Question

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

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

(ii) The purchase goes ahead. Attendances rise as expected, but the club does not reach the Cup Final and 12 months after being bought the player is sold again. The club owner calculates that he has made a prot at that time of K750,898. Calculate the sale price.

(b) A woman who has won a prize is oered a lump sum of K1,000,000 to invest now or K550,000 to invest at the end of this year and another K550,000 to invest at the end of the following year. If all investments are assumed to earn 7% pa, which should she 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 a price of K91 per K100 nominal. After 30 days the investor sold the bill to a second investor for a price of K93.90 per K100 nominal. The second investor held the bill to maturity when it was redeemed at par. Determine which investor obtained the higher annual eective rate of return.

(d) Mr Banda is struggling to repay his loan of K200,000 with payments 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 Banda by restructuring his loan with new monthly payments of K2,744.90 made in arrears.

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

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

(e) A businessman wishes to borrow an amount of K1 million for a term of 5 years. The agreed rate of interest is 8% per annum effective for the first 3 years, and 6% per annum effective thereafter. Repayments on the loan are made annually in arrears.

(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 by the end of year 3.

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

Answer 1

All amounts in K

Given:

discounting rate = 5%

interest rate = 12% p.a (assume repayment of loan (of 10 million) has not been made)

Cash outflows:-

1. purchase cost of player = 10 million

2. increase in wages due to replacement = 20000/month = 240000 per annum

3. interest cost = 10 million * 12% = 1.2 million

Total annual cash outflow (2+3) = 1440000

Cash inflows:-

1. extra income per home match in year 1 = 100000

total home matches = 12 per year

home match access income = 1.2 million per annum

2. cup final access income = 2 million * 40% = 800000 per annum

total cash inflows = 2000000

Net cash flow = total cash inflow - total cash outflow

= 2000000 - 1440000

= 560000

solution:-

a) part i: calculation of NPV

year	cash flows	discounting factor @ 5%	DCF
0	-10000	1.000	-10000
1	560	0.952	533.3
2	560	0.907	507.9
3	560	0.864	483.7
4	560	0.823	460.7
5	560	0.784	438.8
6	560	0.746	417.9
7	560	0.711	398.0
8	560	0.677	379.0
9	560	0.645	361.0
9.5	280	0.629	176.1
		NPV	-5843.5

Ans: since NPV is negetive (- ve), hence new player should not be purchased