SAMPLE ASSIGNMENT
Academic Year 2023-24 (April/August 2023)
Module number: MSO3610
Name of module: FINANCIAL DATA ANALYSIS
ATTEMPT ANY FOUR QUESTIONS
{PLEASE NOTE THIS SAMPLE PAPER HAS NINE QUESTIONS THE ACTUAL EXAM WILL ONLY HAVE SIX QUESTIONS}
Question 1
(a) Briefly describe the difference between simple interest and compound interest. [3 marks]
(b) How much would an investment of $15,550 @ 8.3%/annum simple interest be worth after 4 years? Calculate the interest on this investment. [2 marks]
(c) How much would an investment of $12,550 @ 9.2%/annum compound interest (compounded annually) be worth after 5 years? Calculate the interest on this investment. [2 marks]
(d) How much would an investment of $9,550 @ 5.3%/annum (nominal rate)
compounded monthly be worth after three years and seven months? Calculate the interest on this investment. [3 marks]
(e) Calculate the APR of an investment paying a nominal rate of interest of 8.7%/annum compounded weekly. [3 marks]
(f) If we invested $13,550 at 5.3%/annum (nominal rate) compounded continuously for 15 months, how much would our investment be worth at the end of this period? [3 marks]
(g) Banks often charge customers interest based on daily compounding. Briefly outline why they do this. [4 marks]
(h) If GBP1.0000 = USD1.6203 and annual interest rates in GB are 0.55% and USA are 0.35%. Calculate the 7 month forward rate of exchange.
(You must use the continuous compounding formula.) [5 marks]
Question 2
(a) Briefly describe the concept of Present Value. [2 marks]
(b) A project has the following cash flows:
YEAR CASH INFLOW CASH OUTFLOW
0 0 £4000
1 £9000 £3000
2 £9500 £4000
3 £8500 £3000
4 £5000 £3000
Calculate the NPV if the interest rate is 5%.
Calculate the NPV if the interest rate is 11%
Estimate the IRR of the project. [6 marks]
(c) Explain why we are interested in finding the IRR of a project. [4 marks]
(d) Briefly describe the difference between arepayment mortgage and an interest only mortgage.
Given that an individual can either take arepayment mortgage or an interest only mortgage at the same rate and the same term which one will cost more?
Why would someone choose the more costly option? [4 marks]
(e) A repayment mortgage of £175,000 secured on a house charges 3.75%/annum nominal rate compounded monthly over 25 years. Calculate the monthly payments. [4 marks]
(f) What is the value a bond with a redemption value of $1,000 @ 3% nominal
payable twice annually redeemable in 3 years where the prevailing interest rate is 2%.
(You must use continuous compounding discounting.) [5 marks]
Question 3
A bank is reviewing its bank charges and wishes to find the average charge paid annually by its customers. The bank believes this figure to be $160/annum.
It samples 27 customers and finds the average charge is $145.55/annum with sample standard deviation $35.47/annum.
(a) Develop a 95% confidence interval and a 98% confidence interval for the mean using ± zx S/vn .
What conclusions can you draw from this? [7 marks]
(b) Without doing any calculations discuss the shortcomings of these calculations for the confidence intervals. How would you make the confidence interval more appropriate for the data? What changes would you expect in the confidence intervals in comparison with the ones calculated in part (a)? [5 marks]
(c) Develop a hypothesis test for this situation and clearly state the null hypothesis and the alternate hypothesis. [3 marks]
(d) Using calculate the test statistic. [3 marks]
(e) Discuss the significance of the test statistic. What conclusions can you draw from the value of the test statistic that you calculated in part (d)? [7 marks]
Question 4
(a) In a back office of an investment bank the staff reconcile transactions. It is
thought that the time taken in minutes for a member of staff to reconcile each transaction is governed by the exponential distribution with pdf:
f(x) = { 0.03exp(-0.03x) for x≥0
{ 0 for x<0
(i) Find the probability that it takes less than 15 minutes to reconcile a transaction. [2 marks]
(ii) Find the probability that it takes between 15 and 30 minutes to reconcile a transaction. [2 marks]
(iii) Find the probability that it will take over 30 minutes to reconcile a transaction. [3 marks]
(iv) How many transactions would you expect a member of staff to reconcile in one hour? [4 marks]
(v) Explain when it is appropriate to use the exponential distribution. [3 marks]
(b) Explain the importance of the Normal distribution. [4 marks]
(c) The share price of Company A is thought to follow a normal distribution
with mean €25.00 and standard deviation €0.25.
Calculate the probability that:
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(i) The share price is at most €24.50
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[1 mark]
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(ii) The share price is at least €25.40
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[2 marks]
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(iii) The share price is between €24.30 and €25.50
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[2 marks]
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(iv) What percentage of the time would you expect the share
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price to be between €24.50 and €25.40?
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[2 marks]
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Question 5
Consider the following data of monthly returns based on the closing prices on the last trading day of each month:
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Month
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Share C
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Market
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January
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-0.086
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-0.030
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February
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0.061
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0.005
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March
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0.026
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-0.037
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April
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0.195
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0.029
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May
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0.010
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-0.012
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June
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0.098
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0.014
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July
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-0.043
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-0.022
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August
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-0.041
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0.001
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Assume the risk free monthly return is 0.002 throughout this period.
(a) Calculate and interpret the correlation between Share C returns less the risk free monthly return and Market returns less the risk free monthly returns. [9 marks]
(b) Use the Capital Asset Pricing Model:
(RC,t – RF,t) = αC + βC × (RM,t – RF,t) + eC,t
and the method of least squares to estimate the values of αC and βC. [7 marks]
(c) Write down the equation that links the excess market return to the excess share price. [4 marks]
(d) What can you conclude from the correlation coefficient and the estimated values of αC and βC? [5 marks]
Question 6
A factory producing chairs has fixed annual overheads of $25,000. Their direct cost of producing each chair is $78. They sell each chair for $120.
(a) Write equations (in terms of the quantity) for the factory’s total annual cost, annual revenue, annual profit and average unit cost. [3 marks]
(b) What will be the effect on the average unit cost if the factory produces 5,000 or 50,000 chairs? Comment on your results. [3 marks]
(c) How many chairs does the factory need to produce to break even? [2 marks]
The factory becomes fairly successful and as a result they are producing more chairs. Due to the increased production of the chairs they can no longer sell the chairs for
$120. The selling price of the chairs is now affected by the quantity being produced so the price of chairs is now: P = 120 – 0.005Q. They also find that their total production costs are rising and they need to add a factor 0.006Q2 to the total annual cost.
(d) With this new situation write down equations (in terms of quantity) of the total annual cost, annual revenue, annual profit and average unit cost. [2 marks]
(e) Comment on the effect this new situation will have on profit and average cost. [2 marks]
(f) In terms of Q find the marginal profit. How many chairs does the factory need to produce to maximise their profit? [6 marks]
(g) Find the price elasticity of demand when the profit is maximised. What does this value imply? [7 marks]
Question 7
(a) An asset worth initially €20,000 can either rise by 10% (with probability 0.55) or fall by 10% (with probability 0.45). Using the Binomial Distribution calculate:
(i) The probability that it will rise for two days and fall for one day in any order. [3 marks]
(ii) The value of the asset in the latter case. [1 mark]
(iii) The mean value of the asset after three days. [9 marks]
(b) A loan department in a bank expects 2.5% of short term loans not to be repaid each month. They make 345 loans in the course of March. They believe the default pattern follows a Poisson distribution. Calculate
(i) The probability that none of these 345 loans will default in April. [3 marks]
(ii) The probability that 1 or 2 of the loans will default in April. [3 marks]
(iii) The probability that 3 or more loans will default in April. [3 marks]
(iv) Briefly explain when it is appropriate to use a Poisson distribution. [3 marks]
Question 8
A factory produces two grades of cocoa powder, light and dark.
Light cocoa powder has a profit margin of $80/metric tonne.
Dark cocoa powder has a profit margin of $90/metric tonne.
The cocoa goes through three processes: sorting, roasting and crushing.
Each metric tonnes of light cocoa powder requires 2 hour sorting, 4 hours roasting and 2 hour crushing.
Each metric tonnes of dark cocoa powder requires 4 hour sorting, 6 hours roasting and 2 hour crushing.
Each day the factory allocates 16 hours to sorting, 26 hours to roasting and 12 hours to crushing.
(a) Formulate the above information into a Linear Programming problem. [5 marks]
(b) Work out the maximum profit. [10 marks]
(c) How many hours in each department are utilised when the profit is maximised? [5 marks]
(d) Outline how you would improve the efficiency of the factory. [5 marks]
Question 9
(a) Briefly describe the main characteristics of a European call option. [3 marks]
(b) You have written a European call option for 1000 shares in Company B. The strike price is €10.00 per share and the option price €1.25 per share. The current share price is €10.77 and the option will expire in 60 days. At the expiration date the share price is €13.65.
Explain and quantify your financial situation on the expiration date.
You can assume that you have not taken any additional action that will limit the loss or gain. [6 marks]
(c) Explain why writing a call option can be risky and give an example. [4 marks]
(d) Referring to the situation in Part (b) explain and quantify the holders financial situation on the expiration date.
You can assume that the holder has not taken any additional action that will limit the loss or gain. [4 marks]
(e) Outline the risk involved to the holder of a call option. [2 marks]
(f) Referring to Part (b) and assuming the continuous compounding interest rate is 2.75%, what would you expect the price of a Put option to be at the time you wrote the call option? [6 marks]