# The Finance

1. A loan of a nominal amount of £2m is to be issued with coupons of 8% per annum payable half-yearly in arrear. Capital will be redeemed at 107% on a coupon date between 20 and 25 years after the date of issue, inclusive, with the date of redemption at the option of the borrower. An investor liable to income tax at 30% and capital gains tax of 35% decides to purchase the loan at the date of issue. Calculate the price per £100 nominal which the investor should pay to ensure they will receive a net effective yield of at least 7% per annum. (Total 8 marks) 2. The one-year forward rate of interest at time t = 1 is 8% per annum effective. The gross redemption yield of a two-year fixed interest stock issued at time t = 0 and paying coupons of 6% per annum annually in arrears is 7% per annum effective. The stock is to be redeemed at par. The issue price (at time t = 0) of a 3-year fixed interest stock redeemable at par and bearing coupons of 9% per annum payable annually in arrear is £104 per £100 nominal. a. Calculate the one-year spot rate per annum effective at time t = 0.   (6 marks) b. Calculate the one-year forward rate per annum effective at time t = 2 years. (4 marks) 3. An ordinary share pays annual dividends. The last dividend was 30p per share and has just been paid. Dividends are expected to grow by 4% next year and by 5% the following year. Thereafter, dividends are expected to grow in perpetuity at 6% per annum compound. Calculate the present value of the future dividend stream described above, at a rate of interest of 8% per annum effective for an investor holding 250 shares. (Total 6 marks) 4. An investor purchased a bond with exactly 15 years left to redemption. The bond is redeemable at 110% and has a gross redemption yield of 7% per annum effective. It pays coupons of 6% per annum, half-yearly in arrears. The investor pays income tax at a rate of 25% but does not pay capital gains tax. a. Calculate the price paid by the investor for the bond. (3 marks) b. After exactly 8 years, immediately after payment of the coupon then due, the first investor sells the bond to another investor. The second investor pays income tax at a rate of 20% and capital gains tax at a rate of 35% and purchases the bond at a net return of 5% per annum effective. (i) Calculate the price paid by the second investor. a. Calculate the annual effective rate of return earned by the first investor over the period during which the bond was held. (12 marks) 5. A company is undertaking a property investment project which requires an investment of £8.5 million at inception and £2 million after two years. Income from the project is expected to be received continuously at a rate of £1 million per annum from the beginning of the 3rd year of the project until the end of the 4th year. The rate of payment of income is then expected to increase linearly and continuously from £2 million per annum at the start of the 5th year up to £9 million per annum as at the end of the 11th year of the project, at which time the project ends. a. Calculate the net present value of the project at 9% per annum effective. (6 marks) b. Calculate the discounted payback period, calculated at 9% per annum effective?(5 marks)

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