Summary of Lecture Notes from Chapter 9 and Practice Questions
1. Because savings can earn interest, a sum of money today is more valuable than the same sum of
money in the future. A person can compare sums from different times using the concept of present
value. The present value of any future sum is the amount that would be needed today, given
prevailing interest rates, to produce that future sum.
2. Because of diminishing marginal utility, most people are risk averse. Risk-averse people can reduce
risk using insurance, through diversification, and by choosing a portfolio with lower risk and lower
3. The value of an asset, such as a share of stock, equals the present value of the cash flows the owner
of the share will receive, including the stream of dividends and the final share price. According to the
efficient markets hypothesis, financial markets process valuable information rationally, so a stock
price always equals the best estimate of the value of the underlying business. Some economists
question the efficient markets hypothesis, however, and believe that irrational psychological factors
also influence asset prices.
I. Definition of finance: the field that studies how people make decisions regarding the
allocation of resources over time and the handling of risk.
A. Many of the basic insights of finance are central to understanding how the economy
B. The tools of finance may also help students think through some of the decisions that
they will make in their own lives.
II. Present Value: Measuring the Time Value of Money
A. Money today is more valuable than the same amount of money in the future.
B. Definition of present value: the amount of money today that would be needed
to produce, using prevailing interest rates, a given future amount of money.
1. Example: you put $100 in a bank account today. How much will it be worth in N
2. Definition of future value: the amount of money in the future that an
amount of money today will yield, given prevailing interest rates.
a. Definition of compounding : the accumulation of a sum of money
in, say, a bank account where the interest earned remains in the
account to earn additional interest in the future.
b. If we invest $100 a10an interest rate of 5 percent for 10 years, the future
value will be (1.05) × $100 = $163.
1 2 ☞ Chapter 9/The Basic Tools of Finance
c. Example: you expect to receive $200 in N years. What is the present
value of $200 that will be paid in N years?
i) To compute a present value from a future value, we divide by
the factor (1 + r) .
ii) If the interest rate is 5 percent and the $200 will be received 10
years from now, the present value is $200/(1.05) 10 = $123.
If ris the interest rate, then an amount $ Xto be
received in Nyears has a present value of $ X/(1+ r ) .
d. The higher the interest rate, the more you can earn by depositing your
money at the bank, so the more attractive having $100 today becomes.
e. The concept of present value also helps to explain why investment is
inversely related to the interest rate.
3. The Rule of 70 can help us understand the effects of compounding:
Rule of 70: If a variable grows at X% per year,then
that variable will double in approximately 70/ Xyear s.
III. Managing Risk
A. Risk Aversion
1. Most people are risk averse.
a. People dislike bad things happening to them.
b. In fact, they dislike bad things more than they like comparable good
c. For a risk-averse person, the pain from losing the $1,000 would exceed
the gain from winning $1,000.
Figure 9.1 Chapter 9/The Basic Tools of Finance ☞ 3
2. Economists have developed models of risk aversion using the concept of utility,
which is a person’s subjective measure of well-being or satisfaction.
a. A utility function exhibits the property of diminishing marginal utility: the
more wealth a person has, the less utility he gets from an additional
b. Because of diminishing marginal utility, the utility lost from losing $1,000
is greater than the utility of winning $1,000.
c. As a result, people are risk averse.
B. The Markets for Insurance
1. One way to deal with risk is to purchase insurance.
2. From the standpoint of the economy as a whole, the role of insurance is not to
eliminate the risks inherent in life, but to spread them around more efficiently.
a. Owning insurance does not prevent bad things from happening to you.
b. However, the risk is shared among thousands of insurance-company
stockholders rather than being borne by you alone. 4 ☞ Chapter 9/The Basic Tools of Finance
3. The markets for insurance suffer from two types of problems that impede their
ability to spread risk.
a. A high-risk person is more likely to apply for insurance than a low-risk
person. This is adverse selection.
b. After people buy insurance, they have less incentive to be careful about
their risky behavior. This is moral hazard.
C. Diversification of Idiosyncratic Risk
1. Practical advice that finance offers to risk-averse people: “Don’t put all your eggs
in one basket.”
2. Definition of diversification : the reduction of risk achieved by replacing a
single risk with a large number of smaller unrelated risks.
a. A person who buys stock in a company is placing a bet on the future
profitability of that company.
b. Risk can be reduced by placing a large number of small bets, rather than
a small number of large ones.
3. Risk can be measured by the standard deviation of a portfolio’s return.
a. Standard deviation measures the volatility of a variable.