a) Rank the following alternatives in terms of present value assuming a discount rate of 8 percent.
(i) A growing perpetuity paying £25,000 each year, with the first payment in one year's time. The growth rate of the perpetuity is 4 percent.
(ii) A four-year annuity paying £200,000 each year, with the first payment in one year's time.
(iii) A payment of £750,000 in two years' time.
(iv) A growing perpetuity paying £30,000 each year, with the first payment due immediately. The growth rate of the perpetuity is 3 percent.
b) You are thinking of buying a fridge-freezer. Two competitive retailers, Dickson's Plc and Flurry's sell this machine with a price tag of £500. They have a buy now pay later scheme with Dickson's Plc charging a flat interest rate of 9.4% with monthly compounding and Flurry's Plc charging a rate of 9.2% with quarterly compounding. If you plan to repay in one year's time, which retailer would you prefer to buy your machine from? What are the EARs charged by the two firms?
c) A stock's end-of-year price over a four year period is: 150p, 152p, 145p, and 180p. The dividend in each of the last three years, paid immediately before the date of the end-of-year price, is 8p. What are the returns on the stock in each of the last three years? What is the total return over the three years to an investor who buys the stock at 150p and holds the stock for three years, reinvesting intermediate dividends back into the stock? What is the equivalent constant annual average return over the three year period?