© 2007 Thomson South-Western. The Basic Tools of Finance Finance is the field that studies how people make decisions regarding the allocation of resources

© 2007 Thomson South-Western


The Basic Tools of FinanceFinance is the field that studies how people make decisions regarding the allocation of resources over time and the handling of risk.


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY• Present value refers to the amount of money

today that would be needed to produce, using prevailing interest rates, a given future amount of money.


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY• The concept of present value demonstrates the

following:– Receiving a given sum of money in the present is

preferred to receiving the same sun in the future.– In order to compare values at different points in

time, compare their present values.– Firms undertake investment projects if the present

value of the project exceeds the cost.


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY• If r is the interest rate, then an amount X to be

received in N years has present value of:

X/(1 + r)N

• Because the possibility of earning interest reduces the present value below the amount X, the process of finding a present value of a future some of money is called discounting.


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY • Future Value

– The amount of money in the future that an amount of money today will yield, given prevailing interest rates, is called the future value.


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY • Examples:• Present Value

– You need to put some money in the bank and want to be paid $200 in 10 (N) years…how much will you need to deposit today if the interest rate is 5%?

$200/(1.05)10 = $123

(Assumes interest is paid annually)


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY • Examples:

• Future Value– You put $100 in the bank today…how much will

your account be worth in 10 years if the interest rate is 5%?

$100x(1.05)10 = $163


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY • Examples:

• Present Value– The interest rate is 7%. What is the present value

of $150 to be received in 2 years?


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY • Present / Future Value

• Is this concept valuable? What can you use it for?

– Lottery winnings

– Company build decisions

– Etc.


FYI: Rule of 70

• According to the rule of 70, if some variable grows at a rate of x percent per year, then that variable doubles in approximately 70/x years.


THE BASIC TOOLS OF FINANCE 12

Risk Aversion• Most people are risk averse – they dislike uncertainty.

• Example: You are offered the following gamble.Toss a fair coin.

– If heads, you win $1000.– If tails, you lose $1000.

Should you take this gamble?

• If you are risk averse, the pain of losing $1000 would exceed the pleasure of winning $1000, and both outcomes are equally likely, so you should not take this gamble.



The Utility Function

Wealth

Utility

Current wealth

Current utility

Utility is a subjective measure of well-being that depends on wealth.

Utility is a subjective measure of well-being that depends on wealth.As wealth rises, the curve

becomes flatter due to diminishing marginal utility:

the more wealth a person has, the less extra utility he would get from an extra dollar.

As wealth rises, the curve becomes flatter due to diminishing marginal utility:

the more wealth a person has, the less extra utility he would get from an extra dollar.



The Utility Function and Risk Aversion

Because of diminishing marginal utility, a $1000 loss reduces utility more than a $1000 gain increases it.

Because of diminishing marginal utility, a $1000 loss reduces utility more than a $1000 gain increases it.

Wealth

Utility

–1000 +1000

Utility loss from losing

$1000

Utility gain from winning $1000


MANAGING RISK

• Risk Aversion– Individuals can reduce risk choosing any of the

following:• Buy insurance

• Diversify

• Accept a lower return on their investments



Managing Risk With Insurance

• How insurance works:A person facing a risk pays a fee to the insurance company, which in return accepts part or all of the risk.

• Insurance allows risks to be pooled, and can make risk averse people better off:

E.g., it is easier for 10,000 people to each bear 1/10,000 of the risk of a house burning down than for one person to bear the entire risk alone.



Two Problems in Insurance Markets1. Adverse selection:

A high-risk person benefits more from insurance, so is more likely to purchase it.

2. Moral hazard: People with insurance have less incentive to avoid risky behavior.

Insurance companies cannot fully guard against these problems, so they must charge higher prices.

As a result, low-risk people sometimes forego insurance and lose the benefits of risk-pooling.


A C T I V E L E A R N I N G A C T I V E L E A R N I N G 22

Adverse selection or moral hazard?Adverse selection or moral hazard?

18

Identify whether each of the following is an example of adverse selection or moral hazard.A. Joe begins smoking in bed after buying fire

insurance.

B. Both of Susan’s parents lost their teeth to gum disease, so Susan buys dental insurance.

C. When Gertrude parks her Corvette convertible, she doesn’t bother putting the top up, because her insurance covers theft of any items left in the car.



AnswersAnswers

19

Identify whether each of the following is an example of adverse selection or moral hazard.A. Joe begins smoking in bed after buying fire

insurance.moral hazard

B. Both of Susan’s parents lost their teeth to gum disease, so Susan buys dental insurance.

adverse selectionC. When Gertrude parks her Corvette convertible,

she doesn’t bother putting the top up, because her insurance covers theft of any items left in the car.

moral hazard


Diversification of Firm-Specific Risk

• Diversification refers to the reduction of risk achieved by replacing a single risk with a large number of smaller unrelated risks.

• Firm-specific risk is risk that affects only a single company.

• Market risk is risk that affects all companies in the stock market.

• Diversification cannot remove market risk.


Figure 2 Diversification

Number ofStocks inPortfolio

49

(More risk)

(Less risk)

20

0 1 4 6 8 10 20 40

Risk (standarddeviation of

portfolio return)

30

1. Increasing the number of stocks in a portfolio reduces firm-specificrisk through diversification…

2. …but market risk remains.


Diversification of Firm-Specific Risk

• People can reduce risk by accepting a lower rate of return.


Figure 3 The Trade-off between Risk and Return

Risk(standarddeviation)

0 5 10 15 20

8.0

3.0

Return(percentper year)

50%stocks

25%stocks

Nostocks

100%stocks

75%stocks

© 2007 Thomson South-WesternTHE BASIC TOOLS OF FINANCE 24

Asset Valuation• When deciding whether to buy a company’s stock,

you compare the price of the shares to the value of the company.

– If share price > value, the stock is overvalued.

– If price < value, the stock is undervalued.

– If price = value, the stock is fairly valued.


If you buy a share of AT&T stock today,

– you will be able to sell it in 3 years for $30.

– you will receive a $1 dividend at the end of each of those 3 years.

If the prevailing interest rate is 10%, what is the value of a share of AT&T stock today?


Valuing a share of stockValuing a share of stock

25



AnswersAnswers

26

$30/(1.1)3 = $22.54in 3 years$30

$1/(1.1)3 = $ .75in 3 years$1

$1/(1.1)2 = $ .83in 2 years$1

$1/(1.1) = $ .91in 1 year$1

present value of the amount

when you will receive it

amount you will receive

The value of a share of AT&T stock equals the sum of the numbers in the last column: $25.03


ASSET VALUATION

• Fundamental analysis is the study of a company’s accounting statements and future prospects to determine its value.

• People can employ fundamental analysis to try to determine if a stock is undervalued, overvalued, or fairly valued.

• The goal is to buy undervalued stock.


The Efficient Markets Hypothesis

• The efficient markets hypothesis is the theory that asset prices reflect all publicly available information about the value of an asset.

• A market is informationally efficient when it reflects all available information about the value of an asset in a rational way.

• If markets are efficient, the only thing an investor can do is buy a diversified portfolio.


CASE STUDY: Random Walks and Index Funds

• Random walk refers to the path of a variable whose changes are impossible to predict.

• If markets are efficient, all stocks are fairly valued and no stock is more likely to appreciate than another. Thus stock prices follow a random walk.


Market Irrationality

• Is the stock market really rational?• Keynes suggested asset prices are driven by “animal

spirits” of investors• Fed Chairman Alan Greenspan, in the 1990s,

questioned the “irrational exuberance” of the booming stock market

• A person might be willing to pay more than a stock is worth today, if it is expected to increase in value tomorrow

Summary


• 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 the future sum.

Summary


• 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 returns.

Summary


• 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 sale price.

Summary


• According to the efficient markets hypothesis, financial markets process available 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.

Documents

© 2007 Thomson South-Western. The Basic Tools of Finance Finance is the field that studies how people make decisions regarding the allocation of resources