1. (a) A football club is considering buying a player on 1January for K10 million. The player's wages will be K20,000 permonth higher than those of the man he will replace. The managerexpects the purchase to generate a level increase in atten- dances,which will yield an extra income in the rst year of K100,000 fromeach home match. The manager also expects the new player toincrease the club's chance of reaching the Cup Final in any oneyear from 10% to 40%. The extra amount generated for club funds byan appearance in a Cup Final on 30 April is K2 million. The clubplays a home match on the second of each month throughout the year,but all Cup matches are played away from home. Wages are paid atthe end of each month. Wages, ticket prices and the reward forreaching a Cup Final rise at 5% pa, the increments taking place on1 January. If the player is purchased, the cost will be borrowedfrom a bank, which will charge interest at 1% per month and willaccept repayment at any time. The owner of the club insists thatany purchase should show a prot if the managers expectation areborne out in practice.

(i) If the manager expects that he will keep the player for 9.5years until he retires, calculate the net present value of the cashow, in order to assess whether or not the purchase should goahead.

(ii) The purchase goes ahead. Attendances rise as expected, butthe club does not reach the Cup Final and 12 months after beingbought the player is sold again. The club owner calculates that hehas made a prot at that time of K750,898. Calculate the saleprice.

(b) A woman who has won a prize is oered a lump sum ofK1,000,000 to invest now or K550,000 to invest at the end of thisyear and another K550,000 to invest at the end of the followingyear. If all investments are assumed to earn 7% pa, which shouldshe choose if she intends to withdraw the money after

(i) 4 years,

(ii) 2 years.

(c) A 90-day government bill was bought by an investor for aprice of K91 per K100 nominal. After 30 days the investor sold thebill to a second investor for a price of K93.90 per K100 nominal.The second investor held the bill to maturity when it was redeemedat par. Determine which investor obtained the higher annual eectiverate of return.

(d) Mr Banda is struggling to repay his loan of K200,000 withpayments of K4,279 made monthly in arrears for 5 years.

(i) Find the amount of the level annual repayment.

(ii) Hence, otherwise, calculate the APR of Mr Smiths loan,

After exactly one year, a loan company oers to `help' Mr Bandaby restructuring his loan with new monthly payments of K2,744.90made in arrears.

(iii) Assuming the company charges the same APR as Mr Banda'soriginal loan, calculate the term of the new loan.

(iv) Calculate how much more interest in total Mr Banda will payon his restruc- tured loan than on his original loan.

(e) A businessman wishes to borrow an amount of K1 million for aterm of 5 years. The agreed rate of interest is 8% per annumeffective for the first 3 years, and 6% per annum effectivethereafter. Repayments on the loan are made annually inarrears.

(i) Find the amount of the level annual repayment.

(ii) Draw up the loan schedule for the full ve-year period.

(iii) Calculate what percentage of the loan has been repaid bythe end of year 3.

(iv) Without doing any further calculations, explain how thispercentage gure would alter if the rate of interest had insteadbeen 6% for the rst three years and 8% thereafter.