Transcript Finance I - Universidade Nova de Lisboa

Finanças
Sept 21
Topics covered
Time value of money
 Future value
 Simple interest
 Compound interest
 Present value
 Net present value

Time Value of Money
People always prefer to receive $1 today
than $1 in the future
 The relationship between $1 today and
(possibly uncertain) $1 in the future
shows the time value of money

Future Values
Future Value
Compound Interest
Simple Interest
Future Values
Example - Simple Interest
Interest earned at a rate of 6% for five years on
a principal balance of $100.
Future Values
Example - Simple Interest
Interest earned at a rate of 6% for five years
on a principal balance of $100.
Today
1
Interest Earned
Value
100
Future Years
2
3
4
5
Future Values
Example - Compound Interest
Interest earned at a rate of 6% for five years on
the previous year’s balance.
Interest Earned Per Year =
Future Values
Example - Compound Interest
Interest earned at a rate of 6% for five years
on the previous year’s balance.
Today
Interest Earned
Value
100
1
Future Years
2
3
4
5
Future Values
Future Value of C = FV
FV  C  (1  r)
t
Future Values
FV  C  (1  r )
t
Example - FV
What is the future value of $100 if interest is
compounded annually at a rate of 6% for five years?
Future Values with Compounding
Interest Rates
1.2
0%
1
10%
0.8
15%
0.6
0.4
0.2
Number of Years
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
FV of $100
5%
Manhattan Island Sale
Peter Minuit bought Manhattan Island for $24 in 1626.
Was this a good deal?
To answer, determine $24 is worth in the year 2006,
compounded at 8%.
Present Values

Present Value:

PV Factor:

Discount Rate:
Present Values
P resentValue = P V
PV =
FV
(1+ r) t
Present Values
Example
You just bought a new computer for $3,000. The
payment terms are 2 years same as cash. If you
can earn 8% on your money, how much money
should you set aside today in order to make the
payment when due in two years?
Present Values
PV Factor = PV of $1
PV Factor=

1
(1+ r) t
Discount Factors can be used to compute the
present value of any cash flow.
Present Values with Compounding
1.2
Interest Rates
PV of $100
5%
1
10%
0.8
15%
0.6
0.4
0.2
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of Years
Net Present Value
NPV = - cost + PV

Example:
A project costs $50,000. The project will generate
profits of $25,000 one year from now, $20,000 two
years from now, and $15,000 three years from
now. The discount rate is 7% for this project. What
is the NPV of the project?
Cash
flows
Year 0
-50,000
1
25,000
2
20,000
3
15,000
NPV
PV factor
PV