Mr. Z will need - 18,00,000 after two years for which he wants to make one-time necessary investment now. He has a choice of two types of bonds.…

To decide in which bond Mr. Z should invest, we shall compute duration of each bond as follows: Duration of Bond X Year Cash flow P.V. @ 12% Proportion of bond value Proportion of bond value x time (years) 1 1,080 0.893 964.44 1.000 1.000 Duration of the Bond is 1 year. Duration of Bond Y Year Cash flow P.V. @ 12% Proportion of bond value Proportion of bond value x time (years) 1 90 0.893 80.37 0.089 0.089 2 90 0.797 71.73 0.079 0.158 3 90 0.712 64.08 0.070 0.210 4 1,090 0.636 693.24 0.762 3.048 909.42 1.000 3.505 Thus, duration of the Bond is 3.505 years. Alternatively, it can also be computed as follows: Year Cash Flow PVF @12% Present Value (PV) Year × PV 1 90 0.893 80.37 80.37 2 90 0.797 71.73 143.46 3 90 0.712 64.08 192.24 4 1090 0.636 693.24 2772.96 909.42 3189.03 Duration = 3189.03 / 909.42 = 3.507 Let x 1 be the investment in Bond X and therefore investment in Bond Y shall be (1 - x 1 ). Since the required duration is 2 years the proportion of investment in each of these two securities shall be computed as follows: 2 = X 1 + (1 - x 1 ) 3.505 or 2 = x 1 + (1 - X 1 ) 3.507 X 1 = 0.60 Accordingly, the proportion of investment shall be 60% in Bond X and 40% in Bond Y respectively. Amount of investment Bond X Bond Y PV of 18,00,000 for 2 years @ 12% x 60% PV of 18,00,000 for 2 years @12% x 40% = 18,00,000 (0.797) x 60% = 18,00,000 (0.797) x 40% = 8,60,760 = 5,73,840 No. of Bonds to be purchased No. of Bonds to be purchased = 8,60,760 / 964.44 = 892.50 i.e. = 5,73,840 /909.42 = 631 i.e. Thus, 893 bonds Thus, 631 bonds Note: (i) The investor has to keep the money invested for two years. Therefore, the investor can invest in both the bonds with the assumption that Bond X will be reinvested for another one year on same returns. (ii) Further, in the above computation, Modified Duration can also be used instead of Duration.