Basic Tools of Finance Finance 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. 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, compare their present values. –Firms undertake investment projects if the present value of the project exceeds the cost.

Calculating Future and Present Value An Intuitive Approach: –Money in the future is not worth as much as the same amount of money today. Ignoring purchasing power differences, a simple way to see this is that depositing a dollar today at interest will result in more than a dollar in the future. This implies that you could deposit less than a dollar today to equal a dollar in the future. A Mathematical Approach: –Present Value to Future Value –Future Value to Present Value –Determining the market price of a bond

From PV to FV –Formula: FV t =PV 0 (1 + i) t –Apply to each year –At 6%, the principal plus the interest doubles after 12 years (Rule of 70)

From FV to PV Formula: –PV o =FV t / (1 + i) t Apply to each year At 6%, the PV of a $1 given 12 years in the future is one-half of the FV, that is, $.50

Determining the Market Price of a Bond Determine income stream, using the face value, the coupon rate, and the maturity. For the bond shown, the income stream is $50/year for 12 years, plus in the twelve year your get the face value. Discount each FV using the PV formula (or multiply by the discount factors) and sum together to get the market price of the bond (assuming risk identical to that used in the market rate of interest).

Bond Prices and Market Interest rates Bond prices vary inversely with market interest rates. –As the market interest rate rises, the PV of a bond payments looks less attractive and bond prices fall. –As the market interest falls, the PV of the bond payments is more attractive and bond prices rise. Demand and supply in the loanable funds with bond prices instead of interest rates. Savers or lenders are the demanders and firms or borrowers are the suppliers. The result is the same.

Bonds Vs. Investment Projects The present value of the payment stream from a bond helps determine if it is worthwhile investment. The present value of a stream of income from an investment project can be used in a similar way. –If the present value of stream of income is greater that the cost of the investment, do the project. If not, do not do the project. –Alternatively, if the interest rate (internal rate of return) which makes the present value of a stream of income investment is equal to the cost of the project, do the project. If not, do not do the project. The internal rate of return is simply the project’s rate of return that was given in the Aplia experiment. An investment demand schedule for a firm is simply a list of possible investment projects ranked by their internal rate of return (from highest to lowest). So a firm will do all the projects, whose internal rate of return is greater than the interest rate at which they can borrow – Assuming that the risk is the same for all projects.

MANAGING RISK A person is said to be risk averse if she exhibits a dislike of uncertainty. Individuals can reduce risk choosing any of the following: –Buy insurance –Diversify –Accept a lower return on their investments.

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

Insurance insuranceOne way to deal with risk is to buy insurance. From an insurer’s viewpoint diversification is a strategy that they can develop into a profit-making activity. For example assume two different insurance portfolios: –One house worth $100,000 with a.01/year probability of fire each year. Expected loss = $100,000 x.01= $1,000, but the outcomes are either: No loss, or a $100,000 loss. Extreme outcomes imply risks. –100 houses worth $1,000 each with a probability of fire of.01/year. Expected loss is Σ 1 to 1,000 =.01 x $1,000= $1,000, and the outcome is likely to be very close to $1,000.

Insurance Through diversification, insurance companies can reduce the standard deviation of expected losses and more closely predict expected losses. Thus they are willing to sell insurance to customers to help them avoid risk. To reduce risk a customer pays a fee (the premium) to an insurance company, which in return agrees to accept all or part of the risk of a loss. Adverse selection – those who are more likely to use insurance will likely purchase insurance Moral Hazard – once insured individuals will participate in more risky behaviors.

Diversification Diversification refers to the reduction of risk achieved by replacing a single risk with a large number of smaller unrelated risks. Idiosyncratic risk (firm-specific) is the risk that affects only a single person. The uncertainty associated with specific companies. Aggregate risk (market) is the risk that affects all economic actors at once, the uncertainty associated with the entire economy. Diversification cannot remove aggregate risk.

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. 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.

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 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.

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. 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.