fin 600

Topics: Time value of money, Net present value, Compound interest Pages: 42 (2175 words) Published: September 21, 2014
FIN 600 – Lecture 3
Discounted Cash Flow Valuation

Chapter Outline
Time Value of Money
Valuation: The One-Period Case
The Multiperiod Case
Compounding Periods
Simplifications
What Is a Firm Worth?

Time Value of Money







A dollar received today is worth more than a dollar
received in the future.
Interest - is the return you receive for investing your
money.
The interest rate is the basis for a test that any proposed
investment must pass.
Example:




Putting $100 in the bank
Earn 6% interest
After 1 year $106

$100

$106

Future Values and compound rate
Future Value - Amount to which an investment will grow after earning interest.
Simple Interest - Interest earned only on the original
investment.

Compound Interest - Interest earned on interest.
- The sooner your money can earn interest, the faster the
interest can earn interest.

Future Values
Example - Simple Interest
Interest earned at a rate of 6% for five years
on a principal balance of $100.

Interest Earned Per Year = 100 x .06 = $ 6

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

6
106

Future Years
2
3
4

6
112

Value at the end of Year 5 = $130

6
118

6
124

5

6
130

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 =Prior Year Balance
x .06

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

6
6.36
6.74
7.15
7.57
106 112.36 119.10 126.25 133.82

Value at the end of Year 5 = $133.82

Future Value


The general formula for the future value
of an investment over many periods can
be written as:
FV = C0×(1 + r)T

Where
C0 is cash flow at date 0,

r is the appropriate interest rate, and
T is the number of periods over which the cash
is invested.

Compounding and the Power of Time 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%.

FV  $24  (1  .08)
 $120.57 trillion
380

FYI - The value of Manhattan Island land is
well below this figure.

Compounding and the Power of Time –
Aaron Burr








In 1807, the governor of Mississippi offered a reward for the capture of the notorious traitor Aaron Burr. Burr had been Senator from NY and Vice President under Thomas Jefferson in his first term, but he was now accused of trying to break up the union. Burr was subsequently captured, but the reward was never

claimed.
If one of your ancestors had been part of the group that helped to capture Burr, how much could you now claim from the US
government?
If the original reward 200 years ago was $1500
and you assumed the interest rate of 5%?
$25,938,871
If 10%?
$284,857,914,800

Compounding and the Power of Time –
Cells of a young person


When you are conceived, you consist of exactly one cell. If
your cells double every month on average until you are 3
years old, how many cells do you have at that time?



(1+1)^45 months = 35 trillion cells (A decent, but
imprecise estimate of the actual cells of a young person)
10-100 trillion from various sources.

Present Values

Present Value = PV
PV =

Future Value after t periods
(1+r) t

Present Value and Discounting


How much would an investor have to set
aside today in order to have $20,000 five
years from now if the current rate is 15%?

$20,000

PV
0

1

2

$20,000
$9,943.53 
(1.15)5
PV  FV 

1
( 1 r ) t

3

4

5

How Long is the Wait?
If we deposit $5,000 today in an account paying
10%, how long does it take to grow to $10,000?...
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