Eco 202 ch 27 basic tools of finance

Chapter 27 !

Basic Tools of

Finance

SurveyQuestion 1

What would you prefer? !

A. Win 1,000 riyals !

B. Flip a coin: 50 percent chance you win 2,000 riyals 50 percent chance you win nothing.

SurveyQuestion 2

What would you prefer? !

A. Lose 1,000 riyals !

B. Flip a coin: 50 percent chance you lose 2,000 riyals 50 percent chance you lose nothing.

SurveyMost people avoid risk

on gains !

but prefer to take risks to avoid loss

Key Termsfinance present value future value compounding discounting risk aversion diversification

firm-specific risk market risk fundamental analysis efficient market hypothesis information efficiency random walk

Key Formulas

(1+r)N

r = rate N = number of periods

Compounding Future Value or FV multiplying

Discounting Present Value or PV dividing

(1+r)N1

Finance

Time and Risk

Tomorrow

One Year

Ten Years

Discount the future !

Today is worth more than tomorrow

Grow in the Future

Today

One year

Ten Years

Promissory Note

Trading paper for paper

I.O. U.

10 SAR Dr. Gale

Rates and

Compounding Linear versus

Exponential

0

8

16

24

32

40

48

56

64

1 2 3 4 5 62

48

16

32

64

24

68

1012

Linear versus Exponential Adding versus Compounding

+

^

N Start Add End

0 100.00 7.00 107.00

1 107.00 7.00 114.00

2 114.00 7.00 121.00

3 121.00 7.00 128.00

4 128.00 7.00 135.00

5 135.00 7.00 142.00

Fixed Amount

Grow by a percentage each year,

not a fixed amount

Compounding

Compounding

The process of finding the future value of a

present sum of money !

multiplying

Discounting

The process of finding the present value of a future sum of money

!

dividing

compounding is the inverse of discounting

discounting is the inverse of compounding

7%

N Start Add End

0 100.00 7.00 107.00

1 107.00 7.49 114.49

2 114.49 8.01 122.50

3 122.50 8.58 131.08

4 131.08 9.18 140.26

5 140.26 9.82 150.07

Compounding

Fixed 7%

N Start Add End Start Add End

0 100.00 7.00 107.00 100.00 7.00 107.00

1 107.00 7.00 114.00 107.00 7.49 114.49

2 114.00 7.00 121.00 114.49 8.01 122.50

3 121.00 7.00 128.00 122.50 8.58 131.08

4 128.00 7.00 135.00 131.08 9.18 140.26

5 135.00 7.00 142.00 140.26 9.82 150.07

Fixed vs. Compounding

Compounding8%

4%

2%

time

amount

Rate Amount in 30 years

1% 136.13

2% 184.76

4% 337.31

8% 1,086.77

16% 9,958.59

32% 546,753.87

Future ValueThe amount of money in the future, using an interest rate, that a present amount will

produce

Key Formula 1

(1+r)N

r = rate N = number of periods

Future Value or FV

(1+r)N

r = 10% FV =?

1 1.100 2 1.210 3 1.331 4 1.464 5 1.611

N FV

Present ValueThe amount of money need today, using an

interest rate, to produce a future

amount

Key Formula 2

(1+r)N

r = rate N = number of periods

Present Value or PV1 Reciprocal

of the FV formula

(1+r)N

r = 10% N = 5 PV =?

1 .909 2 .826 3 .751 4 .683 5 .621 3.791

N PV

1

Worth less and less due to time and risk

1 0.935

2 0.873

3 0.816

4 0.763

5 0.713

6 0.666

7 0.623

8 0.582

9 0.54410 0.508

7% discount

Insurance

Sharing risk !

Does not eliminate risk Spread around risk

Risk Aversion

A dislike of uncertainty

ScenarioCost: 1000

Risk: 1 in 100 Expected cost =

cost x risk = 1000 x .01

=10

ScenarioExpected cost =10 Total Cost = 1000

Get 100 people to give 10 each to fund the

account 10 x 100 = 1000

Insurance Problems

Asymmetric Information Adverse Selection

Moral Hazard

Asymmetric Information

Parties to a trade do not have the same

information !

Not Equal

Adverse Selection

Making a bad choice due to asymmetric

information

Moral Hazard

Changing behavior after an agreement

!

Temptation to abuse the other party

Diversification

Replace one large risk with lots of smaller

unrelated risks

Three Risks

Firm Risk Industry Risk Market Risk

Firm Risk

Risk that affects only a single company

Industry Risk

Risk that affects all the companies in an

industry

Market Risk

Risk that affects all the companies in the stock

market

Valuation

What is it worth? !

Analyze financial statements and future

prospects

Speculative Bubble

Price is greater than fundamental value

!

Buy because everyone else is buying