Mr. A will need 1 Crore after two years for which he wants to make one-time necessary investment now. He has a choice of two types of bonds. Their…

Current Price and Duration of Bond X Year Cash flow P.V. @ 10% Proportion of bond value Proportion of bond value x time (years) 1 1,07,000 0.909 97263 1.000 1.000 Duration of the Bond is 1 year. Duration of Bond Y Year Cash flow P.V. @ 10% Proportion of bond value Proportion of bond value x time (years) 1 8,000 0.909 7272 0.077 0.077 2 8,000 0.826 6608 0.071 0.142 3 8,000 0.751 6008 0.064 0.192 4 1,08,000 0.683 73764 0.788 3.152 93652 1.000 3.563 Duration of the Bond is 3.563 years. 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 ) 3.563 x 1 = 0.610 Accordingly, the proportion of investment shall be 61% in Bond X and 39% in Bond Y respectively. Amount of investment Bond X Bond Y PV of 1,00,00,000 for 2 years @ 10% x 61% PV of 1,00,00,000 for 2 years @ 10% x 39% = 1,00,00,000 (0.826) x 61% = 1,00,00,000 (0.826) x 39% = 50,38,600 = 32,21,400 No. of Bonds to be purchased No. of Bonds to be purchased = 50,38,600 /97263 = 51.80 i.e. approx. 52 bonds = 32,21,400/93652 = 34.40 i.e. approx. 34 bonds Note: 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. Further, in the above computation, Modified Duration can also be used instead of Duration.