eco 202 ch 27 basic tools of finance
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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
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