2 Bond Immunization Example 3 Example 4 You need to have $4,000,000 in five years to invest in a piece of equipment needed to finish a project. 5 Assume that the Par Value of each bond is $1,000. Change in the Yield to Maturity 6% $ $ Zero Coupon Bond 3,319,504,209,873.33 3.80% 9.80% 5 0% Bond 1 5,300,224,170,024.02 $ 3.63% 9.63% Bond 2 4,740,784,435,741.76 3.55% 9.55% Bond 3 6,024,814,224,306.99 3.88% 9.88% 11 12 13 10 14 4.50% 3.50% 5.30% 15 Invested Amount Current Yield to Maturity New Yield to Maturity Time to Maturity (Years) Coupon Rate Coupons at New Yield in Five Years Value of Bond and Reinvested Coupons at Current Yield in Five Years Price of bond Today at Current Number of Bonds Purchased Duration $1,000.00 $1,183.24 $1,211.77 $1,148.65 16 17 18 19 $1,000.00 $829.88 4,000,000,000.00 $1,258.44 $1,052.94 5,033,740,930.92 6.18 $1,187.87 $997.75 4,751,495,889.56 4.67 $1,349.81 $1,115.87 5,399,228,132.66 8.13 5.00 21 Questions: 1. Which of the bond portfolios provides the best outcome if interest rates change? Portfolio 1 2. If the duration of a bond is less than the amount of time until the time when the 0.783230846 money is needed for the project and the yield to maturity increases, what happens to the amount of cash available when the cash is needed? Bond 1 Bond 2 0.216769154 24 Bond Portfolio 1 25 Weights 26 Duration 27 28 Bond Portfolio 2 29 Weights 30 Duration Bond 2 Rond 3 0.905443811 3. If the duration of a bond is greater than the amount of time until the time when the money is needed for the project and the yield to maturity increases, what happens to the amount of cash available when the cash is needed? 0.0945561891 31 Change in the Yield to Maturity -5.00% -4.00% -3.00% -2.00% 1.00% Zero Coupon Bond Ending Value $ 4,000,000,000,000.00 $ 4,000,000,000,000.00 $ 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 Portfolio 1 Ending Value Portfolio 2 Ending Value $ 5,814,987,813,878.38 $ 5,845,938,394,493.61 $ 5,808,681,117,943.61 $ 5,832,704,093,057.31 $ 5,803,435,261,686.20 $ 5,821,559,026,476.59 $ 5,799,228,136,431.48 $ 5,812,393,361,368.81 $ 5,796,039,006,600.97 $ 5,805,106,006,873.90 $ 5,792,638,202,309.86 $ 5,795,801,239,674.75 $ 5,792,391,258,500.46 $ 5,793,619,081,468.94 $ 5,793,091,642,313.45 $ 5,792,984,588,617.95 $ 5,794,724,431,992.62 $ 5,793,830,632,020.63 $ 5,797,275,688,866.88 $ 5,796,095,315,385.19 4.0026 0.0096 4.0096 5.00% 2 Bond Immunization Example 3 Example 4 You need to have $4,000,000 in five years to invest in a piece of equipment needed to finish a project. 5 Assume that the Par Value of each bond is $1,000. Change in the Yield to Maturity 6% $ $ Zero Coupon Bond 3,319,504,209,873.33 3.80% 9.80% 5 0% Bond 1 5,300,224,170,024.02 $ 3.63% 9.63% Bond 2 4,740,784,435,741.76 3.55% 9.55% Bond 3 6,024,814,224,306.99 3.88% 9.88% 11 12 13 10 14 4.50% 3.50% 5.30% 15 Invested Amount Current Yield to Maturity New Yield to Maturity Time to Maturity (Years) Coupon Rate Coupons at New Yield in Five Years Value of Bond and Reinvested Coupons at Current Yield in Five Years Price of bond Today at Current Number of Bonds Purchased Duration $1,000.00 $1,183.24 $1,211.77 $1,148.65 16 17 18 19 $1,000.00 $829.88 4,000,000,000.00 $1,258.44 $1,052.94 5,033,740,930.92 6.18 $1,187.87 $997.75 4,751,495,889.56 4.67 $1,349.81 $1,115.87 5,399,228,132.66 8.13 5.00 21 Questions: 1. Which of the bond portfolios provides the best outcome if interest rates change? Portfolio 1 2. If the duration of a bond is less than the amount of time until the time when the 0.783230846 money is needed for the project and the yield to maturity increases, what happens to the amount of cash available when the cash is needed? Bond 1 Bond 2 0.216769154 24 Bond Portfolio 1 25 Weights 26 Duration 27 28 Bond Portfolio 2 29 Weights 30 Duration Bond 2 Rond 3 0.905443811 3. If the duration of a bond is greater than the amount of time until the time when the money is needed for the project and the yield to maturity increases, what happens to the amount of cash available when the cash is needed? 0.0945561891 31 Change in the Yield to Maturity -5.00% -4.00% -3.00% -2.00% 1.00% Zero Coupon Bond Ending Value $ 4,000,000,000,000.00 $ 4,000,000,000,000.00 $ 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 4,000,000,000,000.00 Portfolio 1 Ending Value Portfolio 2 Ending Value $ 5,814,987,813,878.38 $ 5,845,938,394,493.61 $ 5,808,681,117,943.61 $ 5,832,704,093,057.31 $ 5,803,435,261,686.20 $ 5,821,559,026,476.59 $ 5,799,228,136,431.48 $ 5,812,393,361,368.81 $ 5,796,039,006,600.97 $ 5,805,106,006,873.90 $ 5,792,638,202,309.86 $ 5,795,801,239,674.75 $ 5,792,391,258,500.46 $ 5,793,619,081,468.94 $ 5,793,091,642,313.45 $ 5,792,984,588,617.95 $ 5,794,724,431,992.62 $ 5,793,830,632,020.63 $ 5,797,275,688,866.88 $ 5,796,095,315,385.19 4.0026 0.0096 4.0096 5.00%