Suppose a Gratuity Fund needs to make a payment of ₹ 1.70 crore after three years from now. You as a finance advisor wonder how to construct the…

(i) First, we shall calculate the Present Value and Duration of the LiabilityThe amount required after 3 years is:₹ 1.70 crore = ₹ 1,70,00,000The benchmark yield is 6.50% p.a. and the yield curve is flat.Therefore,PV = 1,70,00,000 × 0.8278PV = 1,40,72,600The duration of the liability is 3 years.To suggest a portfolio of investments in both categories of bonds that is immune to both price risk and reinvestment risk, we shall first calculate the duration of each bond. While the duration of the Zero-Coupon GOI Bond is equal to its remaining maturity period of 4 years, the duration of the Corporate Bond shall be calculated as follows: Year (1) Cash Flow (₹) (2) [email protected]% (3) PV (₹) (4) (1) x (4) 1 650 0.9390 610.35 610.35 2 10,650 0.8817 9390.11 18780.22 10000.46 19390.57 Duration of Corporate Bond = 19390.57 / 10000.46 = 1.94 yearsSince the duration of liability is 3 years, we can construct the following formula to match the duration of assets and liabilities:W GB × 4 + W CB × 1.94 = 3And following equation based on amount of investment following equation can be constructed:(ii) W GB + W CB = 1On solving both equation we get following percentage of investment in these bonds:W GB = 51.46% i.e., ₹ 72,41,760 i.e. 932 GOI BondsW CB = 48.54% i.e., ₹ 68,30840 i.e. 683 Corporate Bonds Particulars Number of Bonds Price of the Bond (₹) Investment (₹) Zero-Coupon GOI Bond 932 7,773 72,44,436 Corporate Bond 683 10,000 68,30,000 Total 1,40,74,436 If after 3 years the interest rate rises by 50 bps i.e. 0.50% the revised value of portfolio shall be computed as follows:Revised Interest Rate = 6.50% + 0.50% = 7.00%The Corporate Bond matures after two years. Its maturity proceeds of(₹10,000 + ₹650) + (₹ 650 x 1.065) = ₹ 11,342.25In the end of 2 nd year above sum can then be reinvested for one year at 7% and revised value per Bond stands at end of 3 rd year as follows:₹ 11,342.25 (1.07) = ₹ 12,136.21 per Corporate Bond.The Zero-Coupon GOI Bond has one year remaining at the end of three years. Its value at that point, assuming a 7% yield, would be:10,000 / 1.07 = ₹9,345.79Thus, the value of the portfolio at the end of 3 rd year would be: Particulars Number of Bonds Price of the Bond (₹) Investment (₹) Zero-Coupon GOI Bond 932 9,345.79 8710276 Corporate Bond 683 12,136.21 82,89,031 Total 1,69,99,307 Thus, it can be seen that despite the rise in interest rates the amount available to meet the liability after 3 years shall be approx. ₹ 1.70 Crore.