2. Sinking fund
A series of equal payments per period over
a predetermined term to provide for a fixed
amount on a specific date in the future
(replacement, pension, loan redemption)
3. Sinking fund (continue..)
A loan of R20 million is to be
redeemed in 15 years’ time. A
sinking fund is envisaged for this
purpose. Annual instalments can be
invested over the 15 year period at
10% per annum. What amount
should be invested annually?
8. Bond Amortisation
An employee can obtain a 20 year bond of R200
000 from the bank at 15% interest per annum. The
bond has to be amortized by equal monthly
payments over the next 20 years. The first payment
is due in one month.
10. Nominal and effective rates
interest (p11)
The nominal interest rate is the stated or
contractual rate of interest charged by a
lender or promised by a borrower.
The effective interest rate is the rate
actually paid or earned.
In general, the effective rate > nominal
rate whenever compounding occurs more
than once per year.
11. Basic patterns of cash flow
The cash inflows and outflows of a firm
can be described by its general pattern.
The three basic patterns include a single
amount, an annuity, or a mixed stream:
End of year
Mixed cash flow stream
A B
1 R400 - R50
2 800 100
3 500 80
4 400 - 60
5 300
12. Present value of a mixed
stream (p14 & p15)
Using Tables:
A mixed stream of cash flows reflects no particular
pattern
Find the present value of the following mixed stream
assuming a required return of 9%.
Year Cash Flow PVIF9%n PV
1 400 0.917 $ 366.80
2 800 0.842 $ 673.60
3 500 0.772 $ 386.00
4 400 0.708 $ 283.20
5 300 0.650 $ 195.00
NPV $1 904.60
13. The principle of equivalence
(p15)
A comparison of the financial merits of two or
more alternative investment opportunities with
different cash flow patterns can only be
meaningful if the amounts for each alternative
respectively, are reduced to a specific point in
time.
The principle of equivalence is explained in
the next table:
14. The principle of equivalence
Time of
Receipt
(t)
Cash Flow on Investment
A B C
1 R100 R350 R 50
2 R200 R200 R150
3 R300 R 50 R450
Total R600 R600 R650
NPV @ 10% R481.59 R521.04 R507.50
15. The principle of equivalence
The only difference is the time framework of the
annual cash flows as the total undiscounted cash
flows are the same.
On the basis of time value of money – B would be
preferable to A (due to higher return in the earlier
years)
Compare B to C? What do you think?
Although cash flow initially on B is higher than C,
C nets a higher total cash flow.
According to NPV then B will be preferable to C.
B and C can now be compared on the “basis” of
the principle of equivalence.
16. QUESTIONS
1. Our company considers buying an asset for R3 350. The
investment is very safe, you will sell the asset in 3 years for
R4 000. You know you could invest the money at 10% elsewhere
with very little risk. Is this an acceptable investment?
2. Investment X offers to pay you R2 000 per annum for 4 years
while Investment Y offers to pay you R2 500 per annum for 3
years. Which one of these cash flow streams has the highest
present value if the discount rate is 5% and 20%?
3. It is estimated that your company will generate R27 000 per
annum each year for the next 8 years from a new information
data base. The computer system needed to set up the data base
will cost R180 000. If you borrow the money to buy the system
at 7% per annum, can you afford the new system?
17. Solution 1
Option A: Buy asset for R3 350 and sell for
R4000. Profit = R650
Option B: PV = R3 350
n = 3
i/yr = 10%
FV = R4 458.85
Solution: option B will be more profitable.
