Module Contact: Will Carpenter, CMP Copyright of the University of East Anglia Version 1

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1 UNIVERSITY OF EAST ANGLIA School of Computing Sciences Main Series UG Examination FINANCIAL MATHEMATICS CMP-5009A Time allowed: 3 hours Answer ALL questions. Actuarial Tables are provided on desk. Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. CMP-5009A Module Contact: Will Carpenter, CMP Copyright of the University of East Anglia Version 1

2 1. Page 2 i) Describe how a repayment loan works. ii) Explain briefly two different ways of calculating how much capital is outstanding part-way through a repayment loan. [6 marks] (b) A borrower wishes to take out a repayment loan to purchase a new car. The loan will be for 15,000, repayable monthly in arrear over 4 years, at an effective interest rate of 12% per annum. Calculate the following: i) The amount of each monthly repayment. ii) The capital outstanding at the beginning of the final year, immediately after the repayment due at that point has been made. iii) The amount of interest repaid in the final repayment. [8 marks] (c) Two years after the loan is issued, immediately after the repayment due at that point has been made, the borrower asks the bank to change the frequency of the repayments from monthly in arrear, to quarterly in arrear. i) Calculate the revised quarterly repayment due from this point. ii) Explain why your answer is not three times the monthly repayment calculated in part (b) i). [6 marks] [Total: 20 marks] 2. Calculate the redemption amount for a fixed interest security using the following information: Price: Income: 10 per annum at the end of each year Interest rate: 8% per annum Term: 10 years [3 marks]

3 Page 3 (b) Calculate the yield available on a fixed interest security using the following information: Price: Income: 10 per annum at the end of each year Redemption: 150 Term: 10 years (c) Calculate the price an investor should pay for a fixed interest security using the following information: Interest rate: Income: Redemption: 100 Term: 10 years 15% per annum 5 per annum at the end of the first year and increasing by 1 each year thereafter [3 marks] [Total 10 marks] 3. Explain what a financial derivative is and what they are used for. A 3 month forward contract exists on a zero-coupon corporate bond with a current price per 100 nominal of The yield available on 3 month government securities is 5% p.a. effective. (b) Calculate the forward price. A share has a current price of 8 and pays out annual dividends starting with a dividend of 30p in three months time. (c) Calculate the forward price of a one-year forward contract on the share assuming the risk free rate of return is 6% p.a. effective. [Total 12 marks] TURN OVER

4 Page 4 4. A 15-year fixed interest security with coupon payments of 12% per annum payable half-yearly in arrear has been just been issued by a government. The bond will be redeemed at 110 per 100 nominal. An investor pays 25% tax on income and 35% tax on capital gains. (b) Calculate the maximum annual net redemption yield achieved if the investor does not obtain a capital gain. Calculate the maximum price an investor should pay for the security if they want to achieve a minimum net redemption yield of 9% per annum effective. (c) Calculate the minimum annual net redemption yield (to the nearest 0.1% per annum) obtained by the investor if they pay a price of 101 per 100 nominal. [5 marks] [Total 11 marks] 5. (b) Describe in words the Net Present Value of a project and state why it is an important measure. Give a formula for the Net Present Value of a project with discrete and continuous cashflows, defining any terms you use. A Company is considering a project which has an initial investment of 300,000. The project has an income of 10,000 received at the end of the first year, a continuous income of 150,000 per annum payable continuously for two years from the start of the second year and a final income of 200,000 received at the end of the fifth year. (c) (d) Calculate the Net Present Value for the project using an effective rate of interest of 10% per annum. [5 marks] Define the Internal Rate of Return of an investment project. [Total 13 marks]

5 6. Page 5 Explain briefly why a Government may issue fixed interest securities. (b) Describe the investment characteristics of Government fixed interest securities using the following headings: Security Marketability Investment Return [6 marks] An investment fund has assets of 200m and holds a range of investments including fixed interest securities, equities and property assets. (c) (d) List the types of fixed interest securities, equities and property the Investment fund might invest in. Outline the possible risks associated with investing in equities. [Total 14 marks] 7. An equity investment fund had the following values: Date Fund Value 1 January m 1 January m 1 January m 1 July m 31 December m The fund received a payment of 500,000 on 30 June For the period from 1 January 2015 to 31 December 2017 calculate the annual effective: (b) Money Weighted Rate of Return. Time Weighted Rate of Return. [Total 8 marks] TURN OVER

6 Page 6 8 An insurance company is due to pay out a sum of 88,733 in 3 years time and a sum of 556,966 in 15 years time. The company owns a perpetuity that pays 20,000 at the end of each year. The interest rate is 10% per annum effective. Demonstrate that the company is immunised against small changes in interest rates. [12 marks] END OF PAPER

7 Exam Feedback CMP-5009A Financial Maths Below are some general comments on the paper. Q1 Q2 Generally well answered but some answers did not give enough detail on part (i) (b) Generally well answered but some students struggled with part (iii) (c) Generally well answered but some students missed the fact that the change occurred after 2 years Generally well answered (b) Generally well attempted but some students didn t recognise that the information in part gave a good starting point that the yield was greater than 8% p.a. (c) Generally answered well but some students didn t know how to value the increasing annuity Q3 Q4 Bookwork - generally well answered (b) Generally well answered (c) Generally well answered but some students used the wrong formula. The question stated the dividend was 30p (i.e. fixed rather than expressed as a dividend yield) Many students missed this was a simple application of the capital gains test formula (b) Generally well answered (c) Some students omitted to show there was a capital gain (i.e. Redemption amount > Price but completed the remainder of the question well Q5 Bookwork and generally well answered (b) Bookwork but not always answered well. The questions stated that any terms used should be defined (c) Generally well answered although some students made a few calculations errors (d) Bookwork but often poorly answered Q6 Generally well answered (b) Bookwork but not always answered well with some students not giving enough distinct points on security, marketability and investment return (c) Straightforward bookwork but not always answered well (d) Generally answered well

8 Q7 Well answered by well-prepared students (b) Well answered by well-prepared students Q8 Well answered by well-prepared students