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FIM601S - FINANCIAL MATHEMATICS 2 - 1ST OPP - JUNE 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES & NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BAMS
LEVEL: 6
COURSE CODE: FIM601S
COURSE NAME: Financial Mathematics 2
SESSION: JUNE 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Mrs. H. Y. Nkalle
Dr. V. Katoma
MODERATOR:
Prof. A.S. Eegunjobi
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page)
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Question 1
What is derivative? And mention two purposes of derivatives.
[3]
Question 2
Mention 4 elements under fixed interest government borrowings.
[4]
Question 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]
Question 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]
Question 5
Consider a 3 x 9 FRA for £2000.00 with an FRA rate of 5%. Suppose the reference rate is
LIBOR and the 6-month LIBOR on 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.
Question 6
Consider the cash-flow sequences e = (@p,...,€,) and m = (mg, ..., M,). When is the
cashflow Wo '’e” preferable to '’m'’?
[4]
Question 7
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]
Question 8
VK Investment cc has an existing debt of N$ 2000000 on which it makes annual payments at
an annual effective rate of LIBOR plus 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
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effective rate of 3% in exchange for receiving annual payments at the annual effective
LIBOR rate. The annual effective LIBOR rates 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.
[8]
Question 9
An investor is considering whether to invest in either or both of the following loans:
Loan A: For a purchase price of N$ 10000, the investor will receive N$ 1000 per annum
payable quarterly in arrear for 15 years.
Loan B: For a purchase price N$ 11000, the investor will receive an income of N$605 per
annum, payable annually in arrear for 18 years, and a return of his outlay at the end of this
period.
The investor may borrow money at 4% per annum. Would you advise him to invest in either
loan, and if so which would be the more Profitable?
[8]
Question 10
Consider the following two cash-flow sequence:
Time (Year)
0
1
2
3
Project A
-80
96
1
5
Project B
-80
10
10
90
Find the Internal Rate of Return (JRR) of project A and Project B. And show that IRR(A) >
IRR(B).
[8]
Question 11
A project requires an initial investment of N$ 225000 and is expected to generate the
following Net cash inflows.
Year 1: N$95000, Year 2: 80000, Year 3: 60000, Year 4: 55000. Computer NPV of the
project if the minimum desired rate of return is 12%.
[5]
Question 12
Suppose that A(t) = at? + 108. If X invested at time 0 accumulates to N$ 500.00 at time 4,
and to N$1000.00 at time 10, find the amount of the original investment X.
[10]
Question 13
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A loan is being repaid by 10 equal annual payments of NS 400. Suppose the effective annual
interest rate is 12%. Find the loan outstanding immediately after the payment at the end of
the year 6.
[5]
Question 14
A debt of $10,000 is amortized by making equal payments at the end of every six months for
three years, and interest is 6% compounded semi-annually. Construct an amortization
schedule.
[12]
Question 15
Golda is considering a project which requires an amount of N$3000.00 and another amount
of N$1000.00 after 1 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 Golda can lend and borrow at the same fixed rate of
7.13% per annum.
[10]
End of paper
Total marks:100
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