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FIM601S - FINANCIAL MATHEMATICS 2 -2ND OPP - JULY 2023 |
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nAmlBIA UnlVERSITY
OF SCIEnCE
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENTOF MATHEMATICS, STATISTICSAND ACTUARIALSCIENCE
QUALIFICATION:Bachelor of science; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATIONCODE: 07BSAM
LEVEL: 6
COURSECODE: FIM601S
COURSENAME: FINANCIAL MATHEMATICS 2
SESSION:JULY 2023
PAPER:THEORY
DURATION: 3 HOURS
MARKS: l'fJO
SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER
DrV. Katoma
Mrs. H.Y Nkalle
MODERATOR:
Prof. A.S. Eegunjobi
INSTRUCTIONS
• Answer ALL the questions in the booklet provided.
• Show clearly all the steps used in the calculations.
• All written work must be done in blue or black ink and sketches
must be done in pencil.
PERMISSIBLEMATERIALS
• Non-programmable calculator without a cover.
THIS QUESTION PAPERCONSISTSOF 3 PAGES{Including this front page)
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Question 1 [25]
1.1 What is derivative? Mention two (2) purposes of derivatives.
[3]
1.2 Mention four (4) elements under fixed interest government borrowings.
[4]
1.3 Suppose a stock that pays no dividend is worth N$60.00. The annual compounding
interest rate is 5%. What is the one-year forward price of the stock?
[4]
1.4 Consider a Put Option with a strike of N$500.00.
(a) What would be the payoff to the buyer if the spot price at the expiration date is
N$ 550.00?
[4]
(b) What would be the payoff to the buyer if the spot price at the expiration date is
N$ 450.00?
[3]
1.5 Consider a 3 x 9 FRAfor £2000.00 with an FRArate of 5%. Suppose the reference rate is
LIBORand the 6-month LIBORon the effective date is 6%. Assume ACT/360 and the loan is
for a period of 120 days. Find how much the borrower receives from the lender on the
effective date.
[7]
Question 2 [25]
= = 2.1 Consider the cash-flow sequences e (e0, ••• , en) and m (m 0, ••• , mn). When is the
cashflow "e" preferable to "m"?
[4]
2.2 Consider the net cash flow sequences
A = (SO,51, -4), B = (50,528, -22), at time = t 0,1,2. Suppose the net present value
for A is 108 and that of Bis 594 at time 2. Find the internal rate of return for.each outlay.
Suppose the interest of both cash flows is 7%, which one is a more viable investment?
[7]
2.3 VK Investment cc has an existing debt of N$ 2000000 on which it makes annual payments
at an annual effective rate of LIBORplus 0.5%. VK Investment cc decides to enter a swap with
a notional amount of N$ 2000000 on which it makes annual payments at a fixed annual
effective rate of 3% in exchange for receiving annual payments at the annual effective LIBOR
rate. The annual effective LIBORrates over the first and second years of the swap contract
are 2.5% and 4% respectively. VK Investment cc does not make or receive any other payments.
Calculate the net interest payment that VK Investment cc makes in the second year.
[10]
2.4 Explain the dangers of derivatives
[5]
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Question 3 [25]
3.1 Suppose a certificate of deposit is issued with a face value of N$ 500000.00 and a
coupon of 6% for 90 days. After 30 days, its yield has fallen to 5.75%. What is the price?
[8]
3.2 Consider the cash flow sequence, a= (5, 9,20,4,2), b = (6,7,3,1,36) at time t =
0, ...,4. Find the Net Present Value (NPV) of the cash flow assuming an interest rate of 7%.
[6]
3.3 Suppose a loan size of l0 is repaid by nm equal installments of size x at times
~,~, ..,. = mm
m n. Suppose the interest rate charged is io/oper annum effective. Find an
expression for the capital repayment for the k th installment.
[5]
3.4 Calculate the present value of an annuity of amount N$ 100.00 paid annually for 5 years
at the rate of interest of 9%.
[5]
Question 4 [25]
4.1 An investment of N$ 200.00 returns N$ 120.00 at the end of 1st year and N$ 100.00 at
the end of 2nd year. What is the internal rate of return (/ RR)?
[5]
4.2 Explain the difference between a negotiable and non-negotiable financial instrument
and give an example
[3]
4.3 Frans is considering a project which requires an amount of N$3000.00 and another
amount of N$1000.00 after one year. In two years', time, when the project ends, she
expects an inflow of N$4500.00. what is the internal rate of return (/ RR) of this project? Is
the above Investment profitable? Assume that Frans can lend and borrow at the same fixed
rate of 7.13% per annum.
[9]
4.4 Consider the following two cash-flow sequences:
Time (Year) 0
1
2
3
Project A
-80
96
1
5
Project B
-80
10
10
90
Find the Internal Rate of Return (IRR) of project A and Project B. And show that IRR(A) >
IRR(B).
[8]
ENDof EXAM
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