Two Basic Components of Discount rate

Two Basic Components of Discount rate
Time preferences suggest a positive component to all discount rates Call this the risk-free rate (remember the last lecture?!?) Risk aversion suggests an additional component representative of the asset’s risk Call this the risk premium Variation in discount rates across assets is really variation in risk premia (the second component) Riskier assets should have a higher risk premium In capital budgeting (discussed a couple of lectures from now), riskier projects should be valued with a higher discount rate Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 1

Expected Versus Realized Rates of Return
Expected rate of return (ex ante): Calculated by multiplying each possible outcome by its probability of occurrence and then summing these products Weighted average of outcomes where the weights are the probabilities and weighted average is the expected rate of return Realized rate of return (ex post): Actual rate of return earned during some past period Can be considered the “after-the-fact” rate of return Realized rate of return is often different from the expected rate of return However, on average, these two tend to be fairly close! Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 2

Expected Returns and Risk: An Example
Let us first consider an example of expected rate of return (or ex ante returns): Calculated by multiplying each possible outcome by its probability of occurrence and then summing these products Weighted average of outcomes where the weights are the probabilities and weighted average is the expected rate of return Let us also consider risk in our example Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 3

Holding Period Returns (HPR)
Risk means uncertainty about what an investor’s realized holding period return will be i.e., that realized returns will differ from expected returns We can quantify the uncertainty using probability distributions Example (Stock Fund or SF): Assume there is considerable uncertainty with respect to the end of year price of an index stock fund, which is currently selling for $100 Also, the investor expects a dividend of $4 Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 4

Holding Period Returns (HPR): SF Example
Holding Period Return Formula Holding Period Return: Boom Holding Period Return: Normal Holding Period Return: Recession Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 5

Expected Returns: SF Example Expected Return Equation
The expected return (mean) is the probability weighted average of all possible outcomes Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 6

Measuring Risk Variance = average squared deviation from the mean
Represents the dispersion of a given distribution Variance is a natural measure of risk Standard deviation = square root of variance Higher variance (or standard deviation) represents greater dispersion and, hence, greater risk Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 7

Computing Standard Deviation: SF Example
The standard deviation is the square root of the variance The equation is: The standard deviation of our example follows: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 8

Average (Mean) Realized Returns: Example
What is the average realized rate of return for Stock A and Stock B using the sample data? Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 9

Realized Returns and Risk: Example
Covariance: New Concept in Risk Measurement Consider our two stocks again: Stock A and Stock B Note: As we will see, covariance is a very important concept! Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 10

Realized Returns and Risk: Example
Correlation: New Concept in Risk Measurement Consider our two stocks again: Stock A and Stock B Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 11

What is Stand-Alone Risk? How is Stand-Alone Risk Measured?
Stand-alone risk is the risk an investor faces if he holds a single asset in isolation i.e., rather than as part of a portfolio of assets Stand-alone risk can be measured as the coefficient of variation (CV) Coefficient of variation is the standard deviation divided by the expected return Coefficient of variation (CV) shows the risk per unit of return CV is used by investors to compare two or more alternative investments Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 12

Coefficient of Variation (CV)
Stand-alone risk can be measured as the coefficient of variation (CV) Coefficient of Variation equation follows: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 13

Coefficient of Variation (CV): Example
Assume you have the following three investment options: (1) A T-bill with the following attributes: (2) A Bond with the following attributes: (3) A Stock with the following attributes: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 14

Portfolio Return Portfolio Returns:
To compute the return on a portfolio, first compute the return on each single asset making up the portfolio The return on the portfolio is the weighted average of the individual security returns The historical (ex post) average return is often used as a proxy for the expected (ex ante) returns Example: Assume we have a portfolio made up of 40% of Stock A and 60% of Stock B Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 15

Portfolio Return: Example
Consider our example of Stock A and Stock B again: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 16

Risk in a Portfolio Context
Which will have a higher standard deviation – an individual asset (i.e., stand-alone asset) or a portfolio of assets? Assume returns of different assets are not perfectly correlated Gains in some of the portfolio’s assets will offset losses in other assets End result: Return variability (i.e., variance or standard deviation) is reduced when assets are combined in a portfolio Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 17

Risk in a Portfolio Context continued…
Assume an investor owns an asset and wishes to add another asset to create a portfolio Question: What risk should the investor consider? Answer: Fundamental principle of finance is that investor cannot assess the riskiness of an investment by examining only its own standard deviation! Risk must always be considered in a portfolio context i.e., taking into account the standard deviation of the entire portfolio after adding the asset in question Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 18

Risk in a Portfolio Context: New Example
Your $500,000 home will burn down with probability equal to (i.e., 0.2%) Your expected loss (due to your home burning down) is: x $500,000 = $1,000 An insurance policy (no deductible) costs $1,100 (1) What is expected profit of investment in the policy? (2) What is expected return of investment in the policy? (3) What is standard deviation of profit of an investment in the policy? Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 19

(1) What is the expected profit of investment in the policy? (2) What is the expected return on the policy? Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 20

(3) What is the standard deviation of profit of an investment in the policy? If your house burns down you get $498,900 (i.e., $500,000 - $1,100) If your house doesn’t burn down you get -$1,100 Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 21

Who wants to buy an asset with a negative expected return and a high level of risk (as measured by standard deviation)? Let’s see a show of hands! Raise your hand if you would purchase this asset!! Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 22

In fact, this may be a valuable addition to a portfolio because of its impact on portfolio risk What is the standard deviation of the value of the complete portfolio, which consists of the following two assets? Asset 1: Your House Asset 2: The Insurance Policy Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 23

Diversification Diversification is a strategy designed to reduce risk by spreading a portfolio across many assets The riskiness of a portfolio is usually smaller than the average of the assets’ riskiness (i.e., average of assets’ σs) This is true as long as the returns on the assets making up the portfolio are not perfectly correlated with one another Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 24

Diversification…More Generally
The experiment’s results: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 25

Risk and Diversification
Portfolio standard deviation falls to about 20% when 20 stocks are added to the portfolio Some risk is diversifiable (i.e., it can be eliminated in a portfolio context) and is known as… …Firm-specific risk, also known as… …Idiosyncratic risk, also known as… …Diversifiable risk, also known as… …Unsystematic risk Other risk is not diversifiable even in a portfolio… …Market risk, also known as… …Systematic risk, also known as… …Nondiversifiable risk Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 26

Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 27

Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 28

Risk and a Diversified Investor
An investor is only concerned with the risk of his overall portfolio Implication: To a well-diversified investor, only systematic risk matters On the risk-return tradeoff: Since idiosyncratic risk can be freely diversified away, investors cannot expect to be compensated for bearing it Investors only expect compensation for bearing systematic risk Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 29

Returns Return on investment Gain or loss from an investment
Two components include: (1) Income component (dividend or interest) (2) Price change (capital gain or loss)

Stock Returns Dollar Return Percentage Return
Measure of how much money you make on investment Capital Gain (Loss) is price appreciation (depreciation) on the stock Percentage Return Rate of return for each dollar invested

Example: Calculating Stock Returns
It appears you did quite well! Dollar Return Percentage Return

Holding Period Returns
The holding period return is the return that an investor would get when holding an investment over a period of t years, when the return during year i is given as Ri:

Example: Holding Period Returns
Suppose your investment provides the following returns over a four-year period:

Return Statistics The history of capital market returns can be summarized by describing the following: Average Return Standard Deviation of Returns Frequency Distribution of Returns

Average Stock Returns and Risk-Free Returns
The Risk Premium The added return (over and above the risk-free rate) resulting from bearing risk One of the most significant observations of stock market data is the long-run excess of stock return over the risk-free return Average excess return from large company common stocks for the period 1926 through 2005 was: Average excess return from small company common stocks for the period 1926 through 2005 was:

Risk Premia Suppose that The Wall Street Journal announced that the current rate for one-year Treasury bills (T-bills) is 5% What is the expected return on the market of small-company stocks? Recall the average excess return on small company stocks for the period 1926 through 2005 was 13.6% Given a risk-free rate of 5%, we have an expected return on the market of small-company stocks of:

Risk Statistics There is no universally accepted definition of risk
A useful construct for thinking rigorously about risk is the probability distribution Provides a list of all possible outcomes and their probabilities

Risk Statistics Calculating sample statistics Mean, or Average, Return
Sample Variance Sample Standard Deviation

More on Average Returns
Arithmetic Average Return earned in an average period over multiple periods Geometric Average Average compound return per period over multiple periods The geometric average will be less than the arithmetic average unless all the returns are equal

Forecasting Return Blume’s formula
Arithmetic average overly optimistic for long horizons Geometric average overly pessimistic for short horizons Blume’s formula is a simple way to combine both! Where T is the forecast horizon and N is the number of years of historical data we are working with T must be less than N

Forecasting Return Example: Blume’s formula
Suppose from 25 years of data we calculate arithmetic average of 12% and geometric average of 9% From these averages, we can make 1-year, 5-year, and 10-year average return forecasts:

What is Investment Risk
Risk, in general, refers to the chance that some unfavorable event will occur Investment risk pertains to the probability of realized (actual) returns being less than expected returns The greater the chance of low or negative returns, the riskier the investment

Types of Risk Stand-alone risk Portfolio risk
Riskiness of an asset held in isolation Portfolio risk Riskiness of an asset held as one of a number of assets in a portfolio In a portfolio context, risk can be divided into two components Diversifiable (firm-specific) risk Market (non-diversifiable) risk

Individual Securities
The characteristics of individual securities that are of interest are the: Expected Return: Return on a risky asset expected in the future Variance and Standard Deviation: Measures of dispersion of an asset’s returns around its expected, or mean, return

Expected Return, Variance, Standard Deviation, and Covariance
Consider the following two risky asset world There is a 1/3 chance of each state of the economy The only assets are a stock fund and a bond fund

Expected Return

Variance

Standard Deviation

Covariance Deviation compares return in each state to the expected return Weighted takes the product of the deviations multiplied by the probability of that state

Correlation

Return and Risk for Portfolios
Note that stocks have a higher expected return than bonds and higher risk Now turn to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks

Portfolios The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio

Portfolios Covariance Correlation

Portfolios Observe the decrease risk that diversification offers
Particularly when the two assets are almost perfectly negatively correlated!!! An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than either stocks or bonds held in isolation

The Efficient Set for Many Securities
Consider a world with many risky assets We can still identify the opportunity set of risk-return combinations of various portfolios return Individual Assets P

The Efficient Set for Many Securities
The section of the opportunity set above the minimum variance portfolio is the efficient frontier return efficient frontier minimum variance portfolio Individual Assets P

Diversification and Portfolio Risk
Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another asset However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion

Portfolio Risk and Number of Stocks
In a large portfolio, the variance terms are effectively diversified away, but the covariance terms are not!  Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Nondiversifiable risk; Systematic Risk; Market Risk n

What is Diversifiable Risk?
Caused by company specific events (e.g., lawsuits, strikes, winning or losing major contracts, etc.) Risk factors that affect a limited number of assets Also known as unique risk or unsystematic risk Risk that can be eliminated by combining assets into a portfolio Effects of such events on a portfolio can be eliminated by diversification If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

What is Market Risk? Stems from such external events as war, inflation, recession, changes in GDP and/or interest rates Risk factors that affect a large number of assets Also known as non-diversifiable risk or systematic risk Known as systematic risk since it shows the degree to which a stock moves with other stocks Because all firms are effected simultaneously by these factors, market risk cannot be eliminated by combining assets into a portfolio Effects of such factors on a portfolio cannot be eliminated by diversification

What is Total Risk? Total risk = systematic risk + unsystematic risk
The standard deviation of returns of an individual asset is a measure of total risk For well-diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

Stock Prices and Information
Actual (realized) return = expected return + unexpected return (surprise) Surprise is risk of investment (what we couldn’t forecast prior to buying the asset) General diversification information Most stocks are positively correlated: Average stand-alone risk: Average portfolio risk: Combining stocks in a portfolio lowers risk Except when :

Risk Free Assets Assume there is a risky asset, x, and a risk free asset, f Risky Asset: Risk Free Asset: You have $100, you put $50 in x and $50 in f (i.e., lending $50 at the risk free rate) The weights are:

Riskless Borrowing and Lending
The Capital Market Line (CML) Expected Portfolio Return: Slope = Market Price of Risk: Any portfolio on CML is a combination of M and f If we invest in the risk-free asset, f, and in M: If we borrow money at the risk-free rate and invest in M

Riskless Borrowing and Lending
The Capital Market Line (CML) With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope This is the Capital Market Line (CML) return CML efficient frontier Rf P

Market Equilibrium With the optimal capital allocation line (i.e., the CML) identified, all investors choose a point along the line i.e., some combination of the risk-free asset and the market portfolio, M In a world with homogeneous expectations, M is the same for all investors return CML efficient frontier M Rf P

The Systematic Risk Principal
Risk when holding the Market Portfolio, M Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (β) of the security Beta measures the responsiveness of a security to movements in the market portfolio, i.e., systematic risk The reward for bearing risk depends only upon systematic risk since unsystematic risk can be diversified away

Portfolio Betas (βp) Portfolio Betas
While portfolio variance is not equal to a simple weighted sum of individual security variances, portfolio betas are equal to the weighted sum of individual security betas Where w is the proportion of security i’s market value to that of the entire portfolio, and N is the number of securities in the portfolio

Relationship between Risk and Expected Return (CAPM)
Beta and the Risk Premium A risk-free asset has a beta of zero When a risky asset is combined with a risk-free asset, the resulting portfolio expected return is a weighted sum of their expected returns and the portfolio beta is the weighted sum of their betas Reward-to-Risk Ratio We can vary the amount invested in each type of asset and get an idea of the relationship between portfolio expected return and portfolio beta

What happens if two assets have different reward-to-risk ratios? Since systematic risk is all that matters in determining expected return, the reward-to-risk ratio must be the same for all assets and portfolios in equilibrium If not, investors would only buy the assets (or portfolios) that offer a higher reward-to-risk ratio Because the reward-to-risk ratio is the same for all assets, it must hold for the risk-free asset as well as for the market portfolio Result:

The Security Market Line (SML) The security market line is the line which gives the expected return – systematic risk (beta) combinations of assets in a well functioning, active financial market In an active, competitive market in which only systematic risk affects expected return, the reward-to-risk ratio must be the same for all assets in the market The slope of the SML is the difference between the expected return on the market portfolio and the risk-free rate (i.e., the market risk premium) Result:

Expected Return on the Market Expected Return on an individual security Or This applies to individual securities held within well-diversified portfolios Market Risk Premium

Capital Asset Pricing Model (CAPM) Expected return b βM =1.0

The Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) An equilibrium model of the relationship between risk and required return on assets in a diversified portfolio What determines an asset’s expected return? The risk-free rate: the pure time value of money The market risk premium: the reward for bearing systematic risk The beta coefficient: a measure of the amount of systematic risk present in a particular asset The CAPM:

Example: Capital Asset Pricing Model Suppose a stock has 1.5 times the systematic risk as the market portfolio The risk-free rate as measured by the T-bill rate is 3% and the expected risk premium on the market portfolio is 7% What is the stock’s expected return according to the CAPM?

Example: Capital Asset Pricing Model Expected return b 1.5

What is Value? Economic value defined as: “The intrinsic worth of a financial asset” Intrinsic value derived from long-term cash flow generating ability of a company or project Intrinsic value measured by discounted cash flow (DCF) DCF used to evaluate specific investment opportunities (e.g., capital budgeting projects) or entire company DCF used to obtain economic value of any financial asset (including human capital) Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 80

Discounted Cash Flow (DCF)
Calculating present value is called discounting Interest rate used in discounting is called the discount rate General formula for the present value of $1 to be received t periods from now at discount rate R (per period) is: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 81

NPV in Bond Valuation A 3-year 10% bond that makes annual payments is selling for $960. If the appropriate discount rate (i.e., YTM) is 12%, would you buy the bond? Compute the NPV: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 82

NPV in Stock Valuation A stock just paid a dividend of $4. Its future dividends are expected to grow at 3% indefinitely and the current market price is $80. If the appropriate discount rate (i.e., required rate of return) is 8%, would you purchase the stock? Compute the NPV: Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 83

The Payback Rule Payback period is the time until cash flows recover the initial investment The decision rule Only accept projects with payback periods less than some pre-specified time horizon Does this lead to optimal decisions? Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 84

The Payback Rule Problem #1: Does not consider time value of money
Payback period treats all cash flows the same no matter whether they are received at time 0 or sometime in the future Problem #2: Ignores all cash flows occurring after the cutoff period Payback period considers only cash inflows until they sum to the cash outflow – all other cash flows are ignored Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 85

The Payback Rule Suppose the company accepts all projects with a 2-year payback period Consider the following: Project CF0 CF1 CF2 CF3 Payback 10% A -2,000 500 1,000 10,000 2.05 6,794 B 2 -264 C 2,000 -347 Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 86

Payback Period Unfortunately, many companies use the payback period as an initial screening device Companies that employ payback period as a screening tool typically state that any project that has a payback period that exceeds some pre-specified time frame are automatically rejected Any project that meets the payback period criteria is then analyzed using some other capital budgeting technique (e.g., NPV or IRR) As we can see from the examples on the prior page, such companies would have rejected the only positive NPV project Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 87

Internal Rate of Return (IRR)
IRR is the discount rate that sets NPV equal to 0 (like the YTM does for a bond) IRR Decision Rule: Accept only the projects with IRRs exceeding the discount rate (aka hurdle rate) Hurdle rate typically used is the project’s risk-adjusted discount rate (i.e., the company’s WACC adjusted for the risk of the project relative to the risk of an average project of the firm) Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 88

Internal Rate of Return (IRR)
IRR is the discount rate that sets NPV equal to 0 (like the YTM does for a bond) Without a financial calculator, determining the project’s IRR must be accomplished with trial-and-error (a tedious process) Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 89

IRR Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e., rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. IRR = 12.96% 90

IRR Problems Problem #1: Non-normal cash flows
Possible for a project to have multiple IRRs Manager can’t make a decision because doesn’t know which one to use In general, the number of sign changes in cash flows equals the number of IRRs Problem #2: Choosing between mutually exclusive projects NPV and IRR may tell the manager different things (NPV profile) Since we know NPV is optimal, IRR won’t always lead to the correct decision Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 91

IRR Problems You have two proposals to choose between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer? What about NPV? Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 92

Comparing NPV and IRR Reinvestment rate assumption
NPV assumes cash flows from a project can be reinvested at the project’s cost of capital (i.e., project’s risk-adjusted discount rate) IRR assumes that cash flow from a project can be reinvested at the project’s internal rate of return What is the correct reinvestment rate assumption? Company should be able to reinvest at its WACC (or it should be paying out earning to shareholders rather than reinvesting!) However, a company may find it extremely difficult to reinvest at a project’s IRR if the project’s IRR is extremely high! If a company is unable to reinvest at the project’s IRR, then the project won’t earn its IRR (i.e., the IRR will be overstated) Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 93

Comparing NPV and IRR Independent projects means that the acceptance of one project doesn’t impact the decision of another project For projects with normal cash flows, NPV and IRR criteria always lead to the same accept/reject decision Mutually exclusive projects mean that the manager can only invest in one project from a set of projects NPV will always lead to the correct accept/reject decision If IRR decision is different from NPV it is due to one of two potential problems: (1) Timing difference in cash flows (2) Project size or scale differences Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 94

Comparing NPV and IRR Capital Budgeting Decision Rule: Since NPV always provides the correct accept/reject decision, always use NPV! Question: Why, then, do we even cover IRR? Answer: Many managers still use IRR in their capital budgeting decision-making! Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 95

Other Capital Budgeting Techniques
(1) Average Accounting Return (ARR) (2) Discounted Payback Period (3) Modified Internal Rate of Return (MIRR) (4) Profitability Index (PI) Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 96

Average Accounting Return (AAR)
The AAR is a measure of accounting profit relative to book value ARR = [Average Net Income/Average Book Value] The AAR is similar to the accounting return on assets (ROA) The AAR rule is to undertake a capital budgeting project if the project’s AAR exceeds a benchmark AAR AAR is seriously flawed for a variety of reasons AAR ignores time value AAR uses net income and book value rather than cash flows and market value (therefore not economically meaningful) Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 97

Discounted Payback Period
The Discounted Payback Period is the length of time until the sum of an investment’s discounted cash flows equals its cost The Discounted Payback Period rule is to undertake a capital budgeting project if the project’s discounted payback period is less than some cutoff Discounted Payback Period is flawed This method ignores cash flows that occur after the cutoff period Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 98

Modified Internal Rate of Return (MIRR)
The MIRR is a modification to the IRR where the project’s cash flows are modified by: (1) Discounting the negative cash flows back to the present (2) Compounding all cash flows to the end of the project’s life, or (3) Combining (1) and (2) above An IRR is then computed on the modified cash flows MIRRs are guaranteed to avoid the multiple rate of return problem, but: (1) It is unclear how to interpret them (2) They are not truly “internal” because they depend on externally supplied discounting or compounding rates (3) Most importantly, MIRR, like IRR cannot be used to rank mutually exclusive projects Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 99

Profitability Index (PI)
The PI, also called the benefit-cost ratio, is the ratio of present value to cost Also called the benefit-cost ratio: PI = Present Value/Initial Cost The PI rule is to undertake a capital budgeting project if the index exceeds 1 PI is similar to NPV, but like IRR it cannot be used to rank mutually exclusive projects Understanding Media: Extensions of Man, published in 1964. The medium you use to send a particular message automatically predisposes audience members to make certain tacit assumptions about the message before they even read it. Put another way, people unconsciously judge books by their covers. How does this apply to business communications? If you want to announce cutbacks in your company’s health benefits, don’t deliver the message with a glitzy, over-the-top, no-expenses-spared campaign. Conversely, if you want to position your company as a leader in innovation, don’t advertise your message on sandwich boards dangling from the necks of ragamuffins traipsing around in front of gas stations. 100

Relevant Cash Flows Relevant Cash Flows
The incremental cash flows associated with the decision to invest in a project The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of undertaking the project Difference between cash flows with the project and cash flows without the project Based on free cash flows, not accounting income

Aspects of Incremental Cash Flows
Sunk Costs Costs that have already occurred Example: Test market expenses Opportunity Costs Cost of best foregone alternative Cash flows lost by taking one course of action over another Side Effects or Externalities: Erosion Erosion (or cannibalization): cash flow transferred to new project from customers and sales of existing products

Aspects of Incremental Cash Flows
Net Working Capital Costs associated with an increase in net working capital due to undertaking a project Increase in current assets (e.g., inventory and/or A/R) and/or decrease in current liabilities associated with undertaking a capital budgeting project Financing Costs Costs associated with how the project is financed Includes interest and dividend expenses Other Issues All cash flows should be after-tax cash flows

Net Working Capital (NWC)
NWC is the difference between CA and CL Investment in inventories and A/R net of increase in A/P Generally, firms invest in NWC at beginning of project (t=0) This investment in NWC is recovered at the end of the project ∆NWC should be included in incremental CFs

Net Working Capital (NWC)
GM will increase NWC at the beginning: Firm will increase inventories of raw material Dealers will require increased A/R financing At the end of model’s life, NWC will decline: Inventories will be allowed to run down A/R will be paid down ∆NWC Increases at the beginning are cash outflows Decreases at the end of the project are cash inflows

Additions to NWC Given NWC at the beginning of the project (i.e., t=0), we can calculate future NWC as: NWC will grow at a rate of X% per year (e.g., 3%) i.e., NWCYear2 = NWCYear1 x ( ) NWC will equal Y% of sales each period (e.g., 15%) i.e., NWCYear2 = SalesYear2 x (0.15) Text assumes initial investment in NWC is made in year 0 So assume this is the case unless told otherwise

Recovery of NWC NWC is recovered at the end of the project:
Bring NWC account to zero Inventories are run down Unpaid bills are paid (both A/R and A/P) Text assumes initial investment in NWC made in year 0 is all recovered at the end of the project So assume this is the case unless told otherwise

Recovery of NWC

Treatment of Financing Costs
Should you subtract interest expense or dividends when calculating cash flows? No! We discount project cash flows with a cost of capital that is the rate of return required by all investors Therefore we should discount the total amount of cash flow available to all investors They are part of the cost of capital If we subtracted them from CFs, we would be double counting capital costs

Depreciation and Capital Budgeting
Depreciation is a non-cash charge However, depreciation has cash flow consequences since it affects taxes Companies often calculate depreciation one way for reporting taxes and another for reporting to investors Tax depreciation is typically determined by MACRS Salvage value and economic life are ignored Many firms use straight line method for stockholders Subtract salvage value from cost and divide by asset’s economic useful life (in years)

MACRS Modified Accelerated Cost Recovery System
Set forth guidelines that govern tax depreciation Created several classes of assets, each with a more-or-less arbitrarily prescribed life called a recovery period or class life MACRS class life bears only rough guideline to expected useful economic life Major effect has been to shorten the depreciable lives of assets, giving business larger tax deductions and thus increasing their cash flows available for investment Cash flows increased since higher early (time value of money) depreciation reduces taxes, and therefore increases cash flow to stakeholders Companies often calculate depreciation one way for reporting taxes and another for reporting to investors Tax depreciation is typically determined by MACRS Salvage value and economic life are ignored Many firms use straight line method for stockholders Subtract salvage value from cost and divide by asset’s economic useful life (in years)

MACRS: Major Classes/Asset Lives
Class Type of Property 3-year Certain specialized short-lived property, race horses over 2 years old 5-year Automobiles, trucks, computers 7-year Most industrial equipment, office furniture, books 10-year Certain longer-lived equipment, vessels, barges, tugs 20-year Farm buildings, sewer pipes, very long-lived equipment 27.5-year* Residential rental property such as apartment buildings 31.5-year* Nonresidential property, including commercial and industrial buildings *Note: Real estate must be depreciated using the straight line method. Other classes can use either straight line or the accelerated method. Since higher depreciation expense results in lower taxes and higher cash flows, most elect to use the accelerated method.

Half-Year Convention Under MACRS, assumption is made that the asset is placed in service in the middle of the first year For 3-year class property, the recovery period begins in the middle of the first year and ends three years later The effect of the half-year convention is that the recovery period extends out one more year than the asset class i.e., 3-year assets are depreciated over four fiscal years This convention is incorporated in to the MACRS recovery allowance percentages Half-year convention also applies to straight line

MACRS Depreciation Allowance
Year 3-year 5-year 7-year 1 33.33% 20% 14.29% 2 44.44% 32% 24.49% 3 14.82% 19.2% 17.49% 4 7.41% 11.52% 12.49% 5 11.52% 8.93% 6 5.76% 8.93% 7 8.93% 8 4.45%

Depreciable Basis The depreciable basis under MACRS is:
Purchase price of the asset Plus: Shipping costs Plus: Installation costs The depreciable basis is not adjusted for salvage value i.e., the estimated market value of the asset at the end of the asset’s useful life

Depreciation Summary: For Tax Purposes
Depreciation is a non-cash charge Which has cash flow consequences since it affects taxes To estimate depreciation expense: Calculate depreciable basis Cost of asset plus any shipping and/or installation charges Ignore economic life and future market value i.e., ignore salvage value of asset at end of its useful life Use tax accounting rules for deprecation MACRS and Straight line methods both use half-year convention

Straight Line versus MACRS

Net Capital Spending When starting a new project, we often must invest money in fixed assets at the start (t=0) What happens to those assets at the end of the life of the project? We ignored salvage value when calculating depreciation expense for tax purposes But salvage value must be considered in our cash flows

Salvage Value If an asset’s value when sold (i.e., salvage value) exceeds (is lower than) its book value, the difference is treated as a gain (loss) for tax purposes Taxes = (Market Price – Book Value) x Tax Rate After-Tax Salvage Value = Market Price – Taxes At the end of a project’s life, the book value of a piece of equipment is $0; however, assume you can sell it for $5,000 (and also assume your tax rate is 40%) – What taxes will you pay? Taxes = ($5,000 – $0) x 0.40 = $2,000 After-Tax Salvage Value = $5,000 – $2,000 = $3,000

Salvage Value Assume the asset’s book value was $1,000 at the end of the project’s life: Taxes = ($5,000 – $1,000) x 0.40 = $1,600 After-Tax Salvage Value = $5,000 – $1,600 = $3,400 Assume the book value was $6,000 at the end of a project’s life: Taxes = ($5,000 – $6,000) x 0.40 = -$400 After-Tax Salvage Value = $5,000 –(-$400) = $5,400

Capital Budgeting Problem Cox Casting Company
Cox Casting Company (CCC) Project Is considering adding a new line to its product mix You must complete the capital budgeting analysis Production to be set up in unused space in CCC’s plant The machinery’s invoice price would be approximately $200,000 Shipping and installation costs are $10,000 and $30,000 respectively Machinery has an economic life of 4 years and CCC has obtained a special ruling which places equipment in MACRS 3-year asset class Machinery is expected to have a salvage value of $25,000 after 4 years of use

Proposed Project Summary Depreciable Basis Economic life of machinery = 4 years Salvage value = $25,000 MACRS 3-year asset class

CCC’s Capital Budgeting Project continued New line would generate incremental sales of 1,250 units per year for four years Each unit can be sold for $200 in the first year Incremental costs would be $100 per unit in the first year, excluding depreciation Sales price and costs expected to increase 3% per year CCC’s NWC to increase (starting in year 0) by an amount equal to 12% of next year’s sales revenue CCC’s tax rate is 40% Project’s risk-adjusted cost of capital is 10%

Proposed Project Summary Annual unit sales = 1,250 Unit sales price in year 1 = $200 Unit costs in year 1 = $100 Growth rate in sales and costs = 3% per year (inflation) NWC = 12% of next year’s sales revenue Tax rate = 40% Project cost of capital = 10%

Incremental Costs Suppose the plant space could be leased out for $25,000 a year Should this cost be included in the analysis? Yes! This is an opportunity cost since accepting the project means you will not receive the $25,000 in lease income After-Tax Opportunity Cost:

Side Effects or Externalities Suppose the new product line would decrease sales of CCC’s other products by $50,000 per year Should this cost be included in the analysis? Yes! This is erosion or cannibalization Net CF loss on other lines would be a cost to this project However, the annual loss would not be the full $50,000 since CCC would save on cash operating costs if its sales dropped You would need to figure out the effect on the other products’ operating cash flows

Summary: Side Effects or Externalities Externalities can be negative If the new product is a substitute to existing products Erosion or cannibalization Externalities can be positive If the new product is a complement to existing products Synergy In either case, the incremental impact on CFs must be included in your capital budgeting analysis

Annual Depreciation Expense Year MACRS % x Initial Basis = Depreciation 1 0.3333 $240,000 $79,992 2 0.4444 106,656 3 0.1482 35,568 4 0.0741 17,784 240,000

Annual Sales and Costs Year 1 Year 2 Year 3 Year 4 Units 1,250 Unit Price* $200 $206 $212.18 $218.55 Unit Cost* $100 $103 $106.09 $109.27 Sales $250,000 $257,500 $265,225 $273,188 Costs $125,000 $128,750 $132,613 $136,588 * Price and costs growing at 3% per year after year 1

Adjusting for Inflation Is it important to include inflation when estimating CF? Nominal rate R > real rate r Cost of capital, R, is based on market determined cost of debt and equity and includes a premium for inflation If you discount real CFs with the higher nominal rate, R, then your NPV estimate is too low Since the cost of capital is already in nominal form, it is usually easiest to adjust cash flows to reflect inflation

Operating Cash Flows Year 1 Year 2 Year 3 Year 4 Sales $250,000 $257,500 $265,225 $273,188 Costs $125,000 $128,750 $132,613 $136,588 Deprecation $79,992 $106,656 $35,568 $17,784 EBIT $45,008 $22,094 $97,044 $118,816 Taxes (40%) $18,003 $8,838 $38,818 $47,526 NOPAT $27,005 $13,256 $58,226 $71,290 + Depreciation Net Op. CF $106,997 $119,912 $93,794 $89,074

Change in Net Working Capital (∆NWC) Sales NWC (12% of next year’s sales) CF Due to Investment in NWC Year 0 $30,000 -$30,000 Year 1 $250,000 $30,900 -$900 Year 2 $257,500 $31,827 -$927 Year 3 $265,225 $32,783 -$956 Year 4 $273,182 $0

After-Tax Salvage Value When the project is terminated at the end of year 4, the equipment can be sold for $25,000 But it has been fully depreciated (i.e., its book value is zero) Therefore, taxes must be paid on the full salvage value For this project, the after-tax salvage cash flow is:

Total Cash Flows from Assets Year 0 Year 1 Year 2 Year 3 Year 4 Initial Cost -$240,000 Op. CF $106,997 $119,912 $93,794 $89,074 NWC CF -$30,000 -$900 -$927 -$956 $32,783 Salvage CF $15,000 Net CF -$270,000 $106,097 $118,985 $92,838 $136,857 NPV = $88,012 at R = 10%

NPV Analysis Now you have undertaken NPV analysis for Cox Casting Company in terms of its new product line capital budgeting project Using the project’s 10% cost of capital NPV is $88,012 Undertaking this project is expected to increase CCC’s stockholders’ wealth by $88,012 What do you suggest? Obviously, since the NPV is positive, you should accept the project However…

Limitations of NPV Analysis Fundamental problem in NPV analysis is dealing with uncertain future outcomes NPV is only as good as inputs and assumptions used Need techniques to identify crucial assumptions and explore what could go wrong Techniques Sensitivity analysis Scenario analysis Decision trees

Sensitivity (also called what-if) Analysis Sensitivity analysis examines how sensitive NPV is to changes in the underlying assumptions Does changing your assumptions (e.g., discount rate, estimated expected cash flows, etc.) change your decision to invest? Under sensitivity analysis, one input is changed by a fixed percent while all other inputs are held constant Any input variable that causes a large change in NPV is considered a key variable Key variables must be controlled by managers in order to obtain expected NPV

Sensitivity Analysis Pros Indicates whether NPV analysis can be “trusted” i.e., if NPV is very sensitive to certain key variables Shows where more information is needed i.e., which assumptions have the biggest effect on NPV Cons Treats each variable in isolation, when in reality, variables are often related Says nothing about likelihood of a change in the variable

Sensitivity Analysis % Change WACC UNIT SALES SALVAGE from NPV Units Variable Base Case 88,012 Sold $88,012 Cost -30% 7.0% $113,273 875 $16,651 $17,500 $84,939 -15% 8.5% $100,294 1,063 $52,331 $21,250 $86,476 0% 10.0% 1,250 $25,000 15% 11.5% $76,380 1,438 $123,694 $28,750 $89,549 30% 13.0% $65,352 1,625 $159,375 $32,500 $91,086

Sensitivity Analysis Change from Resulting NPV (000s) Base level WACC (r) Unit sales Salvage -30% $113 $17 $85 -15% $100 $52 $86 0% $88 15% $76 $124 $90 30% $65 $159 $91

Sensitivity Analysis Base (%) 88 NPV (000s) Unit Sales Salvage R

Two Methods Replacement Chain Method
Also called Matching Cycles Method This method replicates multiple cycles of asset lives until the two pieces of equipment have the same number of years Equivalent Annual Cost Method (EAC) Also called the annuity method The present value of a project’s costs calculated on an annual basis Assumptions Initial costs versus maintenance Perpetuity

Example: Two Methods Assumptions
Project requires purchase of machinery Two machine alternatives Machine A has a 3 year life Machine B has a 2 year life Project risk-adjusted cost of capital is 8%

Example: Two Methods Approach 1:Replacement Chain Method
Approach 2: EAC Approach 1: Matching Cycles Two cycles of project A  6 years Three cycles of project B  6 years

Example: Replacement Chain
NPVA=-27.89 NPVA=-27.89 2 3 4 6 NPVB=-20.70 NPVB=-20.70 NPVB=-20.70 For A: NPV = /(1.08)3 = -$50.03 For B: NPV = /(1.08) /(1.08)4 = -$53.66 Choose A

Example: Equivalent Annual Cost
Approach 2: Equivalent Annual Cost EAC = NPVONE CYCLE/[1/r(1 – (1 + r)-T)] = NPVONE CYCLE /ATr For A: EAC = /A38% = /2.577 = -$10.82 For B: EAC = /A28% =-20.70/1.783 = -$11.61 Choose A

Evaluating Cost Cutting Proposals

Consider a project to automate some part of an existing process Necessary equipment costs $80,000 to buy and install Project will save $22,000 per year (pre-tax) by reducing labor and material costs Equipment is 5-year MACRS and is expected to have a salvage value of $20,000 after 5 years The tax rate is 34% The risk-adjusted discount rate is 10% Note: There is no working capital consequences Should you undertake the project?

Step 1: Depreciation: Depreciation of $80,000 of 5-year equipment using MACRS MACRS% Depreciation Book value 1 20.00 16,000 64,000 2 32.00 25,600 3 19.20 15,360 4 11.52 9,216 5 4,608 6 5.76 100.00 80,000

Year 1 Year 2 Year 3 Year 4 Year 5 Rev – Exp 22,000 Deprec. 16,000 25,600 15,360 9,216 EBIT 6,000 -3,600 6,640 12,784 2,040 -1,224 2,258 4,347 NI

NPV = $4,359

Should you undertake the project? Yes! The cost cutting project is expected to produce a positive NPV

What is Value? Economic Value defined as: “The intrinsic worth of a financial asset” Intrinsic value derived from long-term cash flow generating ability of a company or project Intrinsic value measured by discounted cash flow (DCF) DCF used to evaluate Specific investment opportunities Strategy of a business unit An entire company DCF used to obtain economic value of any financial asset (including human capital!)

Discounted Cash Flow (DCF)
Calculating present value is called discounting Interest rate used in discounting is called discount rate General formula for the present value of $1 to be received n periods from now at discount rate i (per period) is:

How is Value Created? Value results from set of interrelated activities that most firms already have in place The issue is to what extent behaviors that promote value creation are a part of the corporate culture Prerequisite for value creation is that firm’s actions be based on a foundation of value thinking Value thinking has two dimensions (1) Value Metrics based on management’s understanding of how value is created and how the stock market values firms Management’s ability to balance short-and long-term results (2) Value Mindset refers to how much management cares about shareholder value creation Management’s willingness to make unpopular decisions if these are necessary to maximize shareholder value in the long-term

Three Revisions to Porter’s Model
First, Composite Competitive Rivalry Force (a) Pressure from substitutes and (b) Threat of new entry combined with traditional competitors into the single category Second, Additional Role of Complementors Market participant considered a complementor if buyers value company’s product more highly when they have access to complementor’s product Third, Addition of Market Turbulence and Market Growth Considers impact of changing market conditions on risk and strategy 157

Financial Research: New Perspective
Financial Research should determine value proposition Answer Question: Does capital budgeting project create or destroy value? Value creation should be management’s primary goal! Discounted Cash Flow (DCF) is primary technique to measure value as Net Present Value (NPV) However, DCF technique does not measure value of flexibility (i.e., NPV does not include value of flexibility) New technique needed to incorporate real (growth) options Growth options include opportunity to expand capacity, make new product introductions, expand basic research, increase advertising Value of the option is the present value of expected cash flows plus the value of any new growth opportunity 158

New Technique: Real Options
Real options technique overcomes restrictiveness of NPV DCF understates project’s value (NPV) due to increased flexibility and additional growth opportunities Real options challenge conventional wisdom about capital budgeting Accepting negative NPV project justified if it creates growth opportunities and sum of NPV of these new opportunities is positive and greater than initial project’s negative NPV Real options advantage is that is integrates capital budgeting with long-range planning Investment decisions today can create basis for future investment decisions 159

Feasibility Study Feasibility study is first step to successful project Feasibility studies require management to… Conduct up-front due diligence Understand project’s risk analysis, cost analysis, completion time frame, stakeholders’ analysis, etc. Follows the ‘ready, aim, fire’ model rather than ‘ready, fire, aim’ Benefits of accurate and reasonable feasibility study Avoids danger of loading up evidence in one direction in order to support a priori decision It locks company into a mode of planning first, then executing, which avoids potential waste 160

Pro Forma Construction
Pro forma, or projected, financial statements reflect expected future performance of firm or project Pro forma financial statements constructed and used to… Evaluate expected future financial condition of firm or project Project financing requirements Determine how alternative courses of action are likely to impact firm’s financial conditions and financial requirement Provide a standard against which to evaluate actual results 161

Free Cash Flows Primary outcome of pro forma financial statement is ability to forecast free cash flows Free cash flows are the amount of cash a firm or project can pay out to investors Usually annual cash flows after paying for all investments necessary for growth Pro forma Excel models typically incorporate a spreadsheet designed to calculate free cash flows Purpose of such spreadsheet models is to be used as a managerial decision-making tool Permits managers to test potential outcomes of various scenarios 162

Time Value of Money Economic value defined as the intrinsic worth of a financial asset Intrinsic value derived from long-term cash flow generating ability of a financial asset (e.g., capital project) To determine economic value future cash flows must be discounted to the present Calculating present values is called discounting Interest rate used in discounting is discount rate Most financial assets require investment at beginning of asset’s life and generate multiple flows in the future Each cash flow is discounted back to the present and summed to obtain the net present value (NPV) 163

Net Present Value NPV is the appropriate value measurement managers should use to determine viability of capital project NPV recognizes time value of money (i.e., dollar today worth more than dollar tomorrow) Dollar today can be invested to start earning interest immediately NPV depends solely on forecasted cash flows from the project and the project’s opportunity cost of capital NPV unaffected by manager’s taste, company’s choice of accounting method, profitability of company’s other independent projects. Therefore, it will not lead to inferior decisions based on these extraneous factors Because present values are all measured in today’s dollars, they can be added up (additive property) Once calculated, can be summed to determine expected value creation 164

Risk Identification Although easy to understand, risk may be difficult to define and quantify Markowitz defined risk of a security as the standard deviation of returns around the mean or expected return Factors causing higher dispersion may be harder to identify What factors cause one security to have a higher standard deviation of returns than another security? In order to manage risks, managers must first be able to identify the factors underlying risk 165

Risk Analysis and Management
Managers often take risks as given To some extent managers can choose risk their business or project undertakes Certain risk can be hedged or insured against View risk as uncertainty Uncertainty resolved through passage of time, actions, and events Managers can make appropriate mid-course corrections through change in decisions and strategies Real options incorporate learning model akin to having a strategic road map Manager can reduce risk by building flexibility into project Traditional analyses neglect managerial flexibility and therefore undervalue certain projects and strategies 166

Cost of Capital The cost of capital is the firm’s discount rate applied to the average risky project’s cash flows in order to determine the present value of those cash flows Often referred to as the Weighted Average Cost of Capital (WACC) The 4-step process to determine the discount rate, or WACC, is to determine firm’s: (1) Optimal capital structure (2) Capital requirements (3) Component costs of capital (4) WACC 167

Sensitivity and Scenario Analyses
Prior steps of Project Analysis provide information to conduct sensitivity and scenario analyses These analyses determine whether results are robust under alternative assumptions Sensitivity analysis determines key variables of project Project’s ultimate value depends upon controlling these key variables Scenario analysis enables manager to combine key variables into probable situations or outcomes Managers use these two analyses to: Measure change in value due to changes in decisions Determine probable range of value that the project creates 168

Capital Budgeting Process
Capital budgeting process summarizes how firms identify and commit to capital investment projects Process entails how companies: Develop plans and budgets for capital investments Authorize specific projects to be undertaken Check to determine whether projects perform as expected and promised Benefits of properly designed capital budgeting process Process provides means of obtaining accurate information and forecasts to decision-makers Process insures managers are rewarded for adding value to firm Process provides performance measurement 169

Valuation Companies thrive when they create real economic value to shareholders Firms create value by investing capital at rates of return that exceed their cost of capital The more capital invested at attractive rates or return, the more value created Value creation principles must be part of important managerial decision-making Value creation plans must be grounded in realistic assessments of product market opportunities and the competitive environment Managers must be able to create tangible links between their strategies and value creation 170

Investment Decision Investment decision is the beginning of learning
As soon as decision is made, managers should begin learning About business conditions, competitors’ actions, quality of preparations, etc. Managers must respond flexibly to what they learn Investment decisions are made under uncertainty Requires approach to valuation that assists managers to think strategically Approach should capture value of managing actively rather than passively Capital budgeting project is a series of options rather than series of static cash flows Executing project involves making sequence of decisions, some now and some in the future Decision to undertake project sets framework within which future decisions will be made But at the same time leaves room for learning and for discretion to act based on what is learned 171

Rick’s Hardware: A Simple Example
Stage 1: The Early Years Rick owns a small chain of hardware stores To keep it simple, FINA 3320 Consultants tell Rick to focus on Return On Invested Capital (ROIC) Rick’s ROIC is 18%, and we suggest WACC is 10% Rick has a store that is earning 14% ROIC If Rick closes the store with the 14% ROIC, he believes he will increase the firm’s average ROIC Should Rick close the store with a 14% ROIC?

Should Rick close the store with the 14% ROIC? NO! FINA 3320 Consultants now tell Rick that he should care not about ROIC itself, but the combination of two items: (1) ROIC relative to WACC (the firm’s cost of capital) (2) Amount of capital invested This information can be expressed as Economic Profit: FINA 3320 Consultants show Rick that as long as there is a positive spread of ROIC over WACC, additional Invested Capital will produce a higher Economic Profit! Rick’s objective should be to maximize long-term Economic Profit

Stage 2: Growing the Business For many years, Rick was happy with the Economic Profit framework (until he developed Rick’s Superhardware idea) If Rick undertakes Superhardware concept, the firm’s Economic Profit will drop for the first four years, after which it will be higher How was Rick to determine the trade-off between short- and long-term Economic Profit? FINA 3320 Consultants now tell Rick that he needs some more sophisticated financial tools, DCF: DCF Value of firm without the Superhardware concept is $53M DCF Value of firm with the Superhardware concept is $62M

Should Rick undertake the new concept? Of course! Rick’s new Superhardware concept is projected to be more valuable than the present concept But now Rick is confused and asks: “When do I use Economic Value and when do I use DCF?” FINA 3320 Consultants tell Rick that Economic Profit and DCF are the same:

Stage 3: Rick Goes Public Using DCF framework, Rick makes many important long-term strategic decisions and Superhardware is successful Rick now wants to expand but needs access to more capital Rick decides he should undertake an IPO and returns for advice… FINA 3320 Consultants tell Rick that he will have to learn to manage both the financial markets and the real markets Real Markets Until now, Rick has had to manage the real markets by addressing: Amount of cash flow earned relative to the amount of capital invested Maximization of value via Economic Profit and DCF Decision Rule for Real Market decisions Choose strategies or make operational decisions that maximize PV of future FCFs

Financial Markets FINA 3320 Consultants explain to Rick that when the firm enters the financial, or capital, markets, the real market decision rule does not change However, life becomes more complicated because management must now simultaneously deal with outside investors and analysts FINA 3320 Consultants tell Rick that he will have to continue maximizing value, but that he must learn to also manage investors’, or the market’s, expectations If the market’s expectations are higher than what is ultimately realized, the stock’s price will fall even though ROIC > WACC The loss of credibility in this instance may take years to overcome If the market’s expectations are too low, share price will be too low, and the firm may be subject to a hostile takeover

Stage 4: Conglomerate Expansion Publicly-traded Rick’s Hardware grew quickly and regularly beat expectations and became a top market performer So, Rick decided to expand into Rick’s Furniture and Rick’s Garden Supplies But Rick was concerned about delegating decision-making to management (as he knew he must if he expanded) FINA 3320 Consultants explain to Rick that he needed a planning and control system to tell him about the “health” of the firm That is, the ability of the firm to continue to grow and create value This required a forward-looking metric, not just backward-looking ones

FINA 3320 Consultants explain to Rick that the problem with financial metrics is that they cannot tell how management is doing in terms of creating future value For example: In the short run, managers could improve short-term financial results by cutting back on customer service i.e., decreasing the number of employees available in the store at any time to help customers, or reducing employee training Or, in the short run, management could improve short-term financial results by deferring maintenance on existing fixed assets, deferring purchase of new fixed assets, or reducing spending on brand-building (e.g., advertising, etc.) Rick’s hardware must incorporate metrics related to customer satisfaction or brand awareness Such metrics provide an idea about the future, not just the present

Summarizing Rick’s Hardware Lessons (1) In the real market, you create value by earning a ROIC greater than the opportunity cost of capital, or WACC (2) The more you can invest above the cost of capital, the more value you create Growth creates more value as long as the ROIC exceeds the WACC (3) You should select strategies that maximize the PV of expected cash flows, or Economic Profit You get the same answer regardless of which you choose (4) The value of a firm’s shares in the stock market is based on the market’s expectations of future performance Market’s expectations can deviate from intrinsic value if the market is less than fully informed about the firm’s true prospects (5) After the initial price is set, shareholders’ returns earned depend more on the changes in expectations about the firm’s future performance than the actual realized performance of the firm

Ingredients of Pro Forma
Sales forecast may be derived using one of two approaches Top-down: Relies heavily on macroeconomic and industry forecasts However, senior management usually establishes firm’s objectives for increased sales Start with reviews of sales and sales growth over past 5-10 years Bottom-up: Begins by talking to customers to assess demand Many firms use a blend of the two approaches

Perfectly accurate forecasts are not available because sales depends on uncertain future state of: (1) Economy (2) Industry (3) Company Scenario analysis should be used to examine what happens under various assumptions and states: (1) Most Likely Worst-case (2) Most Likely, or Base-case (3) Most Likely Best-case

Pro Forma Financial Statements Analyze historical ratios, forecast balance sheet, income statement, and sources and uses of cash Asset requirements What are the firm’s planned capital expenditures? What are firm’s net working capital needs? Financial requirements How will the firm finance its growth? Internal retained earnings (RE): Net income – Dividends External: New Debt and/or New Equity Capital structure and dividend policies

Economic assumptions Interest rates, industry growth rates, etc. Plug Pro forma will usually assume that sales, costs, and net income grow at g1 If pro forma assumes that assets and liabilities grow at g2, a third variable (e.g., equity) may be forced to grow at g3 in order to make the first two growth rates compatible and have the balance sheet identity hold:

Example: Pro Forma – The Plug
Income Statement 2008 Balance Sheet 2008 Sales $1,000 Assets $500 Debt $250 Costs Equity Net Income $ 200 Total $500 Total $500 Assume all variables are directly tied to sales (i.e., grow at same rate) and current relations are optimal What happens to balance sheet and income statement if sales are forecast to increase by 20% in 2009?

Income Statement 2009 Balance Sheet 2009 Sales $1,200 Assets $600 Debt $300 Costs Equity Net Income $ 240 Total $600 Total $600 Net income is $240 in 2009 But equity only increased by $50 since we assumed it grew at the same rate as sales What does this imply about dividends? The firm must have paid $190 in dividends

If firm pays no dividends, but assets still grow by 20%, what does the balance sheet look like? Since equity increased by $240, firm must have bought back $140 of debt in order for assets to grow by 20% Income Statement 2009 Balance Sheet 2009 Sales $1,200 Assets $600 Debt $110 Costs Equity Net Income $ 240 Total $600 Total $600

Percent of Sales Method
Most common technique to forecast balance sheet and income statement Begins with sales forecast expressed as an annual growth rate in sales revenues Assumes that many items on balance sheet and income statement increase proportionally with sales Forecasted value is % of forecasted sales Cash/Sales next year = Cash/Sales this year Or average of Cash/Sales for past x years Remaining items that are not directly tied to sales depend on firm’s dividend policy and its use of debt versus equity financing

(1) Forecast sales (2) Analyze historical ratios Percent of sales approach assumes costs/assets are a specified percentage of that year’s sales Calculate ratio of costs and/or assets to sales in past years and assume ratio remains constant in the future (3) Forecast income statement Note: Interest expense is function of amount of debt and interest rate, and is not assumed to be fixed percent of sales Tax rate and depreciation also not generally assumed to be fixed percent of sales

(4) Forecast balance sheet Note: Firms rarely issue common stock or preferred stock, so their forecasts are usually equal to last year’s amount Further, we usually assume that firms will not issue any new long-term debt, which often requires approval of board of directors Change in RE is function of net income and dividends paid (5) Given above forecasts, are additional funds needed? Compare forecasted assets to forecasted liabilities + equity

Current sales = $20,000,000, and are expected to grow at 10% over the next year Assets and current liabilities vary directly with sales (stay same % of sales) Profit margin = 10% Dividend payout = 50% Given this information, forecast the firm’s pro forma balance sheet Balance Sheet 2008 Current Assets $ 6,000,000 Fixed Assets 24,000,000 Total Assets $30,000,000 Current Liabilities $10,000,000 Long-Term Debt 6,000,000 Common Stock 4,000,000 Retained Earnings 10,000,000 Total Liabs & Equity

Balance Sheet 2008 % of Sales Balance Sheet 2009 Current Assets $ 6,000,000 6/20 = 30% $ 6,600,000 ($22,000,000 x 0.3) Fixed Assets 24,000,000 24/20 = 120% 26,400,000 ($22,000,000 x 1.2) Total Assets $30,000,000 30/20 = 150% $33,000,000 ($22,000,000 x 1.5) Current Liabilities $10,000,000 10/20 = 50% $11,000,000 ($22,000,000 x 0.5) Long-Term Debt 6,000,000 Constant Common Stock 4,000,000 Retained Earnings 10,000,000 11,100,000* Total Liabs & Equity $32,100,000 The firm has $33M in assets, but only $32.1M in liabilities and equity, so it needs to issue $900,000 in external funds

How to Forecast Interest Expense
Interest expense is actually based on the daily balance of debt during the year There are three ways to approximate interest expense Base it on: (1) Debt at end of year (2) Debt at beginning of year (3) Average of beginning and ending debt

Forecasting Interest Expense
(1) Base interest expense on debt at end of year Will over-estimate interest expense if debt is added throughout the year instead of all on January 1st Causes circularity called financing feedback more debt causes more interest, which reduces net income, which reduces retained earnings, which causes more debt, etc. (2) Base interest expense on beginning of year debt Will under-estimate interest expense if debt is added throughout the year instead of all on December 31st But doesn’t cause problem of circularity (3) Base interest expense on average debt Will accurately estimate interest payments if debt is added smoothly throughout year But also has problem of circularity

Forecasting Interest Expense - Solution
If calculating with calculator (by hand), base interest expense on beginning debt, but use a slightly higher interest rate Easy to implement Reasonably accurate If using Excel, the spreadsheet can solve the circularity problem, so use average debt Office 2003: Open Excel and go to: Tools Options Calculation (click on iteration) Office 2007: Click on Microsoft Office Button Excel options Formulas Calculation options (click on Enable iteration)

Additional Funds Needed (AFN)
If ratios are expected to remain constant, the following formula can be used to forecast funds needed: Where A are the assets tied directly to sales L are the liabilities tied directly to sales S0 is this year’s sales ∆S is the change in sales S1 is next year’s projected sales p is the profit margin RR is the retention ratio, or (1 – dividend payout ratio)

Additional Funds Needed (AFN)
Using the information from our previous example: Where A = $30 million (i.e., total assets) L = $10 million (i.e., current liabilities) S0 = $20 million (i.e., given) S1 = $22 million (i.e., $20 x 1.1) ∆S = $2 million (S1 – S0) p = 0.10 (i.e., given) RR = 1 – 0.5 (i.e., dividend payout ratio given)

Problems with AFN and Percent of Sales Methods
In reality, these models are too simple Costs are not always proportional to sales Assets are not always a fixed proportion of sales, etc. Economies of scale may result in the ratios changing over time as firm size increase Fixed assets may be “lumpy” and need to be added in large, discrete units Excess capacity can allow sales to grow with no increase in fixed assets Percent of sales is only a starting point Use common sense and your knowledge of the firm to think more deeply about what items might deviate from a constant proportion

What Determines Sales Growth?
Firms frequently make sales growth assumptions a part of the planning process We know, however, that the goal of management should be shareholder wealth maximization Thus, growth should not be a goal in and of itself, but a consequence of decisions that maximize NPV Otherwise, if management accepts negative NPV projects just to grow the firm, shareholders (but not necessarily managers) will be worse off!

Sustainable Growth Assumptions
(1) Assets grow in proportion to sales (2) Net income is constant proportion of sales i.e., Profit margin is constant (3) Dividend payout (d) and debt/equity ratio (DE) are fixed (4) Number of shares outstanding is fixed i.e., No new equity is issued

Under the previous assumptions, the amount by which a firm can increase sales without increasing leverage (i.e., total debt/total assets) or issuing new equity is fixed and given by: Where , , , Approximation: Where ,

Assumptions 1 and 2 hold investment policy and ROI constant Assumptions 3 and 4 hold dividend and financing policies constant The formula says that a firm’s sustainable growth depends on profit margin, asset turnover, dividend policy, and capital structure Firm cannot grow faster than ∆S/S, unless (1) Issue new equity (2) Change one of the factors in sustainable growth formula Decrease dividend payout, Increase profit margin, or ∆ capital structure

Example: Sustainable Growth
p = profit margin = 10% T = total assets/sales = 150% DE = D/E = 100% D = dividend payout = 50% If firm does not want to grow, what would it need to do? Change dividend payout to 100%!

Uses of Sustainable Growth
Bankers and credit analysts use sustainable growth formula to assess a firm’s creditworthiness If actual growth consistently exceeds sustainable growth, borrower runs the risk of “growing broke” unless it can continue to raise external funds

Calculating FCFs After-tax cash flows (ATCFs) from operations is Net Operating Income (NOI) less Taxes (tc):

To convert ATCF to FCF requires accounting for expenditures including:
P&E: plant and equipment Investments in working capital R&D expenses Advertising, etc.

Determining All the Firm’s FCFs
Necessary to determine all future FCFs Corporations have infinite life therefore infinite FCFs

Determining WACC The 4-step process to determine appropriate discount rate, or WACC, for discounting FCFs of the project (or the firm) (1) Determine firm’s optimal capital structure (2) Determine firm’s capital requirements (i.e., I) (3) Determine firm’s component costs of capital (4) Determine firm’s WACC After calculating firm’s WACC (appropriate cost of capital for firm’s average risky project), need to determine project’s WACC based on specific project risk compared to risk of firm’s average project

Financial distress, or bankruptcy, costs
M&M show that with taxes optimal capital structure is close to 100% debt However, M&M failed to consider financial distress costs and agency costs Financial distress, or bankruptcy, costs As a firm increases its proportion of debt, the interest increases because of two items The dollar amount of debt increases The risk, and therefore the interest rate, increases As interest increases, the probability of default increases and so does the costs associated with bankruptcy Legal fees, loss of asset value, decreased sales, loss of key employees, loss of trade credit, etc.

M&M’s model must be adjusted to reflect these costs:
Agency cost of debt As more debt is used to finance firm, shareholders may pressure management to undertake more risky projects Referred to as “bondholders’ wealth expropriation” Therefore, bondholders must write covenants and contracts to avoid this problem Cost of writing and enforcing these covenants and contracts are part of the agency cost of debt M&M’s model must be adjusted to reflect these costs:

Step 3: Component Costs of Capital

Step 4: WACC First, obtain component weights from optimal capital structure (Step 1) Debt % Preferred Stock % Retained Earnings % New Common Stock % Second, obtain component costs (Step 3) Third, multiply component weights with respective component costs and sum:

Determine Project’s WACC
Firm’s cost of capital defined as expected return on portfolio of all company’s projects Used to discount FCFs on projects of average risk Not the proper discount rate to use if project not average risky Each project should be evaluated at its own opportunity cost of capital True cost of capital dependent on project risk Why estimate firm’s cost of capital? Majority of projects can be treated as average risky Firm’s cost of capital good starting point

Determine Firm’s Valuation
We have… (1) Determined firm’s (or project’s) FCFs (2) Calculated firm’s (or project’s) WACC Final step is to calculate the present value of the stream of the firm’s (project’s) FCFs using WACC as the discount rate This present value is the firm’s (project’s) total valuation Subtracting market value of the firm’s debt provides price of firm’s equity

What if FCFs are Wrong? What if project’s FCFs are overestimated?
The project’s valuation will be too high Realized project returns will probably be lower than anticipated Value of firm will probably be less than projected Project may end up being a negative NPV undertaking What if project’s FCFs are underestimated? The project’s valuation will be too low The project may fail to meet benchmark or hurdle and therefore be rejected (not undertaken) Value of firm will probably not be maximized

What is WACC is Wrong? What is the project’s WACC is too low?
The valuation of the project will be too high Realized project returns will probably be lower than anticipated Value of firm will probably be less than projected Project may end up being a negative NPV undertaking What if project’s WACC is too high? The project’s valuation will be too low The project will fail to meet benchmark or hurdle and therefore be rejected (not undertaken) Value of firm will probably not be maximized

Sensitivity Analysis FCFs and WACC have a significant impact on a capital budgeting project’s valuation Both require sensitivity analysis of the base case: Increase FCF by fixed percent (e.g., 10%) and view changes in NPV Holding all else constant Increase WACC by a fixed percent (e.g., 10%) and view changes in NPV Finally, change the terminal growth rate, g, and other variables view changes in NPV (to determine key variables)

Question? What is the difference between a company’s cost of capital versus a project’s cost of capital?

Answer The company’s cost of capital is defined as the expected return on a portfolio of all the company’s existing securities (or projects) This rate is used to discount the free cash flows on average risky projects of the company This is not the proper rate to use if the project is more or less risky than the average risky project Each project should be evaluated using its own opportunity cost of capital

The Enterprise DCF Model
An General Overview

Enterprise DCF model values the entire firm And then subtracts the value of debt and preferred equity to obtain common equity value Enterprise DCF model useful in multi-business firm Value of firm is sum of values of each operating unit Enterprise DCF model values components of firm that add up to enterprise value instead of just value of equity Assists managers identify and understand separate investment and financing sources of value Helps managers pinpoint key leverage areas and aids in search for value-enhancing ideas Model can be applied consistently at various levels of aggregation

Agile Technologies, Inc.: An Example

Value of Debt and Value of Equity
The value of a company’s debt Equals the present value of cash flow to debt holders discounted at the risk-adjusted rate Discount rate used should be equal to current market rate on similar risk debt with comparable terms The value of a company’s equity Is the value of its operations plus non-operating assets e.g., Investments in unrelated, unconsolidated businesses Less value of its debt and any non-operating liabilities The value of Agile Technologies, Inc. equity Is $ million

What Drives FCF and Value?
Value is based on discounted FCFs and underlying value drivers also must be based on FCFs Two key value drivers of FCFs: ROIC: Return on Invested Capital Company that earns higher profits for every dollar invested will be worth more than similar company that earns less profit on each dollar invested Growth Rate: of company’s revenues, profits, and capital base Faster growing company will be worth more than a slower growing company if both are earning the same ROIC To increase value, company must (1) Increase level of profits it earns on existing capital (2) Ensure return on new capital investment exceeds WACC (3) Increase its growth rate, but only if ROIC exceeds WACC (4)Reduce its cost of capital

Art of Valuation Valuation is a function of:
Understanding the business (analyzing the firms) Understanding the industry (comparative analysis) Understanding the general economic environment Prudently incorporating this information into the valuation model Correct method is the easy part!

Art of Valuation Requirements of the valuation model:
Pro forma model must include complete income statement, balance sheet, and cash flow statement (which ties the first two items together!) Supporting ratios should also be included Ground pro forma model in historical analysis Complete a similar, though less detailed, analysis for competitors

The Value Creation Pyramid Sources of Value Creation
Where is Value? The Value Creation Pyramid Sources of Value Creation

Brief Mention of the Top
Financing Adding debt brings tax savings Interest is tax deductible to the firm But adding debt incurs risk Debt increases the probability of future financial distress (bankruptcy) Cost of debt depends on market risk premia Cash is King! Management’s job Manage firm so as to maximize free cash flow NPV is only as good as the forecasted cash flows Incentives to manipulate CFs in many firms explains why this is in the middle of the pyramid

Method versus Process The base of the value pyramid is process
Management factors Internal contracts creating properly aligned incentives for value creation Historically, most – if not all – of the focus in corporate finance was on method (top three cells) But consulting with CFOs makes it clear that bad process can destroy the best method! With a good process, method is (1) Not all that important, and (2) Usually optimized (i.e., it is secondary to process) Process forms the basis for value creation!

Harsh Realities Wall Street places an increasingly high premium on “transparency” The internal budgeting process affords a vehicle to: Communicate corporate expectations Characterize perceived business opportunities Define managerial ability to execute the business plan Does Wall Street’s attention to quarterly earnings targets damage long-run value creation? Some of the blame should be placed on management’s unwillingness to expand the scope of the “message space” in communications with the Street!

Real Options A dynamic focus means that when you, as a manager, make a decision, you do not act as if you are committing the firm to a locked-in stream of future cash flows Rather, you are positioning the firm to make future decisions The key is identifying the optimal reaction to future states of nature

Big Picture: Dynamic Optimization
A problem with most firms is the focus on the short-term or static optimization There is no easy way to trade-off the competing needs to induce discipline, discourage shirking, and assess talent on the one hand from inducing creativity and a long-term perspective, on the other hand

Conclusion: Some Additional Sources of Value Creation
Transparency Increase in analysts’ coverage Attracting new investors Increasing demand for the firm’s stock Improved operating performance Providing better incentives and focus Improved corporate governance Optimal board makeup, stock option awards, etc. Increase strategic flexibility Real options analysis

Two Basic Components of Discount rate

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