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The force of interest, 6(), at time f is given by: D.04 + 0.003- for 0 8 (i) Calculate the present value (at time / = 0) of an investment of $1,000 due at time / = 10. 141 (ii) Calculate the constant rate of discount per annum convertible quarterly. which would lead to the same present value as that in part (i) being obtained. [2] (iii) Calculate the present value (at time ?= 0) of a continuous payinent stream payable at the rate of 100e". from time / = 10 to f = 18. [4] [Total 10] An ordinary share pays dividends on each 31 December. A dividend of 35p per share was paid on 31 December 2011. The dividend growth is expected to be 3% in 2012, and a further 5% in 2013. Thereafter, dividends are expected to gow at 6% per annum compound in perpetuity. (1) Calculate the present value of the dividend stream described above at a rate of interest of 8% per annum effective for an investor holding 100 shares on 1 January 2012. [4] An investor buys 100 shares for $17.20 each on 1 January 2012. He expects to sell the shores for $18 on 1 January 2015. (ii) Calculate the investor's expected real rate of return. You should assume that dividends grow as expected and use the following values of the inflation index: Year: 2012 2013 2014 2015 Inflation index 110.0 112.3 113.2 113.8 at start of year: [5] |Total 91I'wo bonds paying annual coupons of 5% in arrear and redeemable at par have terms to maturity of exactly one year and two years, respectively. The gross redemption yield from the 1-year bond is 4.5% per annum effective; the gross redemption yield from the 2-year bond is 5.3% per annum effective. You are infonned that the 3-year par yield is 5.6% per annum. Calculate all zero-coupon yields and all one-year forward rates implied by the yields given above. [12] A loan pays coupons of 11% per annum quarterly on 1 January, 1 April, 1 July and 1 October each year. The loan will be redeemed at 1 15% on any 1 January from 1 January 2015 to 1 January 2020 inclusive, at the option of the borrower. In addition to the redemption proceeds, the coupon then due is also paid. An investor purchased a holding of the loan on 1 January 2005. immediately after the payment of the coupon then duc, at a price which gave him a net redemption yield of at least 8% per annum effective. The investor pays tax at 30%% on income and 25 on capital gains. On 1 January 2008 the investor sold the holding, immediately after the payment of the coupon then due, to a fund which pays no tax. The sale price gave the fund a gross redemption yield of at least 9% per annum effective. Calculate the following: (i) The price per $100 nominal at which the investor bought the loan. [6] (ii) The price per $100 nominal at which the investor sold the loan. 141 (iii) The net yield per annum convertible quarterly that was actually obtained by the investor during the period of ownership of the loan. [5] [Total 15]
