Copyright © 2004 South-Western 27 The Basic Tools of Finance

Copyright © 2004 South-Western Objectives a.Calculate present value and future value b.Comprehend implications of compound growth c.Explain how agents (people) tend to shift, or protect themselves, from risk d.Discuss asset price determination

Copyright © 2004 South-Western Finance Finance is study of resource allocation over time and how risk is managed. … it is about the time-value of money Present value is today’s value of a stream of revenue that will occur in the future or some lump sum of money that may be realized in the future … the notion begins with the reality that a sum of money today, say $1, is worth more than that same amount in the future, say one year from now.

Copyright © 2004 South-Western PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY Present Value: Receiving a given sum of money in the present is preferred to receiving the same sum in the future. Why? When you don’t have it, you can’t use it (therefore lower utility)… In order to compare values at different points in time, compare their present values (which is more valuable? $75 one year from now vs. $95 two years from now) Firms undertake investment projects if the present value of the future revenue stream, the result of that project, exceeds the cost of that project (weighing current costs against future benefits by calculating the present value of the future benefits).

Copyright © 2004 South-Western PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY If r is the interest rate, then an amount, PV, to be saved for N years has future value of: FV = PV(1 + r) N where N = number of periods If $5 earns 5% interest per year : After one year: $5(1 +.05) = $5.25 After two years: $5(1 +.05)(1 +.05) = $5.00(1 +.05) 2 = $5.51 After three: $5(1 +.05)(1 +.05)(1 +.05) = $5.00(1 +.05) 3 FV = PV(1 + r) N where N = number of periods (years) Therefore PV = FV / (1 + r) N

Copyright © 2004 South-Western PRESENT VALUE: MEASURING THE TIME VALUE OF MONEY Future ValueFuture 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.

Copyright © 2004 South-Western FYI: Rule of 70 rule of 70 70/x yearsAccording 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. Suppose you could save $25 at an interest rate of 10%… Then, (70 / 10) = 7 Your $25 would become (approximately) $50 in 7 years

Copyright © 2004 South-Western MANAGING RISK A person is risk averse to the extent that he/she reduces his/her exposure to risk Example of risk averse behavior: a.Insurance purchases b.Diversification of holdings * Risk/Return tradeoff Think of decision to buy flood insurance, getting a lower return in order to reduce risk. Buying insurance is a cost (sure loss) but it protects against greater loss. (ensuing slide: flip a coin, heads wins $1,000 while tails loses $1,000… explains risk averse behavior. This is not a good bet, but it is a “fair” bet)

Figure 1 Risk Aversion Wealth 0 Utility Current wealth $1,000 gain $1,000 loss Utility loss from losing $1,000 Utility gain from winning $1,000 Copyright©2004 South-Western

The Markets for Insurance insuranceOne way to deal with (avoid) risk is to buy insurance. A person facing a risk can pay a fee to an insurance company, which in return agrees to accept all or part of the risk. Car insurance – you pay in order to protect yourself from potential loss. You might not ever need insurance coverage, and in fact hope that you do not have to rely on insurance. Buying insurance is a bet you hope to lose.

Copyright © 2004 South-Western Expected Loss (0.99)(0) + (0.01)($ -250,000) = $ - 2,500 The expected loss in any given year is only $2,500 but the actual loss would be $250,000 People are willing to pay – incur a sure loss – in order to protect against (shift the burden of risk) great loss

Copyright © 2004 South-Western Diversification of Idiosyncratic Risk Diversification refers to the reduction of risk achieved by replacing a single risk with a large number of smaller unrelated risks. Buy a single stock – betting on future profitability of that firm Buy many stocks – many, small bets placed on many firms In insurance markets, firms sell many policies (create a big insurance pool) in order to diversify. The probability of loss in example above was 0.01

Copyright © 2004 South-Western Diversification of Idiosyncratic Risk Idiosyncratic risk is the risk that affects only a single person, while aggregate risk is that risk that can affect all people. Diversifying reduces idiosyncratic risk but does not affect, reduce, aggregate risk. Example – if 10,000 people have $250 in a particular stock and the firm does poorly, then the price of the stock falls and those who own the stock are poorer. However, if for each of those people that firm represented a small fraction of their portfolio then each is protected individually.

Figure 2 Diversification Number of Stocks in Portfolio 49 (More risk) (Less risk) Risk (standard deviation of portfolio return) Aggregate risk Idiosyncratic risk 30 Copyright©2004 South-Western

Diversification of Idiosyncratic Risk People can reduce risk by accepting a lower rate of return.

Figure 3 The Tradeoff between Risk and Return Risk (standard deviation) Return (percent per year) 50% stocks 25% stocks No stocks 100% stocks 75% stocks Copyright©2004 South-Western

ASSET VALUATION Fundamental analysis is the study of a company’s accounting statements and future prospects to determine its value – if, as buyer of stock, you become an owner, then you are concerned with how profitable the firm is or will become. (or, is it the “bigger fool” theory?) Fundamental analysis determines if a stock is undervalued, overvalued, or fairly valued. The goal is to buy undervalued stock.

Copyright © 2004 South-Western Asset Valuation Value vs. price (of a share of stock) The value of a share of stock is the PV of the stream of revenue one receives from owning it plus the final sale value. The firm’s dividend payments and final value are closely related to profits and expected profits… what is demand for the product(s) and what are the costs associated with producing the product(s)?

Copyright © 2004 South-Western Efficient Markets Hypothesis The efficient markets hypothesis is the theory that asset prices reflect all publicly available information about the value of an asset, therefore all stock prices equal their value. Markets are efficient if value = price.

Copyright © 2004 South-Western Efficient Markets Hypothesis A market is informationally efficient when it reflects all available information in a rational way. If markets are efficient, the only thing an investor can do is buy a diversified portfolio

Copyright © 2004 South-Western 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.

Copyright © 2004 South-Western Summary Because savings can earn interest, a sum of money today is more valuable than the same sum of money in the future (PV and FV) Sums from different times can be compared – time value of money FV = PF(1 + r) N Due to the diminishing marginal utility of money, most people are risk averse.

Copyright © 2004 South-Western Summary Risk-averse people can reduce risk by purchasing insurance and through diversification, choosing a portfolio with lower risk and lower returns. 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. This includes the stream of dividends and the final sale price of the asset.

Copyright © 2004 South-Western 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 (price = value) Some economists question the efficient markets hypothesis, however, and believe that irrational psychological factors also influence asset prices (“bigger fool” theory)