Finance Question

Need to solve these questions as soon as possible (need to show all workings) Q1 In exchange for a lump sum payment now, Polysuper offers an annual pension over thirty years beginning with a payment of $30,000 at the end of the first year. There are thirty payments in total and the payments will increase at an annual rate of 3%pa. The appropriate opportunity cost of funds is j2 = 8%pa what is the amount of lump sum needed to purchase the pension? (Accurate to the nearest dollar) Q2 a) A ninety day bank bill with 90 days to maturity has a price of $99227.95. What is the effective annual yield implied by this price and maturity? Be careful I am not asking for the annual nominal yield, which by convention is normally quoted in financial markets. Face value is $100,000. b) What would be the price of this bank bill if you decide to sell it with 80 days left to maturity and the appropriate interest rate was 4.21%pa effective? c) Calculate the geometric average rate of return over three years given the following annual rates, year 1 = 5.55%, year 2 = 6.75%, year 3 = 8.37%. (geometric nor arithmetic) (Rates as a percentage accurate to one basis point and prices accurate to two decimal places) Q3 Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $1,500,000. The bonds were issued seven years and three months ago and still have two years and nine months to maturity. They pay a coupon rate of interest of 6.5% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.02% pa. The convention in Zanadu financial markets is that the market yield and coupon rate are quoted as annual nominal rates. What is the current market value of the bonds? (In dollars accurate to three decimal places) Q4 Polycorp has a dividend of $5.00 due in a year’s time and is expected to pay a dividend $5.50 at the end of the second year. Its dividend is expected to grow at 8% pa for the following year. Dividends are then expected to grow at 4% pa for another two years, after which they are expected to grow at 3.5%pa forever. Shareholders required return on equity is 10.85% pa. What is the current price (cum-dividend) of Polycorp shares? Polycorp has just paid a dividend of $4.75.