A company has to pay 2,000 (10-t) at the end of year t, for t=5,6,7,8,9....

Transcribed Image Text:

A company has to pay £ 2,000 (10-t) at the end of year t, for t=5,6,7,8,9. It values these liabilities assuming that there will be a constant effective annual rate of interest of 6% pa. (0) Calculate the present value of the company's liabilities. The company wants to immunise its exposure to the liabilities by investing in two bonds: Bond A pays coupons of 5% pa annually in arrears and is redeemable at par in 15 years" time Bond B is a zero-coupon bond that is redeemable at par in 5 years' time. The gross redemption yield on both stocks is the same as the interest rate used to value the liabilities. (a) (ii) (b) [3] Determine the amount that the company should invest in each of the two bonds to ensure that the present value and discounted mean term of the assets are equal to those of the liabilities. State the third condition required for immunisation. [9] [Total 12] An insurance company has liabilities of £10 million due in 10 years' time and £20 million due in 15 years' time. The company's assets consist of two zero-coupon bonds. One pays £7.404 million in 2 years' time and the other pays £31.834 million in 25 years' time. The current interest rate is 7% per annum effective. Show that Redington's first two conditions for immunisation against small changes in the rate of interest are satisfied for this insurance company. [6] Calculate the present value of profit that the insurance company will make if the interest rate increases immediately to 7.5% per annum effective. [2] Explain, without any further calculation, why the insurance company made a profit as a result of the change in the interest rate. [2] [Total 10] A company has to pay £ 2,000 (10-t) at the end of year t, for t=5,6,7,8,9. It values these liabilities assuming that there will be a constant effective annual rate of interest of 6% pa. (0) Calculate the present value of the company's liabilities. The company wants to immunise its exposure to the liabilities by investing in two bonds: Bond A pays coupons of 5% pa annually in arrears and is redeemable at par in 15 years" time Bond B is a zero-coupon bond that is redeemable at par in 5 years' time. The gross redemption yield on both stocks is the same as the interest rate used to value the liabilities. (a) (ii) (b) [3] Determine the amount that the company should invest in each of the two bonds to ensure that the present value and discounted mean term of the assets are equal to those of the liabilities. State the third condition required for immunisation. [9] [Total 12] An insurance company has liabilities of £10 million due in 10 years' time and £20 million due in 15 years' time. The company's assets consist of two zero-coupon bonds. One pays £7.404 million in 2 years' time and the other pays £31.834 million in 25 years' time. The current interest rate is 7% per annum effective. Show that Redington's first two conditions for immunisation against small changes in the rate of interest are satisfied for this insurance company. [6] Calculate the present value of profit that the insurance company will make if the interest rate increases immediately to 7.5% per annum effective. [2] Explain, without any further calculation, why the insurance company made a profit as a result of the change in the interest rate. [2] [Total 10]

Answer rating: 100% (QA)

Solution Part i To calculate the present value of the companys liabilities we need to discount each payment back to the present time using the given effective annual rate of interest of 6 pa The prese... View the full answer