Lecture02_Canvas.pdf - Lecture 2 Valuing Investment Prof...

Lecture 2
Valuing Investment
Prof. Zhang
University of Texas at Austin
McCombs School of Business
Outline
1
Compounding
2
Discounting
3
Perpetuities
4
Annuities
FIN 367, Lecture 2 Valuing Investment 2 / 42

Outline
1
Compounding
2
Discounting
3
Perpetuities
4
Annuities
FIN 367, Lecture 2 Valuing Investment 2 / 42
Motivation
•
At the most general level, an investment is a claim to a stream of
cash flows.
•
Both real and financial investments.
• In order to choose between different investments, we must therefore
find a way to compare cash flows differing in
•
Size
•
Timing
•
Risk
•
We will first focus on the size and timing of the cash flows and ignore
risk for now.
• Compounding and discounting allow us to compare cash flows
differing in size and timing.
FIN 367, Lecture 2 Valuing Investment 3 / 42

Time Value of Money
In general, a dollar today is worth more than a dollar in one year. The
difference in value between money today and money in the future is called
the time value of money .
• Suppose you deposit $100 in a bank account which pays 10%
interest, you will have $110 at the end of next year.
•
When we compare cash flows at different periods of time, we should
take the time value of money into consideration.
FIN 367, Lecture 2 Valuing Investment 4 / 42
Compounding and Future Value: Illustrative Example
Suppose you deposit $100 in a bank account which pays 10% interest:
•
Money in the account after one year:
Investment: $100
Interest: $10 = $100 × 10%
Total: $110 = $100(1+10%)
•
Suppose that the interest is credited to your account once a year. Money in
the account after two years:
Investment: $110
Interest: $11 =$110 × 10%
Total: $121 = $100(1 + 10%)
2
•
Money in the account after three years:
Investment: $121
Interest: $12.1 = $121 × 10%
Total: $133.1 = $100(1 + 10%)
3
• Continuing this reasoning, you will have $100(1 + 10%)
T
at the end of T
years.
FIN 367, Lecture 2 Valuing Investment 5 / 42

Compounding and Future Value: General Case
More generally, suppose you deposit $ C in a bank account which pays an interest
rate of r % per year:
• Money in the account after one year:
Investment: $C
Interest: $C × r%
Total: $C(1+r%)
•
Suppose that the interest is credited to your account once a year. Money in
the account after two years:
Investment: $C(1+r%)
Interest: $C(1+r%) × r%
Total: $ C (1 + r %)
2
•
Continuing this reasoning, you will have $ C (1 + r %)
T
at the end of T years.
FIN 367, Lecture 2 Valuing Investment 6 / 42
Future Value and Compounding Factor
• $ C (1 + r %)
T
is the future value in T years of an initial investment of
$C that earns r% compounded annually.
•
(1 + r %)
T
is called the T-period compounding factor.
FIN 367, Lecture 2 Valuing Investment 7 / 42

More Frequent Compounding
• Suppose you deposit $ C in a bank account which pays r % interest, and that
interest is credited to your account twice a year:
•
You can then show that you will have $ C (1 +
r %
2
) after 6 months,
$ C (1 +
r %
2
)
2
after a year, ..., $ C (1 +
r %
2
)
2 T
after T years.