# fin 600

**Topics:**Time value of money, Net present value, Compound interest

**Pages:**42 (2175 words)

**Published:**September 21, 2014

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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