2. Time value of money:
Introduction
Understand the concept time value of
money.
Understand the principles underlying the
calculation of present values and future
values.
Understand the applications of present
value and future value in financial
decision-making.
3. Time value of money:
Introduction
is a fundamental concept in financial
management and capital investment
evaluation,
is simply a reflection of the combined
influence of interest and time,
and is fundamental to almost all
financial decisions
4. Time value of money:
Introduction
R100 received today is worth more
than R100 a year from now – interest
can be earned.
Risk and uncertainty.
Inflation – purchasing power of
money.
5. Simple interest
With simple interest, you don’t earn
interest on interest.
Year 1: 5% of $100 = $5 + $100 = $105
Year 2: 5% of $100 = $5 + $105 = $110
Year 3: 5% of $100 = $5 + $110 = $115
Year 4: 5% of $100 = $5 + $115 = $120
Year 5: 5% of $100 = $5 + $120 = $125
6. Compound interest
With compound interest, a depositor earns
interest on interest!
• Year 1: 5%of $100.00 = $5.00 + $100.00 = $105.00
• Year 2: 5%of $105.00 = $5.25 + $105.00 = $110.25
• Year 3: 5%of $110.25 = $5.51+ $110.25 = $115.76
• Year 4: 5%of $115.76 = $5.79 + $115.76 = $121.76
• Year 5: 5% of $121.55= $6.08+ $121.55 = $127.63
7. Time value terms
• PV = present value or beginning amount
• i/YR = interest rate
• FVn = future value at end of “n” periods
• N = number of compounding periods
• PMT = an annuity (series of equal payments or
incomes)
8. Future value of a single
amount
FUTURE VALUE OF A SINGLE AMOUNT
FVn= PV (1 + I)n
Where: FV = Future value at time tn
PV = Present value at time t0
i = interest rate
n = duration of investment
9. Future value of a single
amount (continue..)
Determine the future value of R100 in three years’ time if
invested at 10% per annum.
FV = 100 (1 + 0,10)3
= 100 (1,331)
= R133.10
10. Future value of a single
amount (continue..)
Future value of R100 at 10 percent
Year
Beginning
Amount
Interest Earned Ending Amount
1 R100,00 R10,00 R110,00
2 110,00 11,00 121,00
3 121,00 12,10 133,10
4 133.10 13,31 146.41
5 146.41 14,64 161,05
Total interest R61,05
11. Future value of a single
amount (continue..)
COMPOUNDING MORE FREQUENTLY THAN ANNUALLY
Annually Semi-annually Quarterly
• PV0 R100 R100 R100
• i/YR 12% 6% 3%
• N 5 10 20
• FV R176.23 R179.08 R180.61
12. Present value
The goal is to determine the amount of
money which a firm or investor would
accept at present in place of a given
amount at a future date.
The concept and computation of PV are
important to the capital investment
process since most projects are expected
to yield cash flows over some number of
periods in future.
13. Present value of a single
amount
The present value PV of a future amount FV is the amount of money
which can be invested today at a given interest rate i per period to
accrue to the same future amount FV after n periods.
n
i
FV
PV
)
1
(
14. Present value of a single amount
(continue..)
Determine the present value of R133,10 which is expected in three years’
time if the discount rate is 10% per annum.
00
,
1
)
10
,
1
(
10
,
133
3
R
PV
15. Homework
1.Calculate the future value of R1 000 invested for 5 years at a
compound interest of 10% per year.
2.If you invest R15 000 today and would want to receive R18 895,50
three years from now, at what compound interest rate should this
amount be invested?
3.How long would it take R2 000 invested today at a compound interest
rate of 9% per annum to increase to R3 077, 20?
16. Future value of an annuity (p5)
What is an annuity?
A stream of equal periodic cash flows
The cash flows can be inflows or outflows
2 types:
Ordinary (regular) annuity (payment
received at the end)
Annuity due (payment received upfront /
beginning)
17. Future value of an annuity
An annuity comprises equal annual
payments or receipts over a
predetermined time period.
Time line for future value of a R100 annuity
after 4 years invested at an interest rate of
6% per annum:
18. Future value of an annuity
Timeline:
End of period
t0 t1 t2 t3 t4
R0 R100 R100 R100 R100
(1,06) 106,00
(1,06)2
112,60
(1,06)3
119,10
Future value (FV) = R437,70
19. Present value of an annuity
Present value of a R100 annuity for 4 years
if the discount rate is 6% per annum. (In a
time line presentation)
20. Present value of an annuity
Timeline:
End of period
t0 t1 t2 t3 t4
R0 R100 R100 R100 R100
94,34 (1÷1,06)
89,00 (1÷1,06)2
83,96 (1÷1,06)3
79,21 (1÷1,06)4
R346,51 = Present value
