Introduction 1. Corporate Finance how decision making affects value. 2. Corporate finance is not a number game. 3. Focus: (a) practical issues that arise in valuation, (b) taxes, (c) incentives of different stakeholders. 1 Chapter 7 Risk, Return and the Cost of Capital Final objective: Estimating the opportunity cost of capital. Explain and calculate Expected return Security risk Diversification Portfolio risk beta. 2
Capital Budgeting Example Capital Budgeting Decision Suppose you had the opportunity to buy a tbill which would be worth $400,000 one year from today. Interest rates on tbills are a risk free 7%. What would you be willing to pay for this -$400,000 investment? PV today: 0 1 2 $400,000 / (1.07) = $373,832 3 Cost of Capital Capital Budgeting Decision
Suppose you are offered a construction deal with similar cost and payoff. An important concept in finance is that a risky dollar is worth less than a safe dollar. You are told that the risk is quantified by the cost of capital, which is 12%. NPV= -350,000+400,000/1.12 = $7,142 4 Calculating Returns Suppose you bought 100 shares of BCE one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share 100 shares). At the end of the year, the stock sells for $30. How did you do? 5 Holding Period Returns The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri:
holding period return (1 r1 ) (1 r2 ) (1 rn ) 1 6 The Future Value of an Investment of $1 in 1957: Evidence from Canada 1000 $1(1 r1957 ) (1 r1958 ) (1 r2003 ) $86.17 $42.91 $20.69 10 Common Stocks Long Bonds T-Bills 0.1 1957 1962
1967 1972 1977 1982 1987 1992 1997 2002 7 An Investment of $1 in 1900: US evidence $100,000 $10,000 Common Stock
15,578 US Govt Bonds $1,000 147 61 $100 $10 2004 $1 19 00 19 10 19 20 19 30
19 40 19 50 19 60 19 70 19 80 19 90 20 00 Dollars T-Bills Start of Year 8 An Investment of $1 in 1900: US evidence
$1,000 Real Returns 719 Equities Bonds Bills Dollars $100 $10 6.81 2.80 Start of Year 2004
19 00 19 10 19 20 19 30 19 40 19 50 19 60 19 70 19 80 19 90 20 00
$1 9 How does this relate to cost of capital? Suppose there is an investment project which you know has the same risk as Standard and Poors Composite Index. What rate should you use? 10 Rates of Return 1900-2003 Stock Market Index Returns Percentage Return 80% 60% 40% 20% 0%
-20% 1900 1920 1940 1960 1980 2000 -40% -60% Year Source: Ibbotson Associates 11 Measuring Risk Histogram of Annual Stock Market Returns
# of Years 24 24 19 20 16 10 12 3 2 50 to 60 30 to 40 20 to 30
10 to 20 0 to 10 -10 to 0 Return % -20 to -10 1 -30 to -20 1 -40 to -30 0 13 4
-50 to -40 4 12 40 to 50 8 15 12 Average Stock Returns and Risk-Free Returns The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk. One of the most significant observations of stock (and bond) market data is this longrun excess of security return over the riskfree return. The historical risk premium was 7.6% for the US.
13 Average Market Risk Premia (by country) 10.7 Italy UK 10 Japan Germany 9.3 France Ireland Australia
Canada 8.6 South Africa Spain 8.2 Sweden Switzerland Country 7.6 8.1 USA
5.9 6.6 Netherlands 5.9 6.4 Average 5.3 5.8 4.3 4.7 5.1 6.3
Belgium 11 10 9 8 7 6 5 4 3 2 1 0 Denmark Risk premium, % 14 Measuring Risk
Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation Square root of variance. A measure of volatility. 15 Return Statistics The history of capital market returns can be summarized by describing the average return ( R1 RT ) R T the standard deviation of those returns ( R1 R) 2 ( R2 R) 2 ( RT R) 2 SD VAR T1 16 Canada Returns, 1957-2003 Average
Investment Canadian common stocks Annual Return 10.64% Standard Deviation Distribution 16.41% Long Bonds 8.96 10.36
Treasury Bills 6.80 4.11 Inflation 4.29 3.63 60% 0% 17 + 60% Risk Statistics There is no universally agreed-upon definition of risk. A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
18 Historically Are Returns Normal? S&P 500 Return Frequencies 16 Normal approximation Mean = 12.8% Std. Dev. = 20.4% 16 12 12 12 11 10
9 8 6 5 Return frequency 14 4 2 1 1 2 2 1
0 -58% -48% -38% -28% -18% 0 -8% 2% 12% Annual returns 22% 32% 42% 52% 62%
0 19 Expected Return, Variance, and covariance Rate of Return Scenario Probability Stock fund Bond fund Recession 33.3% -7% 17% Normal 33.3% 12% 7% Boom 33.3% 28% -3% Consider the following two risky asset worlds. There is a 1/3 chance of each state of the economy and the only assets are a stock fund
and a bond fund. 20 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28%
2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% 21 The Return for Portfolios Scenario
Recession Normal Boom Expected return Variance Standard Deviation Rate of Return Stock fund Bond fund Portfolio -7% 17% 5.0% 12% 7% 9.5% 28% -3% 12.5% 11.00% 0.0205 14.31% 7.00%
0.0067 8.16% squared deviation 0.160% 0.003% 0.123% 9.0% 0.0010 3.08% The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio. E (rP ) wB E (rB ) wS E (rS ) 22 The Variance of a Portfolio Scenario Recession
Normal Boom Expected return Variance Standard Deviation Rate of Return Stock fund Bond fund Portfolio -7% 17% 5.0% 12% 7% 9.5% 28% -3% 12.5% 11.00% 0.0205 14.31% 7.00% 0.0067
8.16% squared deviation 0.160% 0.003% 0.123% 9.0% 0.0010 3.08% 23 Portfolio Risk 1 2 3 STOCK To calculate portfolio variance add
up the boxes 4 5 6 N 1 2 3 4 5 6 STOCK N 24
Diversification The variance (risk) of the securitys return can be broken down into: Systematic (Market) Risk Unsystematic (diversifiable) Risk The Effect of Diversification: unsystematic risk will significantly diminish in large portfolios systematic risk is not affected by diversification since it affects all securities in any large portfolio 25 Portfolio Risk as a Function of the Number of Stocks in the Portfolio 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 Thus diversification can eliminate some, but not all of the risk of individual securities. 26 Beta and Unique Risk 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes Expected stock return beta -10% +10% -10%
+10% -10% Copyright 1996 by The McGraw-Hill Companies, Ic Expected market return 27 Beta and Unique Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stocks return to the return on the market portfolio. 28
Definition of Risk When Investors Hold the Market Portfolio Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta ()of the security. Beta measures the responsiveness of a security to movements in the market portfolio. i Cov( Ri , RM ) 2 ( RM ) 29 Chapter 8 Risk and Return Markowitz Portfolio Theory Risk and Return Relationship Validity and the Role of the CAPM 30
Markowitz Portfolio Theory Given a certain level of risk, investors prefer stocks with higher returns. Given a certain level of return, investors prefer less risk. By combining stocks into a portfolio, one can achieve different combinations of return & standard deviation. Correlation coefficients are crucial for ability to reduce risk in portfolio. 31 Markowitz Portfolio Theory Expected Returns and Standard Deviations vary given different weighted combinations of the stocks Expected Return (%) Coca Cola 40% in Coca Cola Exxon Mobil Standard Deviation
32 Efficient Frontier Example Stocks ABC Corp Big Corp 28 42 Correlation Coefficient = .4 % of Portfolio Avg Return 60% 15% 40% 21% 33 Efficient Frontier
Each half egg shell represents the possible weighted combinations for two stocks. The composite of all stock sets constitutes the efficient frontier Expected Return (%) Standard Deviation 34 Efficient Frontier Example Stocks Return ABC Corp Big Corp 28 42 Portfolio 28.1
Correlation Coefficient = .4 % of Portfolio Avg 60% 40% 15% 21% 17.4% Lets Add stock New Corp to the portfolio 35 Efficient Frontier Example Stocks Portfolio New Corp
28.1 30 New Portfolio 23.43 Correlation Coefficient = .3 % of Portfolio Avg Return 50% 17.4% 50% 19% 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION 36 Efficient Frontier Return
B AB A Risk 37 Efficient Frontier Return AB A N B Risk 38 Efficient Frontier Return ABN AB
A N B Risk 39 return 2-Security Portfolios - Various Correlations 100% stocks = -1.0 100% bonds = 1.0 = 0.2
40 return Efficient Frontier c effi ie t i er n o r nt f minimum variance portfolio Individual Assets
P 41 return Riskless Borrowing and Lending CM L 100% stocks Balanced fund rf 100% bonds
Now investors can allocate their money across the T-bills and a balanced mutual fund 42 return Market Equilibrium: CAPM CM L efficient frontier M rf P 43 return Changes in Riskfree Rate
L 0 CML 1 CM 100% stocks 1 f 0 f r r First Optimal Risky Portfolio Second Optimal Risky Portfolio 100% bonds
44 Security Market Line Return Market Return = rm . Efficient Portfolio Risk Free Return = rf 1.0 BETA
45 Security Market Line Return SML rf 1.0 BETA SML Equation = rf + B ( rm - rf ) 46 Expected return Risk & Expected Return 13.5% 3% 1.5
i 1.5 RF 3% R M 10% R i 3% 1.5 (10% 3%) 13.5% 47 Security Returns Estimating with regression ne i L c i is t r te c
ra a Ch Slope = i Return on market % Ri = i + i Rm + e i 48 Estimates of Beta for Selected Stocks Stock Research in Motion Nortel Networks Bank of Nova Scotia Bombardier Investors Group. Maple Leaf Foods Roger Communications Beta
3.04 3.61 0.28 1.48 0.36 0.25 1.17 Canadian Utilities TransCanada Power 0.08 0.08 49 CAPM versus Reality 1. Do investors care about mean and variance? 2. Is there a security that is risk-free? 3. Short selling? 4. Transaction costs? 5. Most important: homogeneous
expectations? 50 Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-2002 30 20 SML Investors 10 Market Portfolio 0 1.0
Portfolio Beta 51 Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-65 SML 30 20 Investors Market Portfolio 10 0
1.0 Portfolio Beta 52 Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1966-2002 30 20 SML Investors 10 Market Portfolio
0 1.0 Portfolio Beta 53 Chapter 9 (part 1) Capital Budgeting and Risk Firm with excess cash Pay cash dividend Shareholder invests in financial asset A firm with excess cash can either pay a dividend or make a capital investment Invest in project
Shareholders Terminal Value Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk. 54 Company Cost of Capital A firms value can be stated as the sum of the value of its various assets Firm value PV(AB) PV(A) PV(B) 55 Company Cost of Capital Category Speculative Ventures Discount Rate
30% New products Expansion of existing business 20% 15% (Company COC) Cost improvement, known technology 10% 56 Company Cost of Capital simple approach Company Cost of Capital (COC) is based on the average beta of the assets The average Beta of the assets is based on the % of funds in each asset Example 1/3 New Ventures B=2.0 1/3 Expand existing business B=1.3 1/3 Plant efficiency B=0.6
AVG B of assets = 1.3 57 Company Cost of Capital If the firm is all equity financed, A companys cost of capital can be compared to the CAPM required return SML Required return 13 Company Cost of Capital 5.5 0 1.26 Project Beta
58 Example Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100-percent equity financed. Assume a risk-free rate of 5-percent and a market risk premium of 10-percent. What is the appropriate discount rate for an expansion of this firm? 59 Example (continued) Suppose Stansfield Enterprises is evaluating the following nonmutually exclusive projects. Each costs $100 and lasts one year. Project Project IRR
NPV at 30% 2.5 Projects Estimated Cash Flows Next Year $150 A 50% $15.38 B 2.5 $130
30% $0 C 2.5 $110 10% -$15.38 60 IRR Project Using the SML to Estimate the RiskAdjusted Discount Rate for Projects Good A projects
30% B 5% C SML Bad projects Firms risk (beta) 2.5 61 Capital Structure Capital Structure - the mix of debt & equity within a company Expand CAPM to include CS (common shares) R = r f + B ( r m - rf )
becomes Requity = rf + B ( rm - rf ) 62 Capital Structure & COC (company cost of capital) COC = rportfolio = rassets rassets = rdebt (D) + requity (E) (V) (V) Bassets = Bdebt (D) + Bequity (E) (V) requity = rf + Bequity ( rm - rf ) (V) IMPORTANT E, D, and V are all market values 63
Capital Structure & COC Expected return (%) Expected Returns and Betas prior to refinancing 20 Requity=15 Rassets=12.2 Rrdebt=8 0 0 0.2 0.8 Bdebt Bassets
1.2 Bequity 64 The Firm versus the Project Suppose the Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%, the market risk premium is 10%, and the firms beta is 1.3. 17% = 4% + 1.3 [14% 4%] This is a breakdown of the companys investment projects: 1/3 Automotive retailer = 2.0 1/3 Computer Hard Drive Mfr. = 1.3 1/3 Electric Utility = 0.6 average of assets = 1.3 When evaluating a new electrical generation investment, which cost of capital should be used? 65
SML IRR Project Capital Budgeting & Project Risk 24% Investments in hard drives or auto retailing should have higher discount rates. 17% 10% Firms risk (beta) 0.6 1.3
2.0 r = 4% + 0.6(14% 4% ) = 10% 10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project. 66 Project IRR Capital Budgeting & Project Risk The SML can tell us why: Hurdle rate SML Incorrectly accepted negative NPV projects RF FIRM ( R M RF )
Incorrectly rejected positive NPV projects Firms risk (beta) rf FIRM 67 Measuring Betas Theoretically, the calculation of beta is straightforward: Cov( Ri , RM ) im 2 Var ( RM ) M Problem 1: Betas may vary over time. 68 Measuring Betas
Dell Computer Price data: May 91- Nov 97 R2 = .10 B = 1.87 Slope determined from plotting the line of best fit. 69 Measuring Betas Dell Computer Price data: Dec 97 - Apr 04 R2 = .27 B = 1.61 Slope determined from plotting the line of best fit. 70 Measuring Betas General Motors
Price data: May 91- Nov 97 R2 = .07 B = 0.72 Slope determined from plotting the line of best fit. 71 Measuring Betas General Motors R2 = .29 GM return (%) Price data: Dec 97 - Apr 04 B = 1.21 Slope determined from plotting the line of best fit. 72
Estimated Betas Beta Burlington Northern & Santa Fe CSX Transportation Norfolk Southern Union Pacific Corp Industry portfolio equity 0.53 0.58 0.47 0.47 0.49 Standard Error 0.2 0.23
0.28 0.19 0.18 73 Beta Stability RISK CLASS % IN SAME CLASS 5 YEARS LATER % WITHIN ONE CLASS 5 YEARS LATER 10 (High betas) 35 69
9 18 54 8 16 45 7 13 41 6 14
39 5 14 42 4 13 40 3 16 45 2 21
61 1 (Low betas) 40 62 Source: Sharpe and Cooper (1972) 74 Using an Industry Beta It is frequently argued that one can better estimate a firms beta by involving the whole industry. If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta. If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firms beta.
75 Problems with Industry Beta One must make sure that the firm is comparable to other industry both in its operation and its financing. Question: Consider Grand Sport, Inc., which is currently allequity and has a beta of 0.90. The firm has decided to lever up to a capital structure of 50% debt and 50% equity. Since the firm will remain in the same industry, its asset beta should remain 0.90. Assuming a zero beta for its debt, what should the equity beta be? 76 Beware of Fudge Factors Common practice to make adjustments to discount rate to offset worries. Example: 1) A new drug wont get FDA approval and wont be able to go on the market. 2) Unexpected weather condition would hurt the
crop. 77 Determinants of Beta Business Risk Cyclicality of Revenues Operating Leverage Financial Risk Financial Leverage 78 Cyclicality of Revenues Highly cyclical stocks have high betas. Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle. Transportation firms and utilities are less dependent upon the business cycle. 79
Operating Leverage The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs. Operating leverage increases as fixed costs rise and variable costs fall. Operating leverage magnifies the effect of cyclicality on beta. The degree of operating leverage is given by: Change in EBIT Sales DOL EBIT Change in Sales 80 Operating Leverage $
Total costs EBIT Fixed costs Volume Fixed costs Volume Operating leverage increases as fixed costs rise and variable costs fall. 81 Chapter 9: Q5 The following table shows estimates of the risk of two well-known Canadian Stocks STD R^2
Beta STD Beta Alcan 24 0.15 0.69 0.21 Inco 29 0.22 1.04 0.26
a. What proportion was market risk, and what proportion unique risk? b. What is the variance of market and unique variance of each stock? c. What is the confidence level of the Incos beta? d. What is expected return of Alcn if Rf=5% and market return=12%? e. Suppose next year the market provides a zero return. What return to you expect for each stock? 82 Chapter 9: Q9 You run a perpetual encabulator machine, which generates revenues averaging $20 million per year. Raw material costs are 50 percent of revenues. These costs are variable they are always proportional to revenues. There are no other operating costs. The cost of capital is 9 percent. Your firms long-term borrowing rate is 6 percent. Now you are approached by Studebaker Capital Corp., which proposes a fixed-price contract to supply raw materials at $10 million per year for 10 years. a. What happens to the operating leverage and
business risk of the encabulator machine if you agree to this fixed-price contact? b. Calculate the present value of the encabulator machine with and without the fixed-price contract? 83 Chapter 9 (part 2) Capital Budgeting and Risk Ct CEQt PV t t (1 r ) (1 rf ) 84 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil
for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project? 85 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project? r rf B ( rm rf ) 6 .75(8) 12% Year 1 2 3 Project A Cash Flow PV @ 12%
100 89.3 100 79.7 100 71.2 Total PV 240.2 86 Risk,DCF and CEQ Example Project B cash flow is 94.6, 89.6, 84.8 in year 1-3 respectively. However, these cash flows are RISK FREE. What is Projects B PV? Year 1 2 3 Project A Cash Flow PV @ 12%
100 89.3 100 79.7 100 71.2 Total PV 240.2 Year Project B Cash Flow PV @ 6% 1 94.6 89.3 2 3
89.6 84.8 79.7 71.2 Total PV 240.2 87 Risk,DCF and CEQ Year 1 2 3 Project A Cash Flow PV @ 12% 100 89.3 100
79.7 100 71.2 Total PV 240.2 Year 1 2 3 Project B Cash Flow PV @ 6% 94.6 89.3 89.6 79.7 84.8 71.2 Total PV 240.2 Since the 94.6 is risk free, we call it a Certainty Equivalent
of the 100. 88 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? The difference between the 100 and the certainty equivalent (94.6) is 5.7%this % can be considered the annual premium on a risky cash flow Risky cash flow certainty equivalent cash flow 1.057 89 Long lived assets and discount rates Example (from text): The scientists at Vegetron have come up with an electric mop and are ready to go ahead with pilot
production. The preliminary phase will take one year and costs $125k. Management feels that there is only a 50% chance that the pilot production will be successful. If the project fails, the project will be dropped. If the project succeeds Vegetron will build a $1million plant that would generate an expected annual cash flow in perpetuity of $250k. Rf=7%, Risk Premium=9%. Regular projects of the firm have a beta of 0.33, however due to the 50% probability of failure management assumes a beta of 2 for the project. 1. What is NPV? 2. Is management correct about its approach for the NPV calculation? 90 International Projects Investment projects abroad may be safer than similar domestic investments. Remember: Beta measures risk relative to investors portfolio (a good question would be to ask who is the investor of the company?) Not clear why home bias persists so
strongly (perhaps information, transaction costs, etc.) 91 What is Liquidity? The idea that the expected return on a stock and the firms cost of capital are positively related to risk is fundamental. Recently a number of academics have argued that the expected return on a stock and the firms cost of capital are negatively related to the liquidity of the firms shares as well. The trading costs of holding a firms shares include brokerage fees, the bid-ask spread, and market impact costs. 92 Liquidity, Expected Returns, and the Cost of Capital The cost of trading an illiquid stock reduces the total return that an investor receives. Investors thus will demand a high expected return when investing in stocks with high trading
costs. This high expected return implies a high cost of capital to the firm. 93 Cost of Capital Liquidity and the Cost of Capital Liquidity An increase in liquidity, i.e., a reduction in trading costs, lowers a firms cost of capital. 94 Liquidity and Adverse Selection There are a number of factors that determine the liquidity of a stock. One of these factors is adverse selection. This refers to the notion that traders with better information can take advantage of specialists and other traders who have less information.
The greater the heterogeneity of information, the wider the bid-ask spreads, and the higher the required return on equity. 95 What the Corporation Can Do The corporation has an incentive to lower trading costs since this would result in a lower cost of capital. A stock split would increase the liquidity of the shares. A stock split would also reduce the adverse selection costs thereby lowering bid-ask spreads. This idea is a new one and empirical evidence is not yet in. 96 What the Corporation Can Do Companies can also facilitate stock purchases through the Internet. Direct stock purchase plans and dividend reinvestment plans handled on-line allow small investors the opportunity to buy securities
cheaply. The companies can also disclose more information, especially to security analysts, to narrow the gap between informed and uninformed traders. This should reduce spreads. 97 Summary and Conclusions The expected return on any capital budgeting project should be at least as great as the expected return on a financial asset of comparable risk. Otherwise the shareholders would prefer the firm to pay a dividend. The expected return on any asset is dependent upon . A projects required return depends on the projects . A projects can be estimated by considering comparable industries or the cyclicality of project revenues and the projects operating and financial leverage. 98
Jones Family Mini-Case Executive summary: The wildcat oil well is going to cost $5 million. The Jones geologists says theres only 30% chance of a dry hole. If oil is found, the expectation is for 300 barrels of crude oil per day (at a price of $25 per barrel) Sales will start next year. Production and shipping costs are $10 per barrel (Mr. Jones argues that they are fixed). Production will start declining at 5% every year. Oil prices expected to grow at 2.5% per year, and pumping will continue for 15 years. The interest rate is 6%, the beta is 0.8, and the risk premium is 7%. 99 Chapter 10: Decision Trees A fundamental problem in NPV analysis is dealing with uncertain future outcomes. There is usually a sequence of decisions in NPV project analysis. Decision trees are used to identify the sequential decisions in NPV analysis.
Decision trees allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions. This graphical representation helps to identify the best course of action. 100 Example of Decision Tree Open circles represent decisions to be made. A Pay wizard $1000? Study finance B Filled circles represent receipt of information e.g., a test score in this
class. C Do not study The lines leading away D from the circles represent the alternatives. F 101 Stewart Pharmaceuticals The Stewart Pharmaceuticals Corporation is considering investing in developing a drug that cures the common cold. A corporate planning group, including representatives from production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase. This preliminary phase will last one year and cost $1 billion. Furthermore, the group believes that there is a 60% chance that tests will prove successful. If the initial tests are successful, Stewart Pharmaceuticals
can go ahead with full-scale production. This investment phase will cost $1,600 million. Production will occur over the next four years. 102 Stewart Pharmaceuticals NPV of Full-Scale Production following Successful Test Investment Year 1 Years 2-5 Revenues $7,000 Variable Costs (3,000) Fixed Costs
(1,800) Depreciation (400) Pretax profit $1,800 Tax (34%) (612) Net Profit Cash Flow $1,188 -$1,600 $1,588 4
$1,588 NPV $1,600 $3,433.75 t t 1 (1.10) Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. 103 Stewart Pharmaceuticals NPV of Full-Scale Production following Unsuccessful Test Investment Year 1 Years 2-5 Revenues $4,050
Variable Costs (1,735) Fixed Costs (1,800) Depreciation (400) Pretax profit $115 Tax (34%) (39.10) Net Profit $75.90
Cash Flow -$1,600 $475 4 $475.90 NPV $1,600 $91.461 t t 1 (1.10) Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. 104 Decision Tree for Stewart Pharmaceutical The firm has two decisions to make: To test or not to test. To invest or not to invest. Success
Test Invest NPV $3,433.75m Do not invest NPV = $0 Failure Do not test NPV $91.461m NPV $0 Invest 105
Stewart Pharmaceutical: Decision to Test Lets move back to the first stage, where the decision boils down to the simple question: should we invest? The expected payoff evaluated at date 1 is: Expected Prob. Payoff Payoff Prob. payoff sucess given success failure given failure Expected .60 $3,433.75 .40 $0 $2,060.25 payoff The NPV evaluated at date 0 is: NPV $1,000
$2,060.25 $872.95 1.10 So we should test. 106 Real Options One of the fundamental insights of modern finance theory is that options have value. The phrase We are out of options is surely a sign of trouble. Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation. 107 Options The Option to Expand Static analysis implicitly assumes that the scale of the project is fixed. If we find a positive NPV project, we should consider the
possibility of expanding the project to get a larger NPV. For example,the option to expand has value if demand turns out to be higher than expected. All other things being equal, we underestimate NPV if we ignore the option to expand. The Option to Delay Has value if the underlying variables are changing with a favourable trend. 108 The Option to Expand: Example Imagine a start-up firm, Campusteria, Inc. which plans to open private (for-profit) dining clubs on university campuses. The test market will be your campus, and if the concept proves successful, expansion will follow nationwide. Nationwide expansion, if it occurs, will occur in year four. The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus). 109
Campusteria pro forma Income Statement Investment Year 0 Revenues Years 1-4 $60,000 Variable Costs ($42,000) Fixed Costs ($18,000) Depreciation ($7,500)
Pretax profit ($7,500) Tax shield 34% $2,550 Net Profit Cash Flow $4,950 $30,000 4 $2,550 $2,550 NPV $30,000 $21,916.84 t t 1 (1.10)
We plan to sell 25 meal plans at $200 per month with a 12-month contract. Variable costs are projected to be $3,500 per month. Fixed costs (the lease payment) are projected to be $1,500 per month. We can depreciate (straight line) our capitalized leaseholder improvements. 110 The Option to Expand: Valuing a Start-Up Note that while the Campusteria test site has a negative NPV, its negativity is relatively small. If we expand, we project opening 20 Campusterias in year four and the size of the project may grow 20 folds. The value of the project is in the option to expand. If we hit it big, we will be in a position to score large.
We wont know if this has value if we do not try. Thus, it seems that we may want to take on this test project and see what it delivers. 111 Discounted Cash Flows and Options We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M = NPV + Opt A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options. 112 The Option to Abandon: Example The option to abandon a project has value if demand
turns out to be lower than expected. Suppose that we are drilling an oil well. The drilling rig costs $300 today and in one year the well is either a success or a failure. The outcomes are equally likely. The discount rate is 10%. The PV of the successful payoff at time one is $575. The PV of the unsuccessful payoff at time one is $0. 113 The Option to Abandon: Example (continued) Traditional NPV analysis would indicate rejection of the project. Expected = Prob. Successful + Prob. Failure Payoff Success Payoff Failure Payoff Expected = (0.50$575) + (0.50$0) = $287.50 Payoff NPV = $300 +
$287.50 = $38.64 1.10 114 The Option to Abandon: Example Traditional NPV analysis overlooks the option to abandon. Success: PV = $575 Sit on rig; stare at empty hole: PV = $0. Drill $300 Failure Do not drill NPV $0 Sell the rig;
salvage value = $250 The firm has two decisions to make: drill or not, abandon or115 stay. The Option to Abandon: Example (continued) When we include the value of the option to abandon, the drilling project should proceed: Expected = Prob. Successful + Prob. Failure Payoff Success Payoff Failure Payoff Expected = (0.50$575) + (0.50$250) = $412.50 Payoff NPV = $300 + $412.50 = $75.00 1.10
116 Valuation of the Option to Abandon Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M NPV Opt $75.00 38.64 Opt $75.00 38.64 Opt Opt $113.64 117 The Option to Delay: Example Year 0 1 2 3 44 Cost $ 20,000
$ 18,000 $ 17,100 $ 16,929 16,760 $$ 16,760 PV $ 25,000 $ 25,000 $ 25,000 $ 25,000 25,000 $$ 25,000 NPV tt $ 5,000 $ 7,000 $ 7,900 $ 8,071 8,240 $$8,240 NPV 0
$ 5,000 $ 6,364 $7,900 $ 6,529 $6,529 (1.10) 2 $ 6,064 $ 5,628 Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remain constant at $25,000, but since costs are declining the NPV at the time of launch steadily rises. The best time to launch the project is in year 2this schedule yields the highest NPV when judged today. 118 Option issues to consider Things to remember in these types of analysis: Cost of the testing Expected future cash flows given the outcome of the test Probability of success of the testing
Discount rate 119
Autonomy, Empowerment, and Protection: responding lawfully to unwise
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