© 2007 thomson south-western. the basic tools of finance this chapter introduces some tools that...


The Basic Tools of Finance

This chapter introduces some tools that help us understand the decisions that people make as they participate in the loanable funds market.

Finance is the field that studies how people make decisions regarding the allocation of resources over time and the handling of risk.


Three topics in Chapter 27

• How to compute the value of money at different points of time

• How to manage risk

• What determines the value of an asset.


PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY

• Present value( 現值， PV) refers to the amount of money today that would be needed to produce, using prevailing interest rates, a given future amount of money at time T ( ):

0 T

PV

TC

TC


Present Value vs. Future Value

• The concept of present value is used to answer the following question: Suppose you are going to be paid 1 dollar in T years. How much would you have to put in a bank account today?

PV× = ＄ 1 → PV=

This process is called discounting. ( 折現 )

(1 )Tr$1

(1 )Tr


Present Value vs. Future Value

• The concept of future value ( 終值， FV) is used to answer the following question: If you put ＄ 1 in a bank account today, how much will it be worth in T year? We can use the compounding ( 複利計息 ) process to get the future value of ＄ 1 today:

FV(T)= ＄ 1

in which r is the interest rate and FV(T) in the future value at time T.

(1 )Tr


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 sum in the future.– In order to compare values at different points in

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

value of the project exceeds the cost of the project.


Valuing a stream of cash flows• Most investment opportunities have multiple cash flow that

occur at different points in time.• Consider a stream of cash flow in different points of time.

0 1 2 3 . . . T

1 2, ,....., :NC C C

1 2 3 TC C C . . . C


Valuing a stream of Cash flows

• We first compute the present valus of each individual cash flow in different points of time:

PV( )=

i= 1, 2, …., T. Then we can sum them up to get

PV=

iC (1 )i

i

C

r

1 1

( )(1 )

T Ti

i ii i

CPV C

r


Application 1: Evaluating the value of default-free bonds

• Elements of bond

--Face value (FV, 面額 )

--Coupon rate (k , 息票率 )

--Maturity date ( 到期日 )

--The date to return principal ( 面額償還時間 )


Application 1: Evaluating the value of default-free bonds

• 高市府將標售五年期公債，面額為 100 萬元，年息票率為 5% ，每年發放票息一次，債劵到期時債還面額，請畫出持有此債劵的現金流量圖。

首先，計算每年公債持有者將收到的票息(coupon payment) 金額 :

票息 =FV × k =100 萬元 ×5% = 5 萬元


• 持有公債的票息現金流量圖為 :

0 5 萬元 5 萬元 5 萬元 5 萬元 5 萬元

0 1 2 3 4 5

‧第五年時，公債持有者還將收到債券面額 (100 萬元 )


• 請問持有此債劵所創造的價值 ? 首先，價值即為持有期間各期現金收益的現值。計算價值前，應先找出持有債劵的資金 ( 機會 ) 成本。持有此債劵表示資金就無法用於其他投資機會，故其他投資機會的報酬率就是持有此債劵的資本 ( 機會 ) 成本 ( 以 r 表示 ) 。利用現值公式就可算出持有公債的價值(PV): 5

i 51

5 100+

(1+r) (1+r)i

PV

萬元萬元


• 由上列公式可知，持有公債的機會成本 ( 即持有債劵必須放棄的收益 ) 變大 ( 變小 ) ，則持有債劵所創造的價值變小 ( 變大 )


Application 2: Evaluating a real investment project

• Suppose firm A is considering a 10-year real investment project. The capital expenditure of this project is . This project will yield this firm operating cash flow in 10 years:

0C

1 2 10C , C , ...., C .


Application 2: Evaluating a real investment protect• The cash flow chart for this project:

0 1 2 3 。。。 10

Then the net present value ( 淨現值， NPV) is given by

in which r is the opportunity cost of capital.

10i

0 ii=1

CNPV= -C +

(1+r)

0-C

1 2 3 10C C C C。。。


Application 2: Evaluating a real investment protect

• Given the market interest rate r. We can compute NPV. If NPV ＞ 0, then we undertake this project. Otherwise, we reject it.

• The concept of net present value helps explain why real investment -and thus the quantity of loanable funds demanded -declines when the interest rate rises.


Application 2: Evaluating a real investment protect

• When the economy is in recession, central bank can lower the interest rate (r) to stimulate the incentive to undertake the investment project, since the NPV will increase as r decreases.


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.


MANAGING RISK

• Risk Aversion– A person is said to be risk averse ( 風險厭惡 )if he

or she exhibits a dislike of uncertainty.– Individuals can reduce risk choosing any of the

following:• Buy insurance

• Diversify ( 分散投資 )

• Accept a lower return on their investments


Risk Aversion

Wealth0

Utility

Currentwealth $1,000

gain$1,000loss

Utility lossfrom losing$1,000

Utility gainfrom winning$1,000


The Markets for Insurance

• One way to deal with risk is to buy insurance.

• The general feature of insurance contracts is that a person facing a risk pays a fee to an insurance company, which in return agrees to accept all or part of the risk.


Diversification of Firm-Specific Risk

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

• Firm-specific risk (or unique risk)is risk that affects only a single company.

• Market risk (or systematic risk)is risk that affects all companies in the stock market.

• Diversification cannot remove market risk.


Diversification can eliminate unique risk

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.


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


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.


Fundamental Analysis

• The value of a stock (PV) is determined by

in which r in the opportunity cost of capital and is the cash dividend received at time i.

ii

i=1

PV=(1+r)

DIV

iDIV



• Cash dividend depends --demand for the firm’s product.--how much competition this firm faces.--how much capital it has in place.--whether its workers are unionized.--how loyal its customers are --what kinds of government regulations and

taxes it faces.



• If the price of stock is less than the value, the stock is said to be undervalued. You should prefer undervalued stocks.

• If the price of stock is said to be overvalued.

• If the price and the value are equal, the stock to be fairly valued.



• In a competitive stock market, the stock is always fairly valued in equilibrium .

• If interest rate falls, which signals the lower opportunity cost of capital, then the value of stock rises. Given the supply of stocks, the price of stock increases.


The Efficient Markets Hypothesis

• The efficient markets hypothesis( 效率市場假設 ) 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


• 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.

Summary

© 2007 thomson south-western. the basic tools of finance this chapter introduces some tools that...

Documents