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ATW216 Test 1

February 2013

Total: 60 marks

1. Theory Questionsi) Describe the cashflow characteristics of an index-linked coupon bond for the borrower. [3]

For the borrower, or issuer, there is a relatively large outflow, followed by regular smaller

inflows and a final larger inflow at maturity [relative size, direction, timing] [2]. The timing is

guaranteed by the contract, but the actual amounts of the coupons and redemption

payment are linked to an index, and are therefore unknown at the start of the transaction

[certainty of timing and amount] [1].

ii) Explain the main differences between issuing a fixed-interest security and a taking out arepayment loan, in terms of the cashflow characteristics of these two transactions. [3]

In both of these scenarios there is an initial large inflow [1]. For the FIS, there are regular

smaller outflows followed by a large outflow repaying the initial capital [1]. For the RL, there

are only regular smaller outflowsthese outflows consist of interest and principal portions,

so the entire loan is repaid by these outflows [1].

iii) List at least 4 factors that would influence the return offered on an investment product. [2]Term (and/or term structure), type of rate, amount invested, risk of the investment, liquidity

of the investment, etc. [0.5 ea.]

2. Explain in words which rates of return are represented by the following:i)

This is the effective 2-year interest rate. [1]

ii) [1]This is 3 times the nominal discount rate compounded every 4 months, or 9 times the

effective four-month discount rate. [1]

iii)

[1]

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This is the nominal interest (or discount) rate compounded continuously (or the force of

interest). [1]

iv) [1]This is the effective month interest rate. [1]

3. Perform the following return equivalence conversions:i) Calculateif the effective 2-month interest rate is 2%. [2]

ii) Calculate if the nominal discount rate compounded once every 2 years is 7%pa. [2]

iii) Calculate the effective monthly discount rate that is in effect over 5 years, if the simplediscount rate applicable over those 5 years is 8%pa. [2]

iv) Calculate the nominal interest rate compounded monthly that would double an investment

after 4 years. [2]

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4. Consider a 180-day Treasury Bill that is floating in the market a number of days after issue.Calculate the number of days till maturity of this Bill, if it is currently trading at a price of R99.5

per R100 face (or final) value, and is currently valued at a simple discount rate of 5%pa. [2]

5. On his birthday on 1 March 1993, James father deposited R5 000 into a savings account to pay

for some of James tuition at university, should he decide to attend university after he was due

to matriculate. On 1 June 1995, another R5 000 was deposited into the account. A third and final

deposit of R5 000 was made into the account on 1 January 2000. The plan was for James is to

receive equal amounts at the start of each of the three years 2012, 2013 and 2014.

i) Calculate the size of these three payments if the savings account was guaranteed an 8%nominal interest returnpa, compounded monthly. [4]

[

[

ii) Another savings option existed at the time the account was made. This option wouldguarantee a nominal interest return of 12% compounded monthly until 1 January 2004.

Thereafter, the guaranteed return would drop to 4% nominal annual interest, compounded

monthly. Would this have been a better investment choice for James father? Show all

calculations. [4]

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[

So this would not have been a better investment. [0.5]

6. You are given the force of interest is, a function of timein years, is as follows: {

i) Explain the Principle of Consistency. [1]PoC states that in a consistent market the return on an investment will be the same

regardless of the action of the investor [1] (as long as the investment is always fully

invested). Or, ii) Prove the relationship between a variable force of interest,, and the

accumulation . [5]

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()

() ()]

iii) Calculate the equivalent constant force of interest in effect over the time period from to . [4]

iv) Calculate the equivalent effective 3-year interest rate in effect between times

and . [3]

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b) and increases continuously by a force of 5% pa. [4]

( )

( )

c) and decreases continuously by a rate of 10%pa. [4]

( )