and 30.37 % respectively.

Topics: Security Valuation

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