Introduction to Finance Summary Inhaltsverzeichnis SW1: FINANCIAL DECISION MAKING AND THE LAW OF ONE PRICE .................................................. 7 NET PRESENT VALUE (NPV) .................................................................................................................. 8 ARBITRAGE AND THE LAW OF ONE PRICE ................................................................................................... 9 NO-ARBITRAGE, SECURITY PRICES & IDENTIFYING ARBITRAGE OPPORTUNITIES ........................................................ 9 NPV OF TRADING SECURITIES....................................................................................................................... 10 SEPARATION PRINCIPLE ............................................................................................................................... 10 SW2: TIME VALUE OF MONEY ....................................................................................................... 10 THE TIMELINE ................................................................................................................................... 10 THREE RULES OF TIME TRAVEL.............................................................................................................. 10 RULE 1: COMPARING AND COMBINING VALUES .............................................................................................. 11 RULE 2: MOVING CASHFLOWS FORWARD IN TIME ........................................................................................... 11 RULE 3: MOVING CASHFLOWS BACK IN TIME .................................................................................................. 11 VALUING A STREAM OF CASHFLOWS ............................................................................................................. 12 PERPETUITIES AND ANNUITIES .............................................................................................................. 12 PERPETUITIES ............................................................................................................................................ 12 ANNUITIES ............................................................................................................................................... 12 PRESENT VALUE OF AN ANNUITY .................................................................................................................. 12 FUTURE VALUE OF AN ANNUITY ................................................................................................................... 12 GROWING ANNUITY ................................................................................................................................... 13 SOLVING FOR CASH PAYMENTS ............................................................................................................. 13 INTERNAL RATE OF RETURN ................................................................................................................. 13 SW3: INVESTMENT DECISION RULES .............................................................................................. 14 NPV AND STAND-ALONE PROJECTS ....................................................................................................... 14 ALTERNATIVE RULES VS THE NPV RULE ......................................................................................................... 14 INTERNAL RATE OF RETURN (IRR) RULE ................................................................................................. 14 PITFALL 1: DELAYED INVESTMENTS ............................................................................................................... 15 PITFALL 2: MULTIPLE IRRS .......................................................................................................................... 15 PITFALL 3: NONEXISTENT IRR ...................................................................................................................... 16 IRR VERSUS THE IRR RULE .......................................................................................................................... 16 PAYBACK RULE.................................................................................................................................. 16 CHOOSING BETWEEN PROJECTS ............................................................................................................ 16 INCREMENTAL IRR RULE ..................................................................................................................... 17 PROFITABILITY INDEX.......................................................................................................................... 17 SW4: VALUING STOCKS ................................................................................................................. 18 DIVIDEND-DISCOUNT MODEL............................................................................................................... 18 TOTAL RETURN ................................................................................................................................. 18 1 DIVIDEND-DISCOUNT MODEL EQUATION ................................................................................................ 19 DIVIDENDS VS INVESTMENT AND GROWTH.............................................................................................. 19 PROFITABLE GROWTH ................................................................................................................................ 20 CHANGING GROWTHRATES .................................................................................................................. 21 LIMITATIONS OF THE DIVIDEND-DISCOUNT MODEL ......................................................................................... 21 TOTAL PAYOUT AND FREE CASH FLOW VALUATION MODELS....................................................................... 21 DISCOUNTED FREE CASH FLOW MODEL .................................................................................................. 22 CONNECTION TO CAPITAL BUDGETING .......................................................................................................... 23 COMPARISON OF DISCOUNTED CASH FLOW MODELS OF STOCK VALUATION ........................................................ 23 VALUATION BASED ON COMPARABLE FIRMS ........................................................................................... 24 VALUATION MULTIPLES .............................................................................................................................. 24 LIMITATIONS OF MULTIPLES ........................................................................................................................ 25 COMPARISON WITH DISCOUNTED CASH FLOW METHODS................................................................................. 25 STOCK VALUATION TECHNIQUES: THE FINAL WORD .................................................................................. 25 INFORMATION IN STOCK PRICES ............................................................................................................ 25 COMPETITION AND EFFICIENT MARKETS ................................................................................................. 25 EFFICIENT MARKETS HYPOTHESIS ................................................................................................................. 25 PUBLIC, EASILY INTERPRETABLE INFORMATION ............................................................................................... 25 PRIVATE OR DIFFICULT-TO-INTERPRET INFORMATION ...................................................................................... 26 LESSONS FOR INVESTORS AND CORPORATE MANAGERS ............................................................................. 26 CONSEQUENCES FOR INVESTORS .................................................................................................................. 26 SW5: CAPITAL MARKETS AND THE PRICING OF RISK ...................................................................... 26 COMMON MEASURES OF RISK AND RETURN............................................................................................ 27 PROBABILITY DISTRIBUTIONS ........................................................................................................................ 27 EXPECTED RETURN..................................................................................................................................... 27 VARIANCE ................................................................................................................................................ 27 STANDARD DEVIATION ............................................................................................................................... 27 HISTORICAL RETURNS OF STOCKS AND BONDS ......................................................................................... 27 REALIZED RETURN ..................................................................................................................................... 27 AVERAGE ANNUAL RETURN ................................................................................................................. 28 VARIANCE AND VOLATILITY OF RETURNS ........................................................................................................ 28 ESTIMATION ERROR: USING PAST RETURNS TO PREDICT THE FUTURE ........................................................... 29 RETURNS OF INDIVIDUAL STOCKS .......................................................................................................... 29 COMMON VERSUS INDEPENDENT RISK ................................................................................................... 29 DIVERSIFICATION IN STOCK PORTFOLIOS ........................................................................................................ 29 TYPE S VS TYPE I ........................................................................................................................................ 30 NO ARBITRAGE AND THE RISK PREMIUM ................................................................................................ 30 MEASURING SYSTEMATIC RISK ............................................................................................................. 30 SENSITIVITY TO SYSTEMATIC RISK: BETA (Β) ................................................................................................... 31 BETA AND THE COST OF CAPITAL .................................................................................................................. 31 SW6: OPTIMAL PORTFOLIO CHOICE AND THE CAPITAL ASSET PRICING MODEL .............................. 32 THE EXPECTED RETURN OF A PORTFOLIO ................................................................................................ 32 VOLATILITY OF A TWO-STOCK PORTFOLIO ............................................................................................... 33 COMBINING RISKS ..................................................................................................................................... 33 DETERMINING COVARIANCE AND CORRELATION ....................................................................................... 33 COVARIANCE ............................................................................................................................................ 33 CORRELATION ........................................................................................................................................... 33 2 COMPUTING A PORTFOLIO’S VARIANCE AND VOLATILITY .................................................................................. 34 VOLATILITY OF A LARGE PORTFOLIO .............................................................................................................. 34 DIVERSIFICATION WITH AN EQUALLY WEIGHTED PORTFOLIO ............................................................................. 35 CHOOSING AN EFFICIENT PORTFOLIO ..................................................................................................... 35 EFFECT OF CORRELATION ..................................................................................................................... 36 SHORT SALES ............................................................................................................................................ 36 EFFICIENT PORTFOLIOS WITH MANY STOCKS ........................................................................................... 37 RISK VERSUS RETURN: MANY STOCKS ........................................................................................................... 37 IDENTIFYING THE TANGENT PORTFOLIO ......................................................................................................... 38 REQUIRED RETURNS ................................................................................................................................... 38 CAPM ASSUMPTIONS ........................................................................................................................ 39 OPTIMAL INVESTING: THE CAPITAL MARKET LINE............................................................................................ 39 DETERMINING THE RISK PREMIUM ............................................................................................................... 40 SECURITY MARKET LINE ...................................................................................................................... 40 BETA OF A PORTFOLIO ................................................................................................................................ 40 SW7: ESTIMATING THE COST OF CAPITAL ...................................................................................... 41 EQUITY COST OF CAPITAL .................................................................................................................... 41 MARKET PORTFOLIO .......................................................................................................................... 41 CONSTRUCTING THE MARKET PORTFOLIO ....................................................................................................... 41 VALUE-WEIGHTED PORTFOLIO..................................................................................................................... 41 MARKET INDEXES ...................................................................................................................................... 41 INVESTING IN A MARKET INDEX .................................................................................................................... 42 MARKET RISK PREMIUM ..................................................................................................................... 42 DETERMINING THE RISK-FREE RATE .............................................................................................................. 42 THE HISTORICAL RISK PREMIUM................................................................................................................... 42 A FUNDAMENTAL APPROACH ...................................................................................................................... 42 BETA ESTIMATION ............................................................................................................................. 42 ESTIMATING BETA FROM HISTORICAL RETURNS .............................................................................................. 42 LINEAR REGRESSION ........................................................................................................................... 43 DEBT COST OF CAPITAL ....................................................................................................................... 43 DEBT YIELDS VERSUS RETURNS .................................................................................................................... 43 ANNUAL DEFAULT RATES BY DEBT RATING..................................................................................................... 44 AVERAGE DEBT BETAS BY RATING AND MATURITY .......................................................................................... 44 A PROJECT’S COST OF CAPITAL ............................................................................................................. 44 ALL-EQUITY COMPARABLES.......................................................................................................................... 44 LEVERED FIRMS AS COMPARABLES ................................................................................................................ 45 ASSET (UNLEVERED) COST OF CAPITAL ........................................................................................................... 45 ASSET (UNLEVERED) BETA ........................................................................................................................... 45 INDUSTRY ASSET BETAS .............................................................................................................................. 45 PROJECT RISK CHARACTERISTICS AND FINANCING ..................................................................................... 46 FINANCING AND THE WEIGHTED AVERAGE COST OF CAPITAL ............................................................................ 46 THE WEIGHTED AVERAGE COST OF CAPITAL ................................................................................................... 46 FINAL THOUGHTS ON USING THE CAPM ................................................................................................ 47 SW8: CAPITAL STRUCTURE ............................................................................................................ 48 FINANCING A FIRM WITH EQUITY .......................................................................................................... 48 FINANCING A FIRM WITH DEBT AND EQUITY ............................................................................................ 49 THE EFFECT OF LEVERAGE ON RISK AND RETURN ............................................................................................. 49 3 SUMMARY ................................................................................................................................................ 50 MODIGLIANI-MILLER I: LEVERAGE, ARBITRAGE, AND FIRM VALUE ............................................................... 51 MM AND THE LAW OF ONE PRICE ................................................................................................................ 51 HOMEMADE LEVERAGE .............................................................................................................................. 51 THE MARKET VALUE BALANCE SHEET..................................................................................................... 52 APPLICATION: A LEVERAGED RECAPITALIZATION ...................................................................................... 53 MODIGLIANI-MILLER II: LEVERAGE, RISK, AND THE COST OF CAPITAL ........................................................... 53 LEVERAGE AND THE EQUITY COST OF CAPITAL ................................................................................................ 53 MM PROPOSITION II: ................................................................................................................................ 54 CAPITAL BUDGETING AND THE WEIGHTED AVERAGE COST OF CAPITAL .......................................................... 54 WACC AND LEVERAGE WITH PERFECT CAPITAL MARKETS ................................................................................ 55 LEVERED AND UNLEVERED BETAS .......................................................................................................... 55 CAPITAL STRUCTURE FALLACIES ............................................................................................................ 56 LEVERAGE AND EARNINGS PER SHARE ........................................................................................................... 56 EQUITY ISSUANCES AND DILUTION......................................................................................................... 56 MM: BEYOND THE PROPOSITIONS ........................................................................................................ 57 CONSERVATION OF VALUE PRINCIPLE FOR FINANCIAL MARKETS......................................................................... 57 SW9: PAYOUT POLICY .................................................................................................................... 57 DISTRIBUTION TO SHAREHOLDERS ......................................................................................................... 57 DIVIDENDS ....................................................................................................................................... 58 SHARE REPURCHASES .......................................................................................................................... 58 COMPARISON OF DIVIDENDS AND SHARE REPURCHASES ............................................................................ 59 ALTERNATIVE POLICY 1: PAY DIVIDEND WITH EXCESS CASH .............................................................................. 59 ALTERNATIVE POLICY 2: SHARE REPURCHASE (NO DIVIDEND) ........................................................................... 59 ALTERNATIVE POLICY 3: HIGH DIVIDEND (EQUITY ISSUE) .................................................................................. 60 MODIGLIANI–MILLER AND DIVIDEND POLICY IRRELEVANCE .............................................................................. 61 THE TAX DISADVANTAGE OF DIVIDENDS ................................................................................................. 61 TAXES ON DIVIDENDS AND CAPITAL GAINS ..................................................................................................... 61 OPTIMAL DIVIDEND POLICY WITH TAXES........................................................................................................ 62 DIVIDEND CAPTURE AND TAX CLIENTELES ...................................................................................................... 62 THE EFFECTIVE DIVIDEND TAX RATE ...................................................................................................... 62 CLIENTELE EFFECTS ............................................................................................................................. 63 DIVIDEND-CAPTURE THEORY ....................................................................................................................... 63 PAYOUT VERSUS RETENTION OF CASH ........................................................................................................... 63 RETAINING CASH WITH PERFECT CAPITAL MARKETS ........................................................................................ 63 TAXES AND CASH RETENTION ...................................................................................................................... 64 ADJUSTING FOR INVESTOR TAXES ................................................................................................................. 64 ISSUANCE AND DISTRESS COSTS ................................................................................................................... 64 AGENCY COSTS OF RETAINING CASH ............................................................................................................. 65 DIVIDEND SIGNALING ................................................................................................................................. 65 SIGNALING AND SHARE REPURCHASES ........................................................................................................... 66 STOCK DIVIDENDS, SPLITS, AND SPIN-OFFS ............................................................................................. 66 STOCK DIVIDENDS AND SPLITS ..................................................................................................................... 66 SPIN OFFS ................................................................................................................................................ 66 SW10: FINANCIAL OPTIONS ........................................................................................................... 67 INTERPRETING STOCK OPTION QUOTATIONS ........................................................................................... 67 OPTIONS ON OTHER FINANCIAL SECURITIES ............................................................................................. 68 4 OPTION PAYOFFS AT EXPIRATION .......................................................................................................... 68 LONG POSITION IN AN OPTION CONTRACT ..................................................................................................... 68 SHORT POSITION IN AN OPTION CONTRACT.................................................................................................... 69 PROFITS FOR HOLDING AN OPTION TO EXPIRATION ......................................................................................... 69 RETURNS FOR HOLDING AN OPTION TO EXPIRATION ........................................................................................ 70 COMBINATIONS OF OPTIONS................................................................................................................ 70 STRADDLE ................................................................................................................................................ 70 STRANGLE ................................................................................................................................................ 70 PUT-CALL PARITY .............................................................................................................................. 71 FACTORS AFFECTING OPTION PRICES ............................................................................................................ 72 ARBITRAGE BOUNDS ON OPTION PRICES ....................................................................................................... 72 OPTION PRICES AND THE EXERCISE DATE ....................................................................................................... 72 OPTION PRICES AND VOLATILITY .................................................................................................................. 72 EXERCISING OPTIONS EARLY ........................................................................................................................ 73 NON-DIVIDEND-PAYING STOCKS .......................................................................................................... 73 DIVIDEND-PAYING STOCKS .................................................................................................................. 73 OPTIONS AND CORPORATE FINANCE ...................................................................................................... 74 DEBT AS AN OPTION PORTFOLIO ........................................................................................................... 75 SW11: RAISING EQUITY CAPITAL ................................................................................................... 75 EQUITY FINANCING FOR PRIVATE COMPANIES.......................................................................................... 75 SOURCES OF FUNDING ................................................................................................................................ 75 VENTURE CAPITAL INVESTING ...................................................................................................................... 76 EXITING AN INVESTMENT IN A PRIVATE COMPANY ........................................................................................... 77 INITIAL PUBLIC OFFERING (IPO) ........................................................................................................... 78 ADVANTAGES AND DISADVANTAGES OF GOING PUBLIC .................................................................................... 78 TYPES OF OFFERINGS.................................................................................................................................. 78 BEST-EFFORTS, FIRM COMMITMENT, AND AUCTION IPOS................................................................................ 78 THE MECHANICS OF AN IPO ........................................................................................................................ 79 IPO PUZZLES ............................................................................................................................................ 80 CYCLICALITY .............................................................................................................................................. 81 COSTS OF AN IPO ...................................................................................................................................... 81 RELATIVE COSTS OF ISSUING SECURITIES ........................................................................................................ 81 LONG-RUN UNDERPERFORMANCE ................................................................................................................ 81 THE SEASONED EQUITY OFFERING (SEO) ................................................................................................ 81 THE MECHANICS OF AN SEO ....................................................................................................................... 81 PRICE REACTION ........................................................................................................................................ 82 SW12: DEBT FINANCING ................................................................................................................ 82 PUBLIC DEBT .................................................................................................................................... 82 TYPES OF CORPORATE DEBT ................................................................................................................. 82 SENIORITY ........................................................................................................................................ 83 BOND MARKETS ................................................................................................................................ 83 INTERNATIONAL RISK.................................................................................................................................. 83 DEBT .............................................................................................................................................. 83 PRIVATE DEBT ........................................................................................................................................... 83 SOVEREIGN DEBT....................................................................................................................................... 84 MUNICIPAL BONDS .................................................................................................................................... 84 ASSET-BACKED SECURITIES .......................................................................................................................... 84 5 BOND COVENANTS .................................................................................................................................... 84 CALLABLE BONDS .............................................................................................................................. 85 PRICES OF CALLABLE AND NON-CALLABLE BONDS ON THE CALL DATE................................................................. 85 CALL PROVISIONS ...................................................................................................................................... 85 SINKING FUND .......................................................................................................................................... 86 CONVERTIBLE PROVISIONS .......................................................................................................................... 86 CONVERTIBLE BOND VALUE ......................................................................................................................... 86 WARRANT ................................................................................................................................................ 86 SW13: WORKING CAPITAL MANAGEMENT .................................................................................... 87 OVERVIEW OF WORKING CAPITAL ......................................................................................................... 87 THE CASH CYCLE ....................................................................................................................................... 87 WORKING CAPITAL IN VARIOUS INDUSTRIES (2018) ........................................................................................ 87 FIRM VALUE AND WORKING CAPITAL ............................................................................................................ 88 TRADE CREDIT TERMS ................................................................................................................................ 88 TRADE CREDIT AND MARKET FRICTIONS ........................................................................................................ 88 MANAGING FLOAT..................................................................................................................................... 89 RECEIVABLES MANAGEMENT ....................................................................................................................... 89 MONITORING ACCOUNTS RECEIVABLE........................................................................................................... 89 AGING SCHEDULES ..................................................................................................................................... 90 PAYABLES MANAGEMENT ........................................................................................................................... 90 DETERMINING ACCOUNTS PAYABLE DAYS OUTSTANDING ................................................................................. 91 STRETCHING ACCOUNTS PAYABLE................................................................................................................. 91 INVENTORY MANAGEMENT ......................................................................................................................... 91 CASH MANAGEMENT ................................................................................................................................. 91 ALTERNATIVE INVESTMENTS ........................................................................................................................ 92 MONEY MARKET INVESTMENT OPTIONS ....................................................................................................... 92 6 SW1: Financial decision making and the law of one price In business decisions are made by comparing costs and benefits. The decision is usually done if the benefits outweigh the costs. In order to do this, you have to convert them to a common unit. Benefits may be in the future, whereas costs are usually in the present. Competitive Market: A market in which goods can be bought and sold for the same price Time Value of Money: Money is not worth the same across time, as it is influenced by many factors such as interest rate, inflation, etc. Interest Rate: The rate at which we can exchange money today for money in the future is determined by the current interest rate. Risk-Free interest rate ππ : The interest rate at which money can be borrowed or lent without risk. • Interest-rate factor: 1 + π" • Discount factor: 1/(1 + π" ) Value of Investment: Shows the net gain/loss from the investment by comparing Cashflows from the same time-period to determine if the investment makes sense economically. Present Value: Value of the investment in terms of currency today. Future Value: Value of the investment in terms of currency in the future. The Value of Investment must be the same, regardless of if the PV or FV is used. This is in relation to the Interest rate of course. 7 EXAMPLE: Consider an investment opportunity with the following certain cash flows. • Cost: $100,000 today • Benefit: $105,000 in one year • Interest rate: 7% • Today = π‘# / In one year = π‘$ $1.07 ππ πππ π¦πππ πΆππ π‘ = ($100,000 π‘ππππ¦) ∗ 5 ; = 107,000 ππ πππ π¦πππ $ π‘ππππ¦ ππππ’π ππ πππ£ππ π‘ππππ‘: CπΆπΉ%! E $105,000 − CπΆπΉ%! E $107,000 = −$2000 ππ πππ π¦πππ $105,000 ππ πππ π¦πππ π΅ππππππ‘ = = $98,130.84 π‘ππππ¦ $1.07 ππ πππ π¦πππ J K $ π‘ππππ¦ ππππ’π ππ πππ£ππ π‘ππππ‘: CπΆπΉ%" E $98,130.84 − CπΆπΉ%" E 100,000 = −$1869.16 π‘ππππ¦ $1.07 ππππ’π ππ π‘βπ π πππ πππππ’π π: − $1869.16 ∗ = −$2000 ππ πππ π¦πππ $1 1 π·ππ πππ’ππ‘ πππ‘π = = 0.93458 1.07 Net Present Value (NPV) The net present value (NPV) of a project or investment is the difference between the present value of its benefits and the present value of its costs. When making a decision, take the alternative with the highest NPV. • Accept projects with a positive NPV (because you make a profit) • Reject projects with a negative NPV (because you make a loss) πππ = ππ(π΅ππππππ‘π ) − ππ(πΆππ π‘π ) πππ = ππ(π΄ππ πππππππ‘ πΆππ βππππ€π ) EXAMPLE: You have $10,000 to invest and are considering three one-year risk-free investment options. 1. Invest up to $10,000 in a T-Bill paying 2%. 2. Invest in a project that cost $6,000 and returns $6,100 in one year. 3. Invest in a project that costs $4,000 and returns $4,100 in one year. Solutions: $ 1. πππ = ($10,000 ∗ 2%) ∗ $.#' − $10,000 = 0 $ 2. πππ = $6100 ∗ $.#' − $6000 = −19.61 $ 3. πππ = $4100 ∗ $.#' − $4000 = 19.61 8 Arbitrage and the law of one price Arbitrage is the practice of buying and selling equivalent goods in different markets to take advantage of a price difference. An arbitrage opportunity occurs when it is possible to make a profit without taking any risk or making any investment. The law of one price implies that if equivalent investment opportunities trade simultaneously in different competitive markets, then they must trade for the same price in both markets. (No Arbitrage if this is assumed) No-Arbitrage, security prices & identifying arbitrage opportunities Assume a security promises a risk-free payment of $1,000 in one year. If the risk-free interest rate is 5%, what can we conclude about the price of this bond in a normal market? 1000 ππ πππ π¦πππ ππ($1000 ππ πππ π¦πππ) = = $952.38 π‘ππππ¦ $1.05 ππ πππ π¦πππ $1 π‘ππππ¦ Assume price of the bond is $940 (underpricing) Today $ In one year Buy the bond -940 +1000 Loan from bank +952.38 -1000 Net CF +12.38 The $12.38 you gain from this loan is the risk-free profit. The opportunity for arbitrage will force the price of the bond to rise until it is equal to $952.38. Assume price of the bond is $960 (overpricing) Today $ In one year Sell the bond +960 -1000 Invest in bank -952.38 +1000 Net CF +7.62 The $7.62 you gain from this sale is the risk-free profit. The opportunity for arbitrage will force the price of the bond to fall until it is equal to $952.38. Unless the price of the security equals the present value of the security’s cash flows, an arbitrage opportunity will appear. π·ππππ(πΊπππππππ) = π·π½(π¨ππ πππππππππ ππππ ππ πππ ππππππππ) 9 NPV of trading securities In a normal market, the NPV of buying or selling a security is zero. πππ(π΅π’π¦ ππππ’πππ‘π¦) = ππ(π΄ππ πππ βππππ€π ππππ ππ¦ π‘βπ π πππ’πππ‘π¦ − πππππ(ππππ’πππ‘π¦) = 0 πππ(ππππ ππππ’πππ‘π¦ = πππππ(ππππ’πππ‘π¦) − ππ(π΄ππ πππ βππππ€π ππππ ππ¦ π‘βπ π πππ’πππ‘π¦) = 0 Separation principle We can evaluate the NPV of an investment decision separately from the decision the firm makes regarding how to finance the investment or any other security transactions the firm is considering. EXAMPLE: You are considering a risk-free investment that costs $7,000 and pays $8,500 in one year. You can either pay all cash for the investment or you can borrow half and pay cash for the other half. If you borrow $3,500, you will be required to pay back $3,710 in one year. The risk-free rate is 6%. 1 πππ(πππππππ‘) = 8500 ∗ = 8018.86 1.06 πΆππ β = 8018.86 − 7000 = 1018.86 1 πππ(πΏπππ) = 3710 ∗ = 3500 1.06 1r πΆππ β + 1r πΏπππ = s(8500 − 3710) ∗ 1 t − 3500 = 1018.86 2 2 1.06 It makes no difference whether you take the loan or pay all in cash. SW2: Time Value of Money The Timeline A timeline is a linear representation of the timing of potential cash flows. Drawing a timeline of the cash flows will help you visualize the financial problem. Assume that you are lending $10,000 today and that the loan will be repaid in two annual $6,000 payments. Timelines can represent cash flows that take place at the end of any time period – a month, a week, a day, etc. Three Rules of Time Travel 10 Rule 1: Comparing and Combining Values A dollar today and a dollar in one year are not equivalent. π‘# ≠ π‘$ It is only possible to compare or combine values at the same point in time. Things such as how much time passes and what the interest is are important evaluate the opportunity costs. Rule 2: Moving cashflows forward in time To move a cash flow forward in time, you must compound it. To calculate the future value we use the formula: πΉπ( = πΆ × (1 + π)( Interest plays a huge part in this as interest compound very quickly. Rule 3: Moving cashflows back in time To move a cash flow backward in time, we must discount it. To calculate the present value we use the formula: πΆ ππ = (1 + π)( Examples: Suppose we plan to save $1,000 today, and $1,000 at the end of each of the next two years. If we can earn a fixed 10% interest rate on our savings, how much will we have three years from today? Assume that an investment will pay you $5,000 now and $10,000 in five years. 11 Valuing a stream of Cashflows Based on the first rule of time travel we can derive a general formula for valuing a stream of cash flows: if we want to find the present value of a stream of cash flows, we simply add up the present values of each. To calculate the PV of a cashflow stream we use: To calculate the FV of a cashflow stream we use: πΉπ = ππ ∗ (1 + π)( Perpetuities and Annuities Perpetuities When a constant cash flow will occur at regular intervals forever it is called a perpetuity. The value of a perpetuity is simply the cash flow divided by the interest rate. πΆ ππ(πΆ ππ ππππππ‘π’ππ‘π¦) = π Annuities When a constant cash flow will occur at regular intervals for a finite number of π periods, it is called an annuity. The value of an annuity calculated by adding the value of every year until π. * πΆ πΆ πΆ πΆ πΆ ππ(πΆ ππ ππππ’ππ‘π¦) = + + + β―+ =x ' ) * (π + 1) (π + 1) (π + 1) (π + 1) (π + 1)( (+$ Present Value of an Annuity The formula for calculating the PV of an Annuity is: π 1 πΆ 1 ππ(ππππ’ππ‘π¦ πππ π πππππππ ) = π − = π y1 − z = y1 − z * * (1 + π) (1 + π) (1 + π)* π , Because: π = Future Value of an Annuity The formula for calculating the FV of an Annuity is: πΉπ(ππππ’ππ‘π¦ πππ π πππππππ ) = ππ ∗ (1 + π)* = πΆ 1 y1 − z ∗ (1 + π)* (1 + π)* π 1 = πΆ ∗ ((1 + π)* − 1) π 12 Growing Annuity The present value of a growing annuity with the initial cash flow c, growth rate g, and interest rate r is defined as: 1 1+π * ππ = πΆ ∗ s1 − y z t (π − π) (1 + π) Example: You want to begin saving for your retirement. You plan to contribute $12,000 to the account at the end of this year. You anticipate you will be able to increase your annual contributions by 3% each year for the next 45 years. If your expected annual return is 8%, how much do you expect to have in your retirement account when you retire in 45 years? 1 1.03 ./ ππ = $12,000 ∗ s1 − y z t = $211,567 0.08 − 0.03 1.08 πΉπ = $211,567 ∗ (1.08)./ = $6,753,314 Solving for Cash payments Sometimes we know the present value or future value, but we do not know one of the variables we have previously been given as an input. For example, when you take out a loan you may know the amount you would like to borrow but may not know the loan payments that will be required to repay it. πππππππππ (π) πΏπππ ππ π΄πππ’ππ‘π¦ πππ¦ππππ‘: πΆππ βππππ€ (πΆ) = 1 1 − y1 z π (1 + π)* Example: You have just graduated and landed your dream job with a nice salary. To reward yourself, you decide to purchase a luxury automobile at a cost of $60,000. The manufacturer is offering a special deal on financing: $0 down and 60 monthly payments with an annual interest rate of 3%. What are the monthly payments? $60,000 πΆ= = $1,078.12 1 1 ∗ |1 − } 0.03r 0.03r E0# C1 + 12 12 #.#) because there are 12 monthly payments for the full year. $' π₯ 0# because there are 60 monthly payments in total. Internal Rate of Return In some situations, you know the present value and cash flows of an investment opportunity, but you do not know the internal rate of return (IRR), the interest rate that sets the net present value of the cash flows equal to zero. πΆπΉ$ πΆπΉ' πΆπΉ3 πππ122 = πΆπΉ# + + + β― + =0 (1 + πΌπ π )3 1 + πΌπ π (1 + πΌπ π )' 13 SW3: Investment Decision Rules NPV and Stand-alone projects Consider a take-it-or-leave-it investment decision involving a single, stand-alone project for Fredrick’s Feed and Farm (FFF). The project costs $250 million and is expected to generate cash flows of $35 million per year, starting at the end of the first year and lasting forever. The NPV of the project is calculated as: 35 πππ = −250 + π The NPV is dependent on the discount rate. Alternative Rules vs the NPV Rule Sometimes alternative investment rules may give the same answer as the NPV rule, but at other times they may disagree. When the rules conflict, the NPV decision rule should be followed. Internal Rate of Return (IRR) Rule The Rule: • Take any investment where the IRR exceeds the cost of capital. • Turn down any investment whose IRR is less than the cost of capital. The IRR Investment Rule will give the same answer as the NPV rule in many, but not all, situations. In general, the IRR rule works for a stand-alone project if all the project’s negative cash flows precede its positive cash flows. In some cases, the IRR Rule may have a different conclusion from the NPV rule. Then the IRR Rule is incorrect, this may be due to the following reasons (Pitfalls): 1. Delayed investments 2. Nonexistent IRR 3. Multiple IRR 14 Pitfall 1: Delayed investments Assume you have just retired as the CEO of a successful company. A major publisher has offered you a book deal. The publisher will pay you $1 million upfront if you agree to write a book about your experiences. You estimate that it will take three years to write the book. The time you spend writing will cause you to give up speaking engagements amounting to $500,000 per year. You estimate your opportunity cost to be 10%. Should you accept the deal? Calculate IRR: −500,000 −500,000 −500,000 πππ = 0 = 1,000,000 + + + (1 + π) (1 + π)' (1 + π)) π = 23.38% = πΌπ π Calculate NPV: 500,000 500,000 500,000 πππ = 1,000,000 − − − 1.1 1.1' 1.1) πππ = −243,426 IRR decision rule indicates you should take the deal since the IRR of 23.38% is higher than the cost of capital of 10%. The NPV rule however indicates that you should reject the deal because the NPV is negative. When the benefits of an investment occur before the costs, the NPV is an increasing function of the discount rate. Pitfall 2: Multiple IRRs Suppose Star informs the publisher that it needs to sweeten the deal before he will accept it. The publisher offers $550,000 advance and $1,000,000 in four years when the book is published. Should he accept or reject the new offer? Calculate IRR: 500,000 500,000 500,000 1,000,000 πππ = 0 = 550,000 − − − + (1 + π)' (1 + π)) (1 + π). 1+π πΌπ π $ = 33.673% πΌπ π ' = 7.164% Because there is more than one IRR, the IRR rule cannot be applied. 15 Pitfall 3: Nonexistent IRR Finally, Star is able to get the publisher to increase his advance to $750,000, in addition to the $1 million when the book is published in four years. With these cash flows, no IRR exists; there is no discount rate that makes NPV equal to zero. No IRR exists because the NPV is positive for all values of the discount rate. Thus, the IRR rule cannot be used. IRR versus the IRR Rule While the IRR rule has shortcomings for making investment decisions, the IRR itself remains useful. IRR measures the average return of the investment and the sensitivity of the NPV to any estimation error in the cost of capital. Payback Rule The payback period is amount of time it takes to recover or pay back the initial investment. If the payback period is less than a pre-specified length of time, you accept the project. Otherwise, you reject the project. Pitfalls: • Ignores the project’s cost of capital and time value of money. • Ignores cash flows after the payback period. • Relies on an ad hoc decision criterion. Choosing between Projects Mutually Exclusive Projects, when you must choose only one project among several possible projects, the choice is mutually exclusive. Rules: - Select the project with the highest NPV. - Selecting the project with the highest IRR may lead to mistakes. 16 Incremental IRR Rule Apply the IRR rule to the difference between the cash flows of the two mutually exclusive alternatives (the increment to the cash flows of one investment over the other). Possible differences: • Discount rate at which one project becomes more profitable than the other • Varying initial investments If the Incremental IRR is higher, it is profitable to go for the larger project with a lower IRR! Shortcomings of the Incremental IRR Rule: • The incremental IRR may not exist. • Multiple incremental IRRs could exist. • The fact that the IRR exceeds the cost of capital for both projects does not imply that either project has a positive NPV. • When individual projects have different costs of capital, it is not obvious which cost of capital the incremental IRR should be compared to. Example: Comparing 2 projects. Cost of Capital = 10% Year 0 Year 1 Year 2 Year 3 Year 4 IRR Project 1 -240 125 125 125 125 38% Project 2 -850 400 400 400 400 31% Incremental -610 275 275 275 275 29% Incremental IRR of 29% is higher than the Cost of Capital, go for the larger project! Profitability Index The profitability index can be used to identify the optimal combination of projects to undertake. Formula: ππππ’π πππππ‘ππ πππ ππππππππππππ‘π¦ πΌππππ₯ = = π ππ ππ’πππ ππππ π’πππ π ππ ππ’πππ ππππ π’πππ Shortcomings of the profitability index: • In some situations, the profitability Index does not give an accurate answer. • In some situations, the profitability Index does not give an accurate answer. 17 SW4: Valuing Stocks Dividend-Discount Model Potential Cashflows for a one year investor are: - Dividend - Sale of Stock Timeline of a one-year investor: Since the cash flows are risky, we must discount them at the equity cost of capital. πΈππ’ππ‘π¦ πππ π‘ ππ πππππ‘ππ = π4 → πππ‘ π‘βπ πππ πππππ πππ‘π (π" ) To calculate the price today of an investment we use: π·ππ£$ + π$ π# = y z 1 + π4 If the current stock price were less than this amount, expect investors to rush in and buy it, driving up the stock’s price. If the stock price exceeded this amount, selling it would cause the stock price to quickly fall. Total Return The expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk. The expected return can be calculating by adding dividend yields and capital gains: Example: 3M (MMM) just paid a dividend of $4.50 per share. You expect the stock price will $178.50 and the dividend to be 5% higher by the end of the year. Investments with equivalent risk have an expected return of 11%. Based on the Dividend-Discount Model, what would pay today for 3M stock? Dividend at start of period: π·ππ£# = $4.50 Expected Stock price: π$ = $178.50 Expected Dividend: π·ππ£$ = π·ππ£# + 5% = $4.50 ∗ 1.05 = $4.725 Expected Return: π4 = 11% π·ππ£$ + π$ 4.725 + 178.5 π# = y z=y z = $165.07 1 + π4 1 + 0.11 To check if it is correct calculate the expected return: π·ππ£$ π$ − π# 4.725 178.5 − 165.07 π4 = + = + = 0.11 = 11% π# π# 165.07 165.07 18 Dividend-Discount Model Equation This Model is used for investors that seek to invest their money for multiple years. To calculate the initial value of a multi-year investment we use: π·ππ£$ π·ππ£' π·ππ£* π* π# = + + β― + + (1 + π4 )* (1 + π4 )* 1 + π4 (1 + π4 )' This is known as the Dividend-Discount Model. The price of any stock is equal to the present value of the expected future dividends it will pay. If dividends are stable it is similar to a perpetuity: πΆ π·ππ£ ππ = = π π4 For forecasting it is important to incorporate a growth rate to the expected dividend. The simplest forecast for the firm’s future dividends states that they will grow at a constant rate, g, forever. Constant dividend growth model: π·ππ£$ π# = π4 − π π·ππ£$ π4 = +π π# The value of the firm depends on the current dividend level, the cost of equity, and the growth rate. Example: AT&T plans to pay $1.44 per share in dividends in the coming year. Its equity cost of capital is 8%. Dividends are expected to grow by 4% per year in the future. Estimate the value of AT&T’s stock. Future dividend: π·ππ£$ = $1.44 Equity cost of capital: π4 = 8% Growth rate: π = 4% π·ππ£$ 1.44 π# = = = $36 π4 − π 0.08 − 0.04 π·ππ£$ 1.44 π4 = +π = + 0.04 = 0.08 π# 36 Dividends vs Investment and Growth How dividends are calculated: EPS = Earnings per Share Assuming the number of shares outstanding is constant, the firm can do two things to increase its dividend: • Increase its earnings (net income) • Increase its dividend payout rate π# ↑ → π·ππ£ ↑ πππ ⁄ππ π ↑ A firm can do one of two things with its earnings: • It can pay them out to investors (dividend) • It can retain and reinvest them (retained earnings) 19 Simple model of growth: πΆβππππ ππ πΈπππππππ = πππ€ πΌππ£ππ π‘ππππ‘ ∗ π ππ‘π’ππ ππ πππ€ πΌππ£ππ π‘ππππ‘ πππ€ πΌππ£ππ π‘ππππ‘ = πΈπππππππ ∗ π ππ‘πππ‘πππ π ππ‘π Retention Rate: Fraction of current earnings that the firm retains To calculate Earnings growth rate: πΆβππππ ππ πΈπππππππ πΈπππππππ πΊπππ€π‘β π ππ‘π = πΈπππππππ (πΈπππππππ ∗ π ππ‘πππ‘πππ π ππ‘π) ∗ π ππ‘π’ππ = πΈπππππππ = π ππ‘πππ‘πππ π ππ‘π ∗ π ππ‘π’ππ ππ πππ€ πΌππ£ππ π‘ππππ‘ π = π ππ‘πππ‘πππ π ππ‘π ∗ π ππ‘π’ππ ππ πππ€ πΌππ£ππ π‘ππππ‘ If the firm keeps its retention rate constant, then the growth rate in dividends will equal the growth rate of earnings. Profitable Growth If a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut investment and increase its dividend? The answer will depend on the profitability of the firm’s investments. Cutting the firm’s dividend to increase investment will raise the stock price if, and only if, the new investments have a positive NPV. Example: Dren Industries is considering expanding into a new product line. Earnings per share are expected to be $5 in the coming year and are expected to grow annually at 5% without the new product line but growth would increase to 7% if the new product line is introduced. To finance the expansion, Dren would need to cut its dividend payout ratio from 80% to 50%. If Dren’s equity cost of capital is 11%, what would be the impact on Dren’s stock price if they introduce the new product line? Assume the equity cost of capital will remain unchanged. Calculate π# without new product line: πΈππ$ = πΈππ# ∗ (1 + π) = 5 ∗ 1.05 = 5.25 π·ππ£$ = πΈππ$ ∗ πππ¦ππ’π‘ πππ‘ππ = 5.25 ∗ 0.8 = 4.20 π·ππ£$ 4.20 π# = = = $70 π4 − π 0.11 − 0.05 Calculate π# with new product line: πΈππ$ = πΈππ# ∗ (1 + π) = 5 ∗ 1.07 = 5.35 π·ππ£$ = πΈππ$ ∗ πππ¦ππ’π‘ πππ‘ππ = 5.35 ∗ 0.5 = 2.675 π·ππ£$ 2.675 π# = = = $66.875 π4 − π 0.11 − 0.07 Stock price would drop with the introduction of the new product line. 20 Changing Growthrates We cannot use the constant dividend growth model to value a stock if the growth rate is not constant. Although we cannot use the constant dividend growth model directly when growth is not constant, we can use the general form of the model to value a firm by applying the constant growth model to calculate the future share price of the stock once the expected growth rate stabilizes. Limitations of the Dividend-Discount Model There is a tremendous amount of uncertainty associated with forecasting a firm’s dividend growth rate and future dividends. Small changes in the assumed dividend growth rate can lead to large changes in the estimated stock price. Total Payout and Free Cash Flow Valuation Models Share Repurchases and the Total Payout Model: ππ# = ππ(πΉπ’π‘π’ππ π·ππ£ππππππ πππ πβπππ) Share repurchases: When the firm uses excess cash to buy back its own stock. Implications for the Dividend-Discount Model: • The more cash the firm uses to repurchase shares, the less it has available to pay dividends. • By repurchasing, the firm decreases the number of shares outstanding, which increases its earnings and dividends per share. Total Payout Model: ππ(πΉπ’π‘π’ππ πππ‘ππ π·ππ£ππππππ πππ π πππ’ππβππ ππ ) ππ# = πβππππ ππ’π‘π π‘ππππππ# Values all of the firm’s equity, rather than a single share. You discount total dividends and share repurchases and use the growth rate of earnings (rather than earnings per share) when forecasting the growth of the firm’s total payouts. 21 Example: Montalvan Inc. expects to have $125 million in earnings for the year and earnings are expected to grow at 6% annually. The firm does not pay any dividends, but it intends to use 25% of its earnings for stock repurchases. Motalvan’s cost of equity is 15%, and it has 25 million shares outstanding. What is Montalvan’s stock price? $125 πππ ∗ 0.25 ππ = = $347.22 πππ 0.15 − 0.06 $347.22 πππ π# = = $13.89 25 πππ Discounted Free Cash Flow Model The discounted free cash flow model determines the value of the firm to all investors, including both equity and debt holders. The enterprise value can be interpreted as the net cost of acquiring the firm’s equity, taking its cash, paying off all debt, and owning the unlevered business. πΈππ‘ππππππ π ππππ’π = ππππππ‘ ππππ’π ππ πΈππ’ππ‘π¦ + π·πππ‘ − πΆππ β π# = (π# ∗ πβππππ ππ’π‘π π‘ππππππ) + π·πππ‘ − πΆππ β 22 Example: At the end of 2016, Newerks Inc. forecasts that its free cash flow will be $50 million in 2017, $60 million in 2018, and $72 million in 2019. After 2019, Newerks expects its free cash flow earnings to grow at an annual rate of 6%. Newerks has $75 million in debt and $25 million in cash. If Newerks has 5 million shares outstanding and a cost of capital of 14%, what is Newerks stock price at the end of 2016? (1 + π6,6 ) π'#$5 = ∗ πΉπΆπΉ'#$5 π78,, − π6,6 1.06 π'#$5 = = $954 0.14 − 0.06 50 60 72 + 954 π'#$0 = + + = $782.55 ' 1.14 (1.14) (1.14)) π'#$0 + πΆππ β − π·πππ‘ 782.55 + 25 − 75 π'#$0 = = = $146.51 πβππππ ππ’π‘π π‘ππππππ 5 Connection to Capital Budgeting The firm’s free cash flow is equal to the sum of the free cash flows from the firm’s current and future investments, so we can interpret the firm’s enterprise value as the total NPV that the firm will earn from continuing its existing projects and initiating new ones. The NPV of any individual project represents its contribution to the firm’s enterprise value. To maximize the firm’s share price, we should accept projects that have a positive NPV. Comparison of Discounted Cash Flow Models of Stock Valuation 23 Valuation Based on Comparable Firms Method of Comparables (Comps) • Estimate the value of the firm based on the value of other, comparable firms or investments that we expect will generate very similar cash flows in the future. • Valuation Multiple o A ratio of firm’s value to some measure of the firm’s scale or cash flow, i.e. The Price-Earnings Ratio: P/E Ratio. § Share price divided by earnings per share Valuation Multiples In Valuation multiples we differentiate between • Trailing Earnings: Trailing P/E o Earnings over the last 12 months • Forward Earnings: Forward P/E o Expected earnings over the next 12 months π# π·ππ£$ ⁄πΈππ$ π·ππ£πππππ‘ πππ¦ππ’π‘ πππ‘π πΉπππ€πππ π ⁄πΈ = = = πΈππ$ π4 − π π4 − π Firms with high growth rates, and which generate cash well in excess of their investment needs so that they can maintain high payout rates, should have high P/E multiples. Example: Best Buy Co. Inc. (BBY) has earnings per share of $2.22. The average P/E of comparable companies’ stocks is 19.7. Estimate a value for Best Buy using the P/E as a valuation multiple. π# πΉπππ€πππ π⁄πΈ = πΈππ$ π# = π⁄πΈ ∗ πΈππ$ = $2.22 ∗ 19.7 = $43.73 Enterprise Value Multiples: This valuation multiple is higher for firms with high growth rates and low capital requirements (so that free cash flow is high in proportion to EBITDA). πΉπΆπΉ$ rπΈπ΅πΌππ·π΄ π# $ = πΈπ΅πΌππ·π΄$ π78,, − π6,6 Example: Best Buy Co. Inc. (BBY) has EBITDA of $2,766,000,000 and 410 million shares outstanding. Best Buy also has $1,963,000,000 in debt and $509,000,000 in cash. If Best Buy has an enterprise value to EBITDA multiple of 7.7, estimate the value for a share of Best Buy stock. π99: = 2766 πππ ∗ 7.7 = $21298.2 πππ π# + πΆππ β − π·πππ‘ 21298.2 πππ + 509 πππ − 1963 πππ π# = = = 48.4 πππ πβππππ ππ’π‘π π‘ππππππ 410 πππ 24 Limitations of Multiples When valuing a firm using multiples, there is no clear guidance about how to adjust for differences in expected future growth rates, risk, or differences in accounting policies. Comparables only provide information regarding the value of a firm relative to other firms in the comparison set. • Using multiples will not help us determine if an entire industry is overvalued. Discounted cash flows methods have the advantage that they can incorporate specific information about the firm’s cost of capital or future growth. • The discounted cash flow methods have the potential to be more accurate than the use of a valuation multiple. Comparison with Discounted Cash Flow Methods Discounted cash flows methods have the advantage that they can incorporate specific information about the firm’s cost of capital or future growth The discounted cash flow methods have the potential to be more accurate than the use of a valuation multiple Stock Valuation Techniques: The Final Word No single technique provides a final answer regarding a stock’s true value. All approaches require assumptions or forecasts that are too uncertain to provide a definitive assessment of the firm’s value. Most real-world practitioners use a combination of these approaches and gain confidence if the results are consistent across a variety of methods. Information in Stock prices Our valuation model links the firm’s future cash flows, its cost of capital, and its share price. Given accurate information about any two of these variables, a valuation model allows us to make inferences about the third variable. For a publicly traded firm, its current stock price should already provide very accurate information, aggregated from a multitude of investors, regarding the true value of its shares. Based on its current stock price, a valuation model will tell us something about the firm’s future cash flows or cost of capital. Competition and Efficient Markets Efficient Markets Hypothesis Implies that securities will be fairly priced, based on their future cash flows, given all information that is available to investors. Public, Easily Interpretable Information If the impact of information that is available to all investors (news reports, financials statements, etc.) on the firm’s future cash flows can be readily ascertained, then all investors can determine the effect of this information on the firm’s value. In this situation, we expect the stock price to react nearly instantaneously to such news. 25 Private or Difficult-to-Interpret Information Private information will be held by a relatively small number of investors. These investors may be able to profit by trading on their information. In this case, the efficient markets hypothesis will not hold in the strict sense. However, as these informed traders begin to trade, they will tend to move prices, so over time prices will begin to reflect their information as well. If the profit opportunities from having private information are large, others will devote the resources needed to acquire it. In the long run, we should expect that the degree of “inefficiency” in the market will be limited by the costs of obtaining the private information. Lessons for Investors and Corporate Managers Consequences for Investors If stocks are fairly priced, then investors who buy stocks can expect to receive future cash flows that fairly compensate them for the risk of their investment. In such cases, the average investor can invest with confidence, even if he is not fully informed. Implications for Corporate Managers • Focus on NPV and free cash flow • Avoid accounting illusions • Use financial transactions to support investment SW5: Capital Markets and the Pricing of Risk Risk and Return: Insights from 89 Years of Investor History: • Standard & Poor’s 500: 90 U.S. stocks up to 1957 and 500 after that. Leaders in their industries and among the largest firms traded on U.S. Markets. • Small stocks: Securities traded on the NYSE with market capitalizations in the bottom 20%. • World Portfolio: International stocks from all the world’s major stock markets in North America, Europe, and Asia. • Corporate Bonds: Long-term, AAA-rated U.S. corporate bonds with maturities of approximately 20 years. • Treasury Bills: An investment in three-month Treasury bills. Small stocks had the highest long-term returns, while T-Bills had the lowest long-term returns. Small stocks had the largest fluctuations in price, while T-Bills had the lowest (higher risk requires higher return.). Few people ever make an investment for 89 years. More realistic investment horizons and different initial investment dates can greatly influence each investment's risk and return. 26 Common Measures of Risk and Return Probability distributions When an investment is risky, it may earn different returns. Each possible return has some likelihood of occurring. This information is summarized with a probability distribution, which assigns a probability, π2 , that each possible return, π , will occur. Expected Return Expected return can be calculated as a weighted average of the possible returns, where the weights correspond to the probabilities. Probability = π Return = π πΈπ₯ππππ‘ππ π ππ‘π’ππ = πΈ [π ] = x π2 ∗ π 2 Variance Variance is the expected squared deviation from the mean. πππ(π ) = πΈ [(π − πΈ [π ])' ] = x π2 ∗ (π − πΈ [π ])' 2 If πΈ [π ] = π" → Var = 0 Standard Deviation The standard deviation is the square root of the Variance. ππ·(π ) = •πππ(π ) Both are measures of the risk of a probability distribution. Example: TXU stock has the following probability distribution: What are its expected return and standard deviation? πΈ [π ] = 0.25 ∗ (0.08) + 0.55 ∗ (0.1) − 0.2 ∗ (0.12) = 0.09 = 9.9% πππ = 0.25 ∗ (0.08 − 0.099)' + 0.55 ∗ (0.1 − 0.099)' + 0.2 ∗ (0.12 − 0.099)' = 0.018% ππ·(π ) = √0.0018 = 0.01338 = 1.338% Historical Returns of Stocks and Bonds Computing historical returns is essential to be able to compute risk and return. Realized Return The return that actually occurs over a particular time period. π·ππ£%;$ + π%;$ π·ππ£%;$ π·ππ£%;$ − π% π %;$ = −1= + π% π% π% π %;$ = π·ππ£πππππ πππππ + πΆππππ‘ππ πΊπππ π ππ‘π If you hold the stock beyond the date of the first dividend, then to compute your return you must specify how you invest any dividends you receive in the interim. Let’s assume that all dividends are immediately reinvested and used to purchase additional shares of the same stock or security. If a stock pays dividends at the end of each quarter, with realized returns π <$ , … , π <. each quarter, then its annual realized return, π =((>=? , is computed as follows: 1 + π =((>=? = C1 + π <$ EC1 + π <' EC1 + π <) E(1 + π <. ) 27 Example: What were the realized annual returns for NRG stock in 2012 and in 2016? First, we look up stock price data for NRG at the start and end of the year, as well as dividend dates. From these data, we construct the following table: π '#$' = (1.0513)(1.0449)(0.7626)(1.1375)(0.9714) − 1 = −0.0743 = −7.43% π '#$0 = (0.8499)(0.8409)(1.0811)(0.4404) − 1 = −0.6597 = −65.97% By counting the number of times, a realized return falls within a particular range, we can estimate the underlying probability distribution. Empirical Distribution: When the probability distribution is plotted using historical data. Average Annual Return 3 1 1 π ‘ = (π $ + π ' + β― + π 3 ) = x π % π π %+$ Where π % is the realized return of a security in year π‘, for the years 1 through π. Variance and Volatility of Returns Variance Estimate Using Realized Returns: 3 1 πππ(π ) = x(π % − π ‘)' π−1 %+$ The estimate of the standard deviation is the square root of the variance. Example: Using the data from the table, what are the variance and standard deviation of Microsoft’s returns from 2008 to 2017? 1 (−0.444 + 0.605 − 0.065 − β― + 0.407) = 0.161 = 16.1% π ‘ = 10 1 [(−0.444 − 0.161)' + (0.605 − 0.161)' … ] = 0.0917 πππ(π ) = 10 − 1 ππ·(π ) = √0.0917 = 0.3028 = 30.28% 28 Estimation Error: Using Past Returns to Predict the Future We can use a security’s historical average return to estimate its actual expected return. However, the average return is just an estimate of the expected return. Standard Error: A statistical measure of the degree of estimation error Standard Error of the Estimate of the Expected Return: ππ·(πΌππππ£πππ’ππ π ππ π) ππ·(π΄π£πππππ ππ πΌπππππππππ‘, πΌππππ‘ππππ π ππ ππ ) = •ππ’ππππ ππ πππ πππ£ππ‘ππππ 95% Confidence Interval: π»ππ π‘ππππππ π΄π£πππππ π ππ‘π’ππ ± (2 ∗ ππ‘ππππππ πΈππππ) ππ·(πΌππππ£πππ’ππ π ππ π) (π ‘) ± •ππ’ππππ ππ πππ πππ£ππ‘ππππ The two results give the range. Example: Using the data from the table in the example before, what is the 95% confidence interval you would estimate for Microsoft’s expected return? π ‘ = 16.1% ππ· = 30.28% 95% Confidence Interval: 30.28% 16.1% ± 2 y z = 16.1% ± 19.1508% √10 16.1% + 19.1508% = 35.2508% 16.1% − 19.1508% = −3.0508% Returns of Individual Stocks There is no precise relationship between volatility and average return for individual stocks. Larger stocks tend to have lower volatility than smaller stocks. All stocks tend to have higher risk and lower returns than large portfolios. Common Versus Independent Risk Common Risk: Risk that is perfectly correlated. Risk that affects all securities. Independent Risk: Risk that is uncorrelated. Risk that affects a particular security Diversification: The averaging out of independent risks in a large portfolio. Diversification in Stock Portfolios Firm-Specific Versus Systematic Risk. • Firm specific news: Good or bad news about an individual company o Independent Risks: Due to firm-specific news § Firm-specific Risk § Idiosyncratic Risk § Unique Risk § Unsystematic Risk § Diversifiable Risk • Market wide news: News that affects all stocks, such as news about the economy o Common Risks: Due to market-wide news § Systematic Risk § Undiversifiable Risk § Market Risk When many stocks are combined in a large portfolio, the firm-specific risks for each stock will average out and be diversified. The systematic risk, however, will affect all firms and will not be diversified. 29 Type S vs Type I Type S firms: Affected only by systematic risk. There is a 50% chance the economy will be strong and type S stocks will earn a return of 40%. There is a 50% change the economy will be weak and their return will be –20%. Because all these firms face the same systematic risk, holding a large portfolio of type S firms will not diversify the risk. Type I firms: Affected only by firm-specific risks. Their returns are equally likely to be 35% or –25%, based on factors specific to each firm’s local market. Because these risks are firm specific, if we hold a portfolio of the stocks of many type I firms, the risk is diversified. Actual firms are affected by both market-wide risks and firm-specific risks. When firms carry both types of risk, only the unsystematic risk will be diversified when many firm’s stocks are combined into a portfolio. The volatility will therefore decline until only the systematic risk remains. No Arbitrage and the Risk Premium The risk premium for diversifiable risk is zero, so investors are not compensated for holding firm-specific risk. The risk premium of a security is, therefore, determined by its systematic risk and does not depend on its diversifiable risk. Standard deviation is not an appropriate measure of risk for an individual security. There should be no clear relationship between volatility and average returns for individual securities. Consequently, to estimate a security’s expected return, we need to find a measure of a security’s systematic risk. Measuring Systematic Risk To measure the systematic risk of a stock, determine how much of the variability of its return is due to systematic risk versus unsystematic risk. To determine how sensitive a stock is to systematic risk, look at the average change in the return for each 1% change in the return of a portfolio that fluctuates solely due to systematic risk. • Efficient Portfolio o A portfolio that contains only systematic risk. o There is no way to reduce the volatility of the portfolio without lowering its expected return. • Market Portfolio o An efficient portfolio that contains all shares and securities in the market 30 Sensitivity to Systematic Risk: Beta (β) The expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio. Beta differs from volatility. Volatility measures total risk (systematic plus unsystematic risk), while beta is a measure of only systematic risk. Interpreting Beta (β): A security’s beta is related to how sensitive its underlying revenues and cash flows are to general economic conditions. Stocks in cyclical industries are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive industries. Example: Suppose the market portfolio tends to increase by 52% when the economy is strong and decline by 21% when the economy is weak. What is the beta of a type S firm whose return is 55% on average when the economy is strong and -24% when the economy is weak? What is the beta of a type I firm that bears only idiosyncratic, firm-specific risk? ππ¦ππ π: Δ = 0.55 − (−0.24) = 0.79 ππππππ‘: Δ = 0.52 − (−0.21) = 0.73 Δ@ 0.79 π½@ = = = 1.082 ΔA=-B4% 0.73 ππ¦ππ πΌ: π½1 = 0 π½ = 1 → ππππππ‘ πππππππππ‘ π½ > 1 → ππππππ‘ ππππ π£ππππ‘πππ π½ < 1 → ππππππ‘ πππ π π£ππππ‘πππ Beta and the Cost of Capital The market risk premium is the reward investors expect to earn for holding a portfolio with a beta of 1. Estimating the Risk Premium: ππππππ‘ π ππ π ππππππ’π = πΈ [π AB% ] − π" Estimating a Traded Security’s Cost of Capital of an investment from Its Beta: πΈ [π ] = π ππ πππππ πΌππ‘ππππ π‘ π ππ‘π + π ππ π ππππππ’π πΈ[π ] = π" + π½ ∗ CπΈ [π AB% ] − π" E This equation is often referred to as the Capital Asset Pricing Model (CAPM). It is the most important method for estimating the cost of capital that is used in practice. Example: Assume the economy has a 60% chance of the market return being 15% next year and a 40% chance the market return will be 5% next year. Assume the risk-free rate is 6%. If Microsoft’s beta is 1.18, what is its expected return next year? πΈ [π AB% ] = (0.6 ∗ 0.15) + (0.40 ∗ 0.05) = 0.11 = 11% πΈ [π A@ ] = 0.06 + 1.18(0.11 − 0.06) = 0.119 = 11.9% 31 SW6: Optimal Portfolio Choice and the Capital Asset Pricing Model The Expected Return of a Portfolio The fraction of the total investment in the portfolio held in each individual investment in the portfolio is the Portfolio weight. The portfolio weights must add up to 1.00 or 100%. ππππ’π ππ πΌππ£ππ π‘ππππ‘ π π₯C = πππ‘ππ ππππ’π ππ ππππ‘πππππ Then the return on the portfolio, π D , is the weighted average of the returns on the investments in the portfolio, where the weights correspond to portfolio weights. π D = π₯$ π $ + π₯' π ' + β― + π₯( π ( = x π₯C π C C Example: Suppose you buy 500 shares of Ford at $11 per share and 100 shares of Citigroup stock at $28 per share. If Ford’s share price goes up to $13 and Citigroup’s rises to $40, what is the new value of the portfolio, and what return did it earn? After the price change, what are the new portfolio weights? Initial Portfolio = 500 ∗ $11 + 100 ∗ $28 = $8300 New Value of Portfolio= 500 ∗ $13 + 100 ∗ $40 = $10500 ''## Return= $2200 → E)## = 0.265 = 26.5% = π D 500 ∗ $11 π₯6F-G = = 66.3% 8300 13 π 6F-G = − 1 = 18.18% 11 100 ∗ $28 π₯,C%C = = 33.7% 8300 40 π ,C%C = − 1 = 42.86% 28 500 ∗ $13 π₯6F-G' = = 61.9% 10500 100 ∗ $40 π₯,C%C' = = 38.1% 10500 Example 2: Assume your portfolio consists of $25,000 of Intel stock and $35,000 of ATP Oil and Gas. Your expected return is 18% for Intel and 25% for ATP Oil and Gas. What is the expected return for your portfolio? Initial Portfolio: $25,000 + $35,000 = $60,000 $25,000 π₯1(%4? = = 41.67% $60,000 $35,000 π₯83D = = 58.33% $60,000 π 1(%4? = 18%. π 83D = 25% π D = 0.4167 ∗ 0.18 + 0.5833 ∗ 0.25 = 22.08% New Value of Portfolio: $25,000 ∗ 1.18 + $35,000 ∗ 1.25 = $73250 32 Volatility of a Two-Stock Portfolio Combining Risks Returns for Three Stocks, and Portfolios of Pairs of Stocks: While the three stocks in the previous table have the same volatility and average return, the pattern of their returns differs. For example, when the airline stocks performed well, the oil stock tended to do poorly, and when the airlines did poorly, the oil stock tended to do well. • Consider the portfolio which consists of equal investments in West Air and Tex Oil. The average return of the portfolio is equal to the average return of the two stocks. • However, the volatility of 5.1% is much less than the volatility of the two individual stocks. • By combining stocks into a portfolio, we reduce risk through diversification. • The amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face common risks, and their prices move together. Determining Covariance and Correlation To find the risk of a portfolio, one must know the degree to which the stocks’ returns move together. Covariance The expected product of the deviations of two returns from their means. Covariance between Returns Ri and Rj: πΆππ£ Cπ C , π H E = πΈ˜(π C − πΈ [π C ])(π H − πΈ˜π H ™)™ Estimate of covariance from historical data: 1 πΆππ£ Cπ C , π H E = x (π − π ‘C )(π H,% − π ‘H ) π − 1 % C,% If the covariance is positive, the two returns tend to move together. If the covariance is negative, the two returns tend to move in opposite directions. Correlation A measure of the common risk shared by stocks that does not depend on their volatility: πΆππ£(π C , π H ) πΆπππCπ C , π H E = ππ·(π C )ππ·(π H ) The correlation between two stocks will always be between –1 and +1. 33 Example: Using the data from the Table, what is the covariance between General Mills and Ford? πΆππ£ ππ· ∗ ππ· πΆππ£ = πΆπππ ∗ ππ· ∗ ππ· πΆππ£ = 0.08 ∗ 0.47 ∗ 0.17 = 0.00639 Computing a Portfolio’s Variance and Volatility For a two-security portfolio: πΆπππ = The Variance of a Two-Stock Portfolio: πππ(π D ) = π₯$ ' πππ(π $ ) + π₯' ' πππ(π ' ) + 2π₯$ π₯' πΆππ£(π $ , π ' ) Example: Continuing with the date from the Table. Assume the annual standard deviation of returns is 43% for Intel and 68% for ATP Oil and Gas. If the correlation between Intel and ATP is 0.49, what is the standard deviation of your portfolio? π₯1(%4? = 0.4167 π₯83D = 0.5833 ππ·(π D ) = [(0.4167)' ∗ (0.43)' + (0.5833)' ∗ (0.68)' $ + 2(0.4167)(0.5833)(0.49)(0.43)(0.68)] J' = 0.5089 = 50.89% Volatility of a Large Portfolio The variance of a portfolio is equal to the weighted average covariance of each stock with the portfolio: πππ(π D ) = πΆππ£(π D , π D ) = πΆππ£ yx π₯C π C , π D z = x π₯C πΆππ£(π C , π D ) C which reduces to: C πππ(π D ) = x π₯C πΆππ£(π C , π D ) = x π₯C πΆππ£Cπ C , ∑H π₯H π H E = x x π₯C π₯H πΆππ£(π C , π H ) C C C H 34 Diversification with an Equally Weighted Portfolio A portfolio in which the same amount is invested in each stock. Variance of an Equally Weighted Portfolio of π Stocks: 1 πππ(π D ) = (π΄π£πππππ ππππππππ ππ πΌππππ£πππ’ππ ππ‘ππππ ) π 1 + y1 − z (π΄π£πππππ πΆππ£πππππππ πππ‘π€πππ ππ‘ππππ ) π Choosing an Efficient Portfolio In an inefficient portfolio, it is possible to find another portfolio that is better in terms of both expected return and volatility. In an efficient portfolio there is no way to reduce the volatility of the portfolio without lowering its expected return. Example: 35 Effect of Correlation Correlation has no effect on the expected return of a portfolio. However, the volatility of the portfolio will differ depending on the correlation. The lower the correlation, the lower the volatility we can obtain. As the correlation decreases, the volatility of the portfolio falls. The curve showing the portfolios will bend to the left to a greater degree. Short Sales Long Position: Short Position: A positive investment in a security. A negative investment in a security. In a short sale, you sell a stock that you do not own and then buy that stock back in the future. Short selling is an advantageous strategy if you expect a stock price to decline in the future. Consider investing 100% in Coca-Cola stock. As shown in on the previous graphic, other portfolios, such as the portfolio with 20% in Intel stock and 80% in Coca-Cola stock make the investor better off in two ways: It has a higher expected return, and it has lower volatility. As a result, investing solely in Coca-Cola stock is inefficient. 36 Efficient Portfolios with Many Stocks Consider adding Bore Industries to the two-stock portfolio: Although Bore has a lower return and the same volatility as Coca-Cola, it still may be beneficial to add Bore to the portfolio for the diversification benefits. Risk versus Return: Many Stocks The efficient portfolios, those offering the highest possible expected return for a given level of volatility, are those on the northwest edge of the shaded region, which is called the efficient frontier for these three stocks. In this case, none of the stocks, on its own, is on the efficient frontier, so it would not be efficient to put all our money in a single stock. 37 Identifying the Tangent Portfolio To earn the highest possible expected return for any level of volatility we must find the portfolio that generates the steepest possible line when combined with the riskfree investment. Sharpe Ratio: Measures the ratio of reward-to-volatility provided by a portfolio ππππ‘πππππ πΈπ₯πππ π π ππ‘π’ππ πΈ [π D ] − π" πβππππ π ππ‘ππ = = ππππ‘πππππ πππππ‘ππππ‘π¦ ππ·(π D ) The portfolio with the highest Sharpe ratio is the portfolio where the line with the riskfree investment is tangent to the efficient frontier of risky investments. The portfolio that generates this tangent line is known as the tangent portfolio. Combinations of the risk-free asset and the tangent portfolio provide the best risk and return trade-off available to an investor. This means that the tangent portfolio is efficient and that all efficient portfolios are combinations of the risk-free investment and the tangent portfolio. Every investor should invest in the tangent portfolio independent of his or her taste for risk. An investor’s preferences will determine only how much to invest in the tangent portfolio versus the risk-free investment. • Conservative investors will invest a small amount in the tangent portfolio. • Aggressive investors will invest more in the tangent portfolio. • Both types of investors will choose to hold the same portfolio of risky assets, the tangent portfolio, which is the efficient portfolio. Required Returns Portfolio Improvement: Beta and the Required Return. Beta of Portfolio π with Portfolio π: ππ·(π C ) ∗ πΆπππ(π C , π D ) πΆπππ(π C , π D ) π½CD = = ππ·(π D ) πππ(π D ) Increasing the amount invested in π will increase the Sharpe ratio of portfolio π if its expected return πΈ [π C ] exceeds the required return πC , which is given by: πC = π" + π½CD ∗ (πΈ [π D ] − π" ) 38 Example: Assume you own a portfolio of 25 different “large cap” stocks. You expect your portfolio will have a return of 12% and a standard deviation of 15%. A colleague suggests you add gold to your portfolio. Gold has an expected return of 8%, a standard deviation of 25%, and a correlation with your portfolio of -0.05. If the risk-free rate is 2%, will adding gold improve your portfolio’s Sharpe ratio? 0.25 ∗ (−0.05) π½KF?G = = −0.0833 0.15 πKF?G = 0.02 + (−0.0833) ∗ (0.12 − 0.02) = 0.01167 = 1.167% πΈ [πKF?G ] > πKF?G → πππ ππππππ πΊπππ π€πππ ππππππ£π π‘βπ ππππ‘πππππ CAPM Assumptions Three Main Assumptions: Assumption 1: Investors can buy and sell all securities at competitive market prices (without incurring taxes or transactions costs) and can borrow and lend at the risk-free interest rate. Assumption 2: Investors hold only efficient portfolios of traded securities— portfolios that yield the maximum expected return for a given level of volatility. Assumption 3: Investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities. Homogeneous Expectations: All investors have the same estimates concerning future investments and returns. Optimal Investing: The Capital Market Line When the CAPM assumptions hold, an optimal portfolio is a combination of the riskfree investment and the market portfolio. When the tangent line goes through the market portfolio, it is called the capital market line (CML). The expected return and volatility of a capital market line portfolio are: 39 Determining the Risk Premium Given an efficient market portfolio, the expected return of an investment is: The beta is defined as follows: Example: Assume the risk-free return is 5% and the market portfolio has an expected return of 12% and a standard deviation of 44%. ATP Oil and Gas has a standard deviation of 68% and a correlation with the market of 0.91. What is ATP’s beta with the market? 0.68 ∗ 0.91 π½83D = = 1.41 0.44 Under the CAPM assumptions, what is its expected return? πΈ [π 83D ] = 0.05 + 1.41(0.12 − 0.05) = 0.1487 = 14.87% Security Market Line There is a linear relationship between a stock’s beta and its expected return. The security market line (SML) is graphed as the line through the risk-free investment and the market. According to the CAPM, if the expected return and beta for individual securities are plotted, they should all fall along the SML. Beta of a Portfolio The beta of a portfolio is the weighted average beta of the securities in the portfolio. 40 SW7: Estimating the Cost of Capital Equity Cost of Capital The Capital Asset Pricing Model (CAPM) is a practical way to estimate. The cost of capital of any investment opportunity equals the expected return of available investments with the same beta. The estimate is provided by the Security Market Line equation: Example: Suppose you estimate that Walmart’s stock has a volatility of 16.1% and a beta of 0.20. A similar process for Johnson & Johnson yields a volatility of 13.7% and a beta of 0.54. Which stock carries more total risk? Which has more market risk? If the riskfree interest rate is 4% and you estimate the market’s expected return to be 12%, calculate the equity cost of capital for Walmart and Johnson & Johnson. Which company has a higher cost of equity capital? Total risk (volatility): πππππππ‘ = 16.1%. π½πβππ ππ & π½πβππ ππ = 13.7% Market risk (π½): πππππππ‘ = 0.2. π½πβππ ππ & π½πβππ ππ = 0.54 πL(L = 0.04 + 0.54(0.12 − 0.04) = 8.32% π7 = 0.04 + 0.2(0.12 − 0.04) = 5.6% Market Portfolio Constructing the market portfolio Market Capitalization: the total market value of a firm’s outstanding shares: Value-Weighted Portfolio A portfolio in which each security is held in proportion to its market capitalization: A value-weighted portfolio is an equal-ownership portfolio; it contains an equal fraction of the total number of shares outstanding of each security in the portfolio. Market Indexes Market Indexes report the value of a particular portfolio of securities. Examples: • S&P 500: A value-weighted portfolio of the 500 largest U.S. stocks. • Wilshire 5000: A value-weighted index of all U.S. stocks listed on the major stock exchanges. • Dow Jones Industrial Average (DJIA): A price-weighted portfolio of 30 large industrial stocks. • Swiss Performance Index (SPI): A value-weighted index of Switzerland’s overall stock market 41 Investing in a Market Index Passive Portfolio: A portfolio that is not rebalanced in response to price changes. Index Funds: Mutual funds that invest in the S&P 500, the Wilshire 5000, or some other index. Exchange-traded funds (ETFs): Trade directly on an exchange but represent ownership in a portfolio of stocks. Market index: Most practitioners use the S&P 500 as the market proxy, even though it is not actually the market portfolio. Market Risk Premium Determining the Risk-Free Rate The yield on U.S. Treasury securities. Surveys suggest most practitioners use 10- to 30-year treasuries. The Historical Risk Premium Estimate the risk premium (πΈ [π AB% ] − π" ) using the historical average excess return of the market over the risk-free interest rate. A Fundamental Approach Using historical data has two drawbacks: • Standard errors of the estimates are large • Backward looking, so may not represent current expectations. One alternative is to solve for the discount rate that is consistent with the current level of the index. Beta Estimation Estimating Beta from Historical Returns Recall, beta is the expected percent change in the excess return of the security for a 1% change in the excess return of the market portfolio. Consider Cisco Systems stock and how it changes with the market portfolio. As the scatterplot shows, Cisco tends to be up when the market is up, and vice versa. We can see that a 10% change in the market’s return corresponds to about a 20% change in Cisco’s return. Thus, Cisco’s return moves about two for one with the overall market, so Cisco’s beta is about 2. Beta corresponds to the slope of the best-fitting line in the plot of the security’s excess returns versus the market excess return. 42 Linear Regression Linear regression is the statistical technique that identifies the best-fitting line through a set of points. πΌC is the intercept term of the regression. π½C (π AB% − π" ) represents the sensitivity of the stock to market risk. When the market’s return increases by 1%, the security’s return increases by π½C %. πC is the error term and represents the deviation from the best-fitting line and is zero on average. Since πΈ [πC ] = 0: πΌC represents a risk-adjusted performance measure for the historical returns. • If πΌC is positive, the stock has performed better than predicted by the CAPM. • If πΌC is negative, the stock’s historical return is below the SML. Given data for πC , π C πππ π AB% statistical packages for linear regression can estimate π½C . A regression for Cisco using the monthly returns for 2000–2017 indicates the estimated beta is 1.56 with a 95% confidence interval from 1.3 to 1.8. Assuming Cisco’s sensitivity to market risk will remain stable over time, we would expect Cisco’s beta to be in this range in the near future. Example: Suppose you have estimated Tikyberd’s beta to be 0.8 with a 95% confidence interval of 0.65 to 0.95. Assuming the risk-free rate is 2% and the market is expected to return 12%, what range would you estimate for Tikyberd’s equity cost of capital? πΈ [π C ] = 2% + 0.65(12% − 2%) = 8.5% πΈ [π C ] = 2% + 0.95(12% − 2%) = 11.5% Debt Cost of Capital Debt Yields Versus Returns Yield to maturity is the IRR an investor will earn from holding the bond to maturity and receiving its promised payments. πΌπ π = πΈ [π G ] If there is little risk the firm will default, yield to maturity is a reasonable estimate of investors’ expected rate of return. If there is significant risk of default, yield to maturity will overstate investors’ expected return. Consider a one-year bond with YTM of y. For each $1 invested in the bond today, the issuer promises to pay $(1 + y) in one year. Suppose the bond will default with probability p, in which case bond holders receive only $(1 + y - L), where L is the expected loss (usually 60%) per $1 of debt in the event of default. So the expected return of the bond is: The importance of the adjustment depends on the riskiness of the bond. 43 Annual Default Rates by Debt Rating The average loss rate for unsecured debt is 60%. According to the Table, during average times the annual default rate for B-rated bonds is 5.5%. So, the expected return to B-rated bondholders during average times is 0.055 x 0.60=3.3% below the bond’s quoted yield. Debt Betas: • Alternatively, we can estimate the debt cost of capital using the CAPM. • Debt betas are difficult to estimate because corporate bonds are traded infrequently. • One approximation is to use estimates of betas of bond indices by rating category. Average Debt Betas by Rating and Maturity Example: In early 2013, auto parts retailer Autozone had outstanding 10-year bonds with a yield to maturity of 3% and a BBB rating. If corresponding risk-free rates were 1.5% and the market risk premium is 8%, estimate the expected return of Autozone’s debt. A Project’s Cost of Capital All-equity comparables Find an all-equity financed firm in a single line of business that is comparable to the project. Use the comparable firm’s equity beta and cost of capital as estimates. 44 Levered firms as comparables For levered firms, the cash flows generated by the firm’s assets are used to pay both debt and equity holders. As a result, the returns of the firm’s equity alone are not representative of the underlying assets; in fact, because of the firm’s leverage, the equity will often be much riskier. Thus, the beta of a levered firm’s equity will not be a good estimate of the beta of its assets and of our project. Asset (unlevered) cost of capital Expected return required by investors to hold the firm’s underlying assets. Weighted average of the firm’s equity and debt costs of capital. Asset (unlevered) beta Because the beta of a portfolio is the weighted-average of the betas of the securities in the portfolio, we have a similar expression for the firm’s asset or unlevered beta, which we can use to estimate the beta of our project: Example: Apple’s market capitalization in mid-2016 was $484 billion, and its beta was 1.03. At that same time, the company had $55 billion in cash and $69 billion in debt. Based on this data, estimate the beta of Apple’s underlying business enterprise. Industry Asset Betas We can combine estimates of asset betas for multiple firms in the same industry. Doing this will reduce the estimation error of the estimated beta for the project. 45 Project Risk Characteristics and Financing Differences in Project Risk: • Firm asset betas reflect market risk of the average project in a firm. • Individual projects may be more or less sensitive to market risk. Financial managers in multidivisional firms should evaluate projects based on asset betas of firms in a similar line of business. Another factor that can affect market risk of a project is its degree of operating leverage. Operating leverage is the relative proportion of fixed versus variable costs. A higher proportion of fixed costs increases the sensitivity of the project’s cash flows to market risk. • The project’s beta will be higher. • A higher cost of capital should be assigned. Financing and the Weighted Average Cost of Capital How might the project’s cost of capital change if the firm uses leverage to finance the project? Perfect capital markets: • In perfect capital markets, choice of financing does not affect cost of capital or project NPV. Taxes – A Big Imperfection: • When interest payments on debt are tax deductible, the net cost to the firm is given by: πΈπππππ‘ππ£π πππ‘ππ π‘ππ₯ πππ‘ππππ π‘ πππ‘π = π(1 − ππΆ) The Weighted Average Cost of Capital Weighted Average Cost of Capital (WACC) Given a target leverage ratio, How does π78,, compare with πM ? • Unlevered cost of capital (or pretax WACC) o Expected return investors will earn by holding the firm’s assets o In a world with taxes, it can be used to evaluate an all-equity project with the same risk as the firm. In a world with taxes, WACC is less than the expected return of the firm’s assets. • With taxes, WACC can be used to evaluate a project with the same risk and the same financing as the firm. 46 Example: Cavo Corp’s equity cost of capital is 15%, and its debt cost of capital is 7%. The corporate tax rate is 34%. The firm has $100 million in debt outstanding and a market capitalization of $250 million. What is Cavo’s unlevered cost of capital? What is Cavo’s weighted average cost of capital? Final Thoughts on Using the CAPM There are a large number of assumptions made in the estimation of cost of capital using the CAPM. How reliable are the results? The types of approximation are no different from those made throughout the capital budgeting process. Errors in cost of capital estimation are not likely to make a large difference in NPV estimates. CAPM is practical, easy to implement, and robust. CAPM imposes a disciplined approach to cost of capital estimation that is difficult to manipulate. CAPM requires managers to think about risk in the correct way. 47 SW8: Capital Structure Capital Structure is the relative proportions of debt, equity, and other securities that a firm has outstanding. Financing a Firm with Equity You are considering an investment opportunity: For an initial investment of $800 this year, the project will generate cash flows of either $1400 or $900 next year, depending on whether the economy is strong or weak, respectively. Both scenarios are equally likely. The project cash flows depend on the overall economy and thus contain market risk. As a result, you demand a 10% risk premium over the current risk-free interest rate of 5% to invest in this project. What is the NPV of this investment opportunity? The cost of capital for this project is 15% (risk free premium + risk free return. The expected cash flow in one year is: The NPV of the project is If you finance this project using only equity, how much would you be willing to pay for the project: If you can raise $1000 by selling equity in the firm, after paying the investment cost of $800, you can keep the remaining $200, the NPV of the project NPV, as a profit. Unlevered Equity: Equity in a firm with no debt Because there is no debt, the cash flows of the unlevered equity are equal to those of the project. Shareholder’s returns are either 40% or 10%. Because the cost of capital of the project is 15%, shareholders are earning an appropriate return for the risk they are taking. 48 Financing a Firm with Debt and Equity Suppose you decide to borrow $500 initially, in addition to selling equity. Because the project’s cash flow will always be enough to repay the debt, the debt is risk free, and you can borrow at the risk-free interest rate of 5%. You will owe the debt holders: $500 ∗ 1.05 = $525 ππ πππ π¦πππ Levered Equity: Equity in a firm that also has debt outstanding (2 types of Equity: Equity + Debt) Given the firm’s $525 debt obligation, shareholders will receive only $875 ($1400 $525 = $875) if the economy is strong and $375 ($900 − $525 = $375) if the economy is weak. What price E should the levered equity sell for? Which is the best capital structure choice for the entrepreneur? Modigliani and Miller argued that with perfect capital markets, the total value of a firm should not depend on its capital structure. • They reasoned that the firm’s total cash flows still equal the cash flows of the project and, therefore, have the same present value. Because the cash flows of the debt and equity sum to the cash flows of the project, by the Law of One Price the combined values of debt and equity must be $1000. Therefore, if the value of the debt is $500, the value of the levered equity must be $500. Because the cash flows of levered equity are smaller than those of unlevered equity, levered equity will sell for a lower price ($500 versus $1000). However, you are not worse off. You will still raise a total of $1000 by issuing both debt and levered equity. Consequently, you would be indifferent between these two choices for the firm’s capital structure. The Effect of Leverage on Risk and Return Leverage increases the risk of the equity of a firm. Therefore, it is inappropriate to discount the cash flows of levered equity at the same discount rate of 15% that you used for unlevered equity. Investors in levered equity will require a higher expected return to compensate for the increased risk. 49 The returns to equity holders are very different with and without leverage. • Unlevered equity has a return of either 40% or –10%, for an expected return of 15%. (Range of 50%) • Levered equity has higher risk, with a return of either 75% or –25%. (Range of 100%) • To compensate for this risk, levered equity holders receive a higher expected return of 25%. The relationship between risk and return can be evaluated more formally by computing the sensitivity of each security’s return to the systematic risk of the economy. Because the debt’s return bears no systematic risk, its risk premium is zero. In this particular case, the levered equity has twice the systematic risk of the unlevered equity and, as a result, has twice the risk premium. Summary In Summary: • In the case of perfect capital markets, if the firm is 100% equity financed, the equity holders will require a 15% expected return. • If the firm is financed 50% with debt and 50% with equity, the debt holders will receive a return of 5%, while the levered equity holders will require an expected return of 25% (because of their increased risk). • Leverage increases the risk of equity even when there is no risk that the firm will default. • Thus, while debt may be cheaper, its use raises the cost of capital for equity. Considering both sources of capital together, the firm’s average cost of capital with leverage is the same as for the unlevered firm. Example: Suppose the entrepreneur borrows $700 when financing the project. According to Modigliani and Miller, what should the value of the equity be? What is the expected return? (Use Returns for weak and strong economy of the tables above) Investment: $1000 Debt: $700 Equity: $300 1 1400 − 700(1.05) 1 900 − 700(1.05) πΈπ₯ππππ‘ππ π ππ‘π’ππ = s − 1t + s − 1t = 38.3% 2 300 2 300 50 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value The Law of One Price implies that leverage will not affect the total value of the firm. Instead, it merely changes the allocation of cash flows between debt and equity, without altering the total cash flows of the firm Modigliani and Miller (MM) showed that this result holds more generally under a set of conditions referred to as perfect capital markets: • Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows. • There are no taxes, transaction costs, or issuance costs associated with security trading. • A firm’s financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them. MM Proposition I: In a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure. MM and the Law of One Price MM established their result with the following argument: • In the absence of taxes or other transaction costs, the total cash flow paid out to all of a firm’s security holders is equal to the total cash flow generated by the firm’s assets. • Therefore, by the Law of One Price, the firm’s securities and its assets must have the same total market value. Homemade Leverage Homemade leverage is when investors use leverage in their own portfolios to adjust the leverage choice made by the firm. MM demonstrated that if investors would prefer an alternative capital structure to the one the firm has chosen, investors can borrow or lend on their own and achieve the same result. Assume you use no leverage and create an all−equity firm: An investor who would prefer to hold levered equity can do so by using leverage in his own portfolio. If the cash flows of the unlevered equity serve as collateral for the margin loan (at the risk-free rate of 5%), then by using homemade leverage, the investor has replicated the payoffs to the levered equity, as illustrated in the previous slide, for a cost of $500. By the Law of One Price, the value of levered equity must also be $500. Now assume you use debt, but the investor would prefer to hold unlevered equity. The investor can re-create the payoffs of unlevered equity by buying both the debt and the equity of the firm. Combining the cash flows of the two securities produces cash flows identical to unlevered equity, for a total cost of $1000 51 Example: Suppose there are two firms, each with date 1 cash flows of $1400 or $900 (as shown in the table before). The firms are identical except for their capital structure. One firm is unlevered, and its equity has a market value of $990. The other firm has borrowed $500, and its equity has a market value of $510. Does MM Proposition I hold? What arbitrage opportunity is available using homemade leverage? Unlevered Equity: $990 Levered Equity: $1010 ($500+$510) These prices violate MM Proposition I. Arbitrage Opportunity exists! The Market Value Balance Sheet A balance sheet where: • All assets and liabilities of the firm are included (even intangible assets such as reputation, brand name, or human capital that are missing from a standard accounting balance sheet). • All values are current market values rather than historical costs. The total value of all securities issued by the firm must equal the total value of the firm’s assets. Using the market value balance sheet, the value of equity is computed as follows: ππ ππ πΈππ’ππ‘π¦ = ππ ππ π΄π π ππ‘π − ππ ππ π·πππ‘ πππ ππ‘βππ πΏππππππ‘πππ Example: Assume that the social media app you developed has gone viral and you decided to sell the company, which has $60 million in assets. You plan on splitting the firm into equity, debt, and warrants, and you expect to sell $10 million in debt and $15 million in warrants. What will the value of the equity be in a perfect capital market? $60 πππ − 15 πππ − 10 πππ = 35 πππ 52 Application: A Leveraged Recapitalization Leveraged Recapitalization: When a firm uses borrowed funds to pay a large special dividend or repurchase a significant amount of outstanding shares Example: Harrison Industries is currently an all−equity firm operating in a perfect capital market, with 50 million shares outstanding that are trading for $4 per share. Harrison plans to increase its leverage by borrowing $80 million and using the funds to repurchase 20 million of its outstanding shares. Modigliani-Miller II: Leverage, Risk, and the Cost of Capital Leverage and the Equity Cost of Capital MM’s first proposition can be used to derive an explicit relationship between leverage and the equity cost of capital. • E: Market value of equity in a levered firm • D: Market value of debt in a levered firm • U: Market value of equity in an unlevered firm • A: Market value of the firm’s assets MM Proposition I states that: πΈ+π· =π =π΄ The total market value of the firm’s securities is equal to the market value of its assets, whether the firm is unlevered or levered. The cash flows from holding unlevered equity can be replicated using homemade leverage by holding a portfolio of the firm’s equity and debt The return on unlevered equity (π M ) is related to the returns of levered equity (π N ) and debt (π O ): Solving for π N : The levered equity return equals the unlevered return, plus a premium due to leverage. The amount of the premium depends on the amount of leverage, measured by the firm’s market value debt−equity ratio. 53 MM Proposition II: The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt−equity ratio. Cost of Capital of Levered Equity: Example: If the firm is all−equity financed, the expected return on unlevered equity is 15%. If the firm is financed with $500 of debt, the expected return of the debt is 5%. Therefore, according to MM Proposition II, the expected return on equity for the levered firm is: Example: Suppose the entrepreneur in the tables before borrows only $700 when financing the project. Recall that the expected return on unlevered equity is 15% and the risk-free rate is 5%. According to MM Proposition II, what will be the firm’s equity cost of capital? Capital Budgeting and the Weighted Average Cost of Capital If a firm is unlevered, all of the free cash flows generated by its assets are paid out to its equity holders. The market value, risk, and cost of capital for the firm’s assets and its equity coincide and therefore: • If a firm is levered, project π8 is equal to the firm’s weighted average cost of capital. Unlevered Cost of Capital (Pretax WACC): πM = π8 π78,, = πM = π8 54 WACC and Leverage with Perfect Capital Markets (a) Equity, debt, and weighted average costs of capital for different amounts of leverage. The rate of increase of πG and π4 , and thus the shape of the curves, depends on the characteristics of the firm’s cash flows. (b) Calculating the WACC for alternative capital structures. Example: Honeywell International Inc. (HON) has a market debt-equity ratio of 0.5. Assume its current debt cost of capital is 6.5%, and its equity cost of capital is 14%. If HON issues equity and uses the proceeds to repay its debt and reduce its debt-equity ratio to 0.4, it will lower its debt cost of capital to 5.75%. With perfect capital markets, what effect will this transaction have on HON’s equity cost of capital and WACC? Computing the WACC with Multiple Securities: If the firm’s capital structure is made up of multiple securities, then the WACC is calculated by computing the weighted average cost of capital of all of the firm’s securities. Levered and Unlevered Betas The effect of leverage on the risk of a firm’s securities can also be expressed in terms of beta: Unlevered Beta: A measure of the risk of a firm as if it did not have leverage, which is equivalent to the beta of the firm’s assets. If you are trying to estimate the unlevered beta for an investment project, you should base your estimate on the unlevered betas of firms with comparable investments. Leverage amplifies the market risk of a firm’s assets, π½M , raising the market risk of its equity. 55 Capital Structure Fallacies Leverage and Earnings per Share Example: LVI is currently an all−equity firm. It expects to generate earnings before interest and taxes (EBIT) of $10 million over the next year. Currently, LVI has 10 million shares outstanding, and its stock is trading for a price of $7.50 per share. LVI is considering changing its capital structure by borrowing $15 million at an interest rate of 8% and using the proceeds to repurchase 2 million shares at $7.50 per share. Suppose LVI has no debt. Because there is no interest and no taxes, LVI’s earnings would equal its EBIT and LVI’s earnings per share without leverage would be: If LVI recapitalizes, the new debt will obligate LVI to make interest payments each year of $1.2 million/year ($15 million × 8% interest/year = $1.2 million/year). As a result, LVI will have expected earnings after interest of $8.8 million. • Earnings = EBIT− Interest • Earnings = $10 million − $1.2 million = $8.8 million • Earnings per share rises to $1.10 LVI’s expected earnings per share increases with leverage. Are shareholders better off? NO! Although LVI’s expected EPS rises with leverage, the risk of its EPS also increases. While EPS increases on average, this increase is necessary to compensate shareholders for the additional risk they are taking, so LVI’s share price does not increase as a result of the transaction. Equity Issuances and Dilution Dilution: An increase in the total of shares that will divide a fixed amount of earnings It is sometimes (incorrectly) argued that issuing equity will dilute existing shareholders’ ownership, so debt financing should be used instead. As long as the firm sells the new shares of equity at a fair price, there will be no gain or loss to shareholders associated with the equity issue itself. Any gain or loss associated with the transaction will result from the NPV of the investments the firm makes with the funds raised. 56 Example: Suppose Jet Sky Airlines (J S A ) currently has no debt and 500 million shares of stock outstanding, which is currently trading at a price of $16. Last month the firm announced that it would expand and the expansion will require the purchase of $1 billion of new planes, which will be financed by issuing new equity. The current (prior to the issue) value of the equity and the assets of the firm is $8 billion. (500 million shares × $16 per share = $8 billion) Suppose JSA sells 62.5 million new shares at the current price of $16 per share to raise the additional $1 billion needed to purchase the planes. The market value of JSA’sassets grows because of the additional $1 billion in cash the firm has raised. Although the number of shares has grown to 562.5 million, the value per share is unchanged at $16 per share: MM: Beyond the Propositions Conservation of Value Principle for Financial Markets With perfect capital markets, financial transactions neither add nor destroy value, but instead represent a repackaging of risk (and therefore return). This implies that any financial transaction that appears to be a good deal may be exploiting some type of market imperfection. SW9: Payout Policy Distribution to Shareholders Payout Policy: The way a firm chooses between the alternative ways to distribute free cash flow to equity. 57 Dividends Important dates for dividend payout: • Declaration Date: The date on which the board of directors authorizes the payment of a dividend • Record Date: When a firm pays a dividend, only shareholders on record on this date receive the dividend • Ex-dividend Date: A date, two days prior to a dividend’s record date, on or after which anyone buying the stock will not be eligible for the dividend • Payable Date (Distribution Date): A date, generally within a month after the record date, on which a firm mails dividend checks to its registered stockholders If you buy a dividend between the Ex-dividend date and the payable date you won’t receive that dividend. Special types of dividends: • Special Dividend: A one-time dividend payment a firm makes, which is usually much larger than a regular dividend • Stock Split (Stock Dividend): When a company issues a dividend in shares of stock rather than cash to its shareholders Share repurchases An alternative way to pay cash to investors is through a share repurchase or buyback. The firm uses cash to buy shares of its own outstanding stock and reduce the numbers of shares. Types of repurchases: • Open Market Repurchase o When a firm repurchases shares by buying shares in the open market o Open market share repurchases represent about 95% of all repurchase transactions. • Tender Offer o A public announcement of an offer to all existing security holders to buy back a specified amount of outstanding securities at a prespecified price (typically set at a 10% to 20% premium to the current market price) over a prespecified period of time (usually about 20 days) o If shareholders do not tender enough shares, the firm may cancel the offer, and no buyback occurs. • Dutch Auction o A share repurchase method in which the firm lists different prices at which it is prepared to buy shares, and shareholders in turn indicate how many shares they are willing to sell at each price. The firm then pays the lowest price at which it can buy back its desired number of shares • Targeted Repurchase o When a firm purchases shares directly from a specific shareholder • Greenmail o When a firm avoids a threat of takeover and removal of its management by a major shareholder by buying out the shareholder, often at a large premium over the current market price 58 Comparison of Dividends and Share Repurchases Consider Genron Corporation. The firm’s board is meeting to decide how to pay out $20 million in excess cash to shareholders. Genron has no debt, its equity cost of capital equals its unlevered cost of capital of 12%. Alternative Policy 1: Pay Dividend with Excess Cash With 10 million shares outstanding, Genron will be able to pay a $2 dividend '# ACF immediately.$# ACF = $2 The firm expects to generate future free cash flows of $48 million per year; thus, it anticipates paying a dividend of $4.80 per share each year thereafter. Cum-dividend: When a stock trades before the ex-dividend date, entitling anyone who buys the stock to the dividend The cum-dividend price of Genron will be: After the ex-dividend date, new buyers will not receive the current dividend and the share price and the price of Genron will be: In a perfect capital market, when a dividend is paid, the share price drops by the amount of the dividend when the stock begins to trade ex-dividend. Alternative Policy 2: Share Repurchase (No Dividend) Suppose that instead of paying a dividend this year, Genron uses the $20 million to repurchase its shares on the open market. With an initial share price of $42, Genron will repurchase 476,000shares. ($20 million / $42 per share = 0.476 million shares) This will leave only 9.524 million shares outstanding. (10 million − 0.476 million = 9.524 million) The net effect is that the share price remains unchanged. Genron’s future dividends: It should not be surprising that the repurchase had no effect on the stock price. Expecting a future cashflow of $48 million, after the repurchase, the future dividend would rise to $5.04per share. ($48 million / 9.524 million shares = $5.04per share) Genron’s share price is: 59 In perfect capital markets, an open market share repurchase has no effect on the stock price, and the stock price is the same as the cum-dividend price if a dividend were paid instead. Investor Preferences: In perfect capital markets, investors are indifferent between the firm distributing funds via dividends or share repurchases. By reinvesting dividends or selling shares, they can replicate either payout method on their own. In the case of Genron, if the firm repurchases shares and the investor wants cash, the investor can raise cash by selling shares. This is called a homemade dividend. If the firm pays a dividend and the investor would prefer stock, they can use the dividend to purchase additional shares. Example: You own 1,000 shares in a firm that has historically paid dividends at a rate of 50% of earnings per share. Although earnings per share this year are $5, the firm has decided to retain all of the earnings and not pay a dividend. The current market price is $50 per share. How could you create a homemade dividend based on the firm’s dividend history? Alternative Policy 3: High Dividend (Equity Issue) Suppose Genron wants to pay dividend larger than $2 per share right now, but it only has $20 million in cash today. Thus, Genron needs an additional $28 million to pay the larger dividend now. To do this, the firm decides to raise the cash by selling new shares. Given a current share price of $42, Genron could raise $28 million by selling 0.67 million shares. ($28 million / $42 per share = 0.67 million shares) This will increase the total number of shares to 10.67 million. The new dividend per share will be: And the cum-dividend share price will be: Again, the share value is unchanged. Only after the dividend payment the price drops. 60 Modigliani–Miller and Dividend Policy Irrelevance There is a trade-off between current and future dividends. • If Genron pays a higher current dividend, future dividends will be lower. • If Genron pays a lower current dividend, future dividends will be higher. MM Dividend Irrelevance: In perfect capital markets, holding fixed the investment policy of a firm, the firm’s choice of dividend policy is irrelevant and does not affect the initial share price. The Tax Disadvantage of Dividends Taxes on Dividends and Capital Gains Shareholders must pay taxes on the dividends they receive, and they must also pay capital gains taxes when they sell their shares. Dividends are typically taxed at a higher rate than capital gains. In fact, long-term investors can defer the capital gains tax forever by not selling. The higher tax rate on dividends makes it undesirable for a firm to raise funds to pay a dividend. When dividends are taxed at a higher rate than capital gains, if a firm raises money by issuing shares and then gives that money back to shareholders as a dividend, shareholders are hurt because they will receive less than their initial investment. Example: A firm raises $25 million from shareholders and uses this cash to pay them $25 million in dividends Dividends are taxed at a 39% tax rate. Capital gains are taxed at a 20% tax rate. How much will shareholders receive after taxes? 61 Optimal Dividend Policy with Taxes When the tax rate on dividends is greater than the tax rate on capital gains, shareholders will pay lower taxes if a firm uses share repurchases rather than dividends. This tax savings will increase the value of a firm that uses share repurchases rather than dividends. The optimal dividend policy when the dividend tax rate exceeds the capital gain tax rate is to pay no dividends at all. The payment of dividends has declined on average over the last 30 years while the use of repurchases has increased. Trends in the Use of Dividends and Repurchases: Dividend Capture and Tax Clienteles The preference for share repurchases rather than dividends depends on the difference between the dividend tax rate and the capital gains tax rate. • Tax rates vary by income, by jurisdiction, and by whether the stock is held in a retirement account. • Given these differences, firms may attract different groups of investors depending on their dividend policy. The Effective Dividend Tax Rate Consider buying a stock just before it goes ex-dividend and selling the stock just after. The equilibrium condition must be: Which can be stated as: Where πQ>R is the cum-dividend price, π4S is the ex-dividend price, πT is the capital gains tax, and πG is the dividend tax rate 62 Thus, the effective dividend tax rate is: This measures the additional tax paid by the investor per dollar of after-tax capital gains income that is received as a dividend. Clientele Effects When the dividend policy of a firm reflects the tax preference of its investor clientele. Individuals in the highest tax brackets have a preference for stocks that pay no or low dividends, whereas tax-free investors and corporations have a preference for stocks with high dividends. Dividend-Capture Theory The theory that absent transaction costs, investors can trade shares at the time of the dividend so that non-taxed investors receive the dividend. An implication of this theory is that we should see large trading volume in a stock around the ex-dividend day, as high-tax investors sell and low-tax investors buy the stock in anticipation of the dividend, and then reverse those trades just after the exdividend date. Payout Versus Retention of Cash In perfect capital markets, once a firm has taken all positive-NPV investments, it is indifferent between saving excess cash and paying it out. With market imperfections, there is a trade-off: Retaining cash can reduce the costs of raising capital in the future, but it can also increase taxes and agency costs. Retaining Cash with Perfect Capital Markets If a firm has already taken all positive-NPV projects, any additional projects it takes on are zero or negative-NPV investments. Rather than waste excess cash on negative-NPV projects, a firm can use the cash to purchase financial assets. In perfect capital markets, buying and selling securities is a zero-NPV transaction, so it should not affect firm value. Thus, with perfect capital markets, the retention versus payout decision is irrelevant. Example: Payne Enterprises has $20,000,000 in excess cash. Payne is considering investing the cash in one-year Treasury bills paying 5% interest and then using the cash to pay a dividend next year. Alternatively, the firm can pay a dividend immediately, and shareholders can invest the cash on their own. In a perfect capital market, which option will shareholders prefer? 63 Taxes and Cash Retention Corporate taxes make it costly for a firm to retain excess cash. Cash is equivalent to negative leverage, so the tax advantage of leverage implies a tax disadvantage to holding cash. Example: What if Payne, from Example before, has a marginal tax rate of 39%. Would a taxexempt endowment prefer that Payne use its excess cash to pay the dividend immediately or invest the cash in a Treasury bill paying 5% interest and then pay out a dividend? Adjusting for Investor Taxes The decision to pay out versus retain cash may also affect the taxes paid by shareholders. When a firm retains cash, it must pay corporate tax on the interest it earns. In addition, the investor will owe capital gains tax on the increased value of the firm. In essence, the interest on retained cash is taxed twice. If the firm paid the cash to its shareholders instead, they could invest it and be taxed only once on the interest that they earn. The cost of retaining cash therefore depends on the combined effect of the corporate and capital gains taxes, compared to the single tax on interest income. Issuance and Distress Costs Generally, firms retain cash balances to cover potential future cash shortfalls, despite the tax disadvantage to retaining cash. A firm might accumulate a large cash balance if there is a reasonable chance that future earnings will be insufficient to fund future positive-NPV investment opportunities. The cost of holding cash to cover future potential cash needs should be compared to the reduction in transaction, agency, and adverse selection costs of raising new capital through new debt or equity issues 64 Example: Altgreen is an all-equity firm with 250 million shares outstanding.Altgreen has $300 million in cash and expects future free cash flows of $150 million per year. Management plans to use the cash to expand the firm’s operations, which will in turn increase future free cash flows by 10%. repurchase rather than the expansion change the share price? Agency Costs of Retaining Cash Firms should choose to retain to help with future growth opportunities and to avoid financial distress costs. It is not surprising that high-tech and biotechnology firms tend to retain and accumulate large amounts of cash. Dividend Smoothing: • The practice of maintaining relatively constant dividends • Firm change dividends infrequently, and dividends are much less volatile than earnings. Dividend Signaling Dividend Signaling Hypothesis: The idea that dividend changes reflect managers’ views about a firm’s future earning prospects. If firms' smooth dividends, the firm’s dividend choice will contain information regarding management’s expectations of future earnings. When a firm increases its dividend, it sends a positive signal to investors that management expects to be able to afford the higher dividend for the foreseeable future. When a firm decreases its dividend, it may signal that management has given up hope that earnings will rebound in the near term and so need to reduce the dividend to save cash. 65 Signaling and Share Repurchases Share repurchases are a credible signal that the shares are underpriced, because if they are overpriced a share repurchase is costly for current shareholders. If investors believe that managers have better information regarding the firm’s prospects and act on behalf of current shareholders, then investors will react favorably to share repurchase announcements. Stock Dividends, Splits, and Spin-Offs Stock Dividends and Splits With a stock dividend, a firm does not pay out any cash to shareholders. As a result, the total market value of the firm’s equity is unchanged. The only thing that is different is the number of shares outstanding. The stock price will therefore fall because the same total equity value is now divided over a larger number of shares. Example: Suppose Genron paid a 50% stock dividend (a 3:2 stock split) rather than a cash dividend. A shareholder who owns 100 shares before the dividend has a portfolio worth $4,200. ($42 x 100 = $4,200) After the dividend, the shareholder owns 150 shares. Because the portfolio is still worth $4,200, the stock price will fall to $28. ($4,200/150 = $28) Stock dividends are not taxed, so from both the firm’s and shareholders’ perspectives, there is no real consequence to a stock dividend. The number of shares is proportionally increased, and the price per share is proportionally reduced so that there is no change in value. The typical motivation for a stock split is to keep the share price in a range thought to be attractive to small investors. If the share price rises “too high,” it might be difficult for small investors to invest in the stock. Keeping the price “low” may make the stock more attractive to small investors and can increase the demand for and the liquidity of the stock, which may in turn boost the stock price. On average, announcements of stock splits are associated with a 2% increase in the stock price. Reverse Split: When the price of a company’s stock falls too low and the company reduces the number of outstanding shares. Spin Offs Spin offs are when a firm sells a subsidiary by selling shares in the subsidiary alone. Non-cash special dividends are commonly used to spin off assets or a subsidiary as a separate company. Advantages of Spin offs: • It avoids the transaction costs associated with a subsidiary sale. • The special dividend is not taxed as a cash distribution. 66 SW10: Financial Options Financial Option: A contract that gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price as some future date Option Basics: • Call Option: A financial option that gives its owner the right to buy an asset • Put Option: A financial option that gives its owner the right to sell an asset • Option Writer: The seller of an option contract Understanding Option Contracts: • Exercising an Option: When a holder of an option enforces the agreement and buys or sells a share of stock at the agreed-upon price • Strike Price (Exercise Price): The price at which an option holder buys or sells a share of stock when the option is exercised • Expiration Date: The last date on which an option holder has the right to exercise the option • American Option: Options that allow their holders to exercise the option on any date up to, and including, the expiration date • European Option: Options that allow their holders to exercise the option only on the expiration date American option is better than the European option! • The option buyer (holder): Holds the right to exercise the option and has a long position in the contract • The option seller (writer): Sells (or writes) the option and has a short position in the contract. Because the long side has the option to exercise, the short side has an obligation to fulfill the contract if it is exercised. The buyer pay the writer a premium. (One-time payment) Interpreting Stock Option Quotations Stock options are traded on organized exchanges. By convention, all traded options expire on the Saturday following the third Friday of the month. Open Interest: The total number of contracts of a particular option that have been written. • • • At-the-money: Describes anoption whose exerciseprice is equal to the current stock price In-the-money: Describes anoption whose value, if immediately exercised, would be positive Out-of-the-money: Describes anoption whose value, if immediately exercised, would be negative 67 • Deep in-the-money: Describes an option that is in-the-money and for which the strike price and the stock price are very far apart • Deep out-of-the-money: Describes an option that is out-of–the-money and for which the strike price and the stock price are very far apart The maximum amount you can be out-of-the-money is the premium paid for the option. Example: You have decided to purchase 2/15/2019 put contracts on the D J I A with an exercise price of $246. How much money will this purchase cost you? Is this option in-the-money or out-of-the-money? Options on Other Financial Securities Although the most commonly traded options are on stocks, options on other financial assets, like the S&P 100 index, the S&P 500 index, the Dow Jones Industrial index, and the NYSE index, are also traded. • Hedge: To reduce risk by holding contracts or securities whose payoffs are negatively correlated with some risk exposure • Speculate: When investors use contracts or securities to place a bet on the direction in which they believe the market is likely to move Option Payoffs at Expiration Long Position in an Option Contract The value of a call option at expiration is: πΆ = max (π − πΎ, 0) Where S is the stock price at expiration, K is the exercise price, C is the value of the call option, and max is the maximum of the two quantities in the parentheses. The value of a put option at expiration is: π = max (πΎ − π, 0) Where S is the stock price at expiration, K is the exercise price, P is the value of the put option, and max is the maximum of the two quantities in the parentheses. 68 Example: You own a put option on Dell stock with an exercise price of $12.50 that expires today. Plot the value of this option as a function of the stock price. Short Position in an Option Contract An investor that sells an option has an obligation. This investor takes the opposite side of the contract to the investor who bought the option. Thus, the seller’s cash flows are the negative of the buyer’s cash flows. Profits for Holding an Option to Expiration Although payouts on a long position in an option contract are never negative, the profit from purchasing an option and holding it to expiration could be negative because the payout at expiration might be less than the initial cost of the option. 69 Returns for Holding an Option to Expiration The maximum loss on a purchased call option is 100% (when the option expires worthless). Out-of-the money call options are more likely to expire worthless, but if the stock goes up sufficiently, it will also have a much higher return than an in-themoney call option. Call options have more extreme returns than the stock itself. The maximum loss on a purchased put option is 100% (when the option expires worthless). Put options will have higher returns in states with low stock prices. Put options are generally not held as an investment, but rather as insurance to hedge other risk in a portfolio. Combinations of Options Straddle A portfolio that is long a call option and a put option on the same stock with the same exercise date and strike price. This strategy may be used if investors expect the stock to be very volatile and move up or down a large amount but do not necessarily have a view on which direction the stock will move. Strangle A portfolio that is long a call option and a put option on the same stock with the same exercise date but the strike price on the call exceeds the strike price on the put. 70 Other Combinations of Options: • Protective Put: A long position in a put held on a stock you already own • Portfolio Insurance: A protective put written on a portfolio rather than a single stock. When the put does not itself trade, it is synthetically created by constructing a replicating portfolio. Portfolio insurance can also be achieved by purchasing a bond and a call option. Example of Portfolio Insurance: The plots show two different ways to insure against the possibility of the price of Amazon stock falling below $45. The orange line in (a) indicates the value on the expiration date of a position that is long one share of Amazon stock and one European put option with a strike of $45 (the blue dashed line is the payoff of the stock itself). The orange line in (b) shows the value on the expiration date of a position that is long a zero coupon risk-free bond with a face value of $45 and a European call option on Amazon with a strike price of $45 (the green dashed line is the bond payoff). Put-Call Parity Consider the two different ways to construct portfolio insurance discussed previously. • Purchase the stock and a put. • Purchase a bond and a call. Because both positions provide exactly the same payoff, the Law of One Price requires that they must have the same price. Therefore: π + π = ππ(πΎ) + πΆ Where K is the strike price of the option (the price you want to ensure that the stock will not drop below), C is the call price, P is the put price, and S is the stock price. Rearranging the terms gives an expression for the price of a European call option for a non-dividend-paying stock: πΆ = π + π − ππ(πΎ) This relationship between the value of the stock, the bond, and call and put options is known as put-call parity. If the stock pays a dividend, put-call parity becomes: πΆ = π + π − ππ(πΎ) − ππ(π·ππ£) 71 Example: You want to buy a one-year call option and put option on Dellibar. The strike price for each is $15. The current price per share of Dellibar is $14.79. Dellibar does not pay a dividend. The risk-free rate is 2.5%. The price of each call is $2.23. Using put-call parity, what should be the price of each put? Factors Affecting Option Prices Strike Price and Stock Price: • The value of a call option increases (decreases) as the strike price decreases (increases), all other things held constant. • The value of a put option increases (decreases) as the strike price increases (decreases), all other things held constant. • The value of a call option increases (decreases) as the stock price increases (decreases), all other things held constant. • The value of a put option increases (decreases) as the stock price decreases (increases), all other things held constant. Arbitrage Bounds on Option Prices An American option cannot be worth less than its European counterpart. A put option cannot be worth more than its strike price. A call option cannot be worth more than the stock itself. Intrinsic Value: • The amount by which an option is in-the-money, or zero if the option is out-ofthe-money • An American option cannot be worth less than its intrinsic value. Time Value: • The difference between an option’s price and its intrinsic value • An American option cannot have a negative time value. Option Prices and the Exercise Date American options, the longer the time to the exercise date, the more valuable the option. An American option with a later exercise date cannot be worth less than an otherwise identical American option with an earlier exercise date. However, a European option with a later exercise date can be worth less than an otherwise identical European option with an earlier exercise date. Option Prices and Volatility The value of an option generally increases with the volatility of the stock. Example: You are considering investing in Finray, which currently trades at $13.10 per share. A one-year call option with a strike price of $13 costs $0.87, while a put option with the same strike price and expiration costs $0.98. f the risk-free rate is 0.10%, what is Finray’s expected dividend? 72 Exercising Options Early Although an American option cannot be worth less than its European counterpart, they may have equal value. Non-Dividend-Paying Stocks πΆ = π + π − ππ(πΎ) For a non-dividend paying stock, Put-Call Parity can be written as: Where dis(K) is the amount of the discount from face value of the zero-coupon bond K. Because dis(K) and P must be positive before the expiration date, a European call always has a positive time value. Because an American option is worth at least as much as a European option, it must also have a positive time value before expiration. Thus, the price of any call option on a non-dividend-paying stock always exceeds its intrinsic value prior to expiration. This implies that it is never optimal to exercise a call option on a non-dividend paying stock early. You are always better off just selling the option. Because it is never optimal to exercise an American call on a non-dividend-paying stock early, an American call on a non-dividend paying stock has the same price as its European counterpart. However, it may be optimal to exercise a put option on a non-dividend paying stock early: When a put option is sufficiently deep in-the-money, dis(K) will be large relative to the value of the call, and the time value of a European put option will be negative. In that case, the European put will sell for less than its intrinsic value. However, its American counterpart cannot sell for less than its intrinsic value, which implies that an American put option can be worth more than an otherwise identical European option. Dividend-Paying Stocks The put-call parity relationship for a dividend-paying stock can be written as: If PV(Div) is large enough, the time value of a European call option can be negative, implying that its price could be less than its intrinsic value. Because anAmerican option can never be worth less than its intrinsic value, the price of the American option can exceed the price of a European option. With a dividend paying stock, it may be optimal to exercise the American call option early. When a company pays a dividend, investors expect the price of the stock to drop. When the stock price falls, the owner of a call option loses. Unlike the owner of the stock, the option holder does not get the dividend as compensation. However, by exercising early and holding the stock, the owner of the call option can capture the dividend. The put-call parity relationship for puts can be written as: As stated earlier, European options may trade for less than their intrinsic value. 73 Note that all the puts with a strike price of $1400 or higher trade for less than their exercise value. Options and Corporate Finance Equity as a Call Option: A share of stock can be thought of as a call option on the assets of the firm with a strike price equal to the value of debt outstanding. If the firm’s value does not exceed the value of debt outstanding at the end of the period, the firm must declare bankruptcy and the equity holders receive nothing. If the value exceeds the value of debt outstanding, the equity holders get whatever is left once the debt has been repaid. 74 Debt as an Option Portfolio Debt holders can be viewed as owners of the firm having sold a call option with a strike price equal to the required debt payment. • If the value of the firm exceeds the required debt payment, the call will be exercised; the debt holders will therefore receive the strike price and give up the firm. • If the value of the firm does not exceed the required debt payment, the call will be worthless, the firm will declare bankruptcy, and the debt holders will be entitled to the firm’s assets. Debt can also be viewed as a portfolio of riskless debt and a short position in a put option on the firm’s assets with a strike price equal to the required debt payment. • When the firm’s assets are worth less than the required debt payment, the owner of the put option will exercise the option and receive the difference between the required debt payment and the firm’s asset value. This leaves the debt holder with just the assets of the firm. • If the firm’s value is greater than the required debt payment, the debt holder only receives the required debt payment. SW11: Raising Equity Capital Equity Financing for Private Companies The initial capital that is required to start a business is usually provided by the entrepreneur and the immediate family. Often, a private company must seek outside sources that can provide additional capital for growth. It is important to understand how the infusion of outside capital will affect the control of the company. Sources of Funding • Friends and Family Financing • Angel Investors: Individual Investors who buy equity in small private firms. Finding angels is typically difficult. (Shark Tank) • Venture Capital Firm: A limited partnership that specializes in raising money to invest in the private equity of young firms • Venture Capitalists: One of the general partners who work for and run a venture capital firm Venture capital firms offer limited partners advantages over investing directly in startups themselves as angel investors. • Limited partners are more diversified. • They also benefit from the expertise of the general partners. The advantages come at a cost. General partners usually charge substantial fees. Most firms charge 20% of any positive return they make (carried interest). They also generally charge an annual management fee of about 2% of the fund’s committed capital. 75 • Private Equity Firms: Organized very much like a venture capital firm, but it invests in the equity of existing privately held firms rather than start-up companies. o Private equity firms initiate their investment by finding a publicly traded firm and purchasing the outstanding equity, thereby taking the company private in a transaction called a leveraged buyout (LBO). o In most cases, the private equity firms use debt as well as equity to finance the purchase. • Institutional Investors: Institutional investors, such as pension funds, insurance companies, endowments, and foundations, are active investors in private companies. o Institutional investors may invest directly in private firms, or they may invest indirectly by becoming limited partners in venture capital firms. • Corporate Investors: A corporation that invests in private companies. Also known as corporate partner, strategic partner, and strategic investor. o Although most other types of investors in private firms are primarily interested in the financial returns of their investments, corporate investors might invest for corporate strategic objectives, in addition to the financial returns. • Preferred Stock: Preferred stock issued by mature companies usually has a preferential dividend and seniority in any liquidation and sometimes special voting rights. o Preferred stock issued by young companies has seniority in any liquidation but typically does not pay regular cash dividends and often contains a right to convert to common stock. • Convertible Preferred Stock: Preferred stock that gives the owner an option to convert it into common stock on some future date. • Institutional Investors: Institutional investors, such as pension funds, insurance companies, endowments, and foundations, are active investors in private companies. o Institutional investors may invest directly in private firms, or they may invest indirectly by becoming limited partners in venture capital firms. • Corporate Investors: A corporation that invests in private companies. Also known as corporate partner, strategic partner, and strategic investor. o Although most other types of investors in private firms are primarily interested in the financial returns of their investments, corporate investors might invest for corporate strategic objectives, in addition to the financial returns. Venture Capital Investing Preferred Stock: Preferred stock issued by mature companies usually has a preferential dividend and seniority in any liquidation and sometimes special voting rights. Preferred stock issued by young companies has seniority in any liquidation but typically does not pay regular cash dividends and often contains a right to convert to common stock. Convertible Preferred Stock: Preferred stock that gives the owner an option to convert it into common stock on some future date. 76 RealNetworks, which was founded by Robert Glaser in 1993, was initially funded with an investment of approximately $1 million by Glaser. As of April 1995, Glaser’s $1 million initial investment in RealNetworks represented 13,713,439 shares of Series A preferred stock, implying an initial purchase price of about $0.07 per share. RealNetworks needed additional capital and management decided to raise this money by selling equity in the form of convertible preferred stock. The company’s first round of outside equity funding was Series B preferred stock. RealNetworks sold 2,686,567 shares of Series B preferred stock at $0.67 per share in April 1995.After this funding round the distribution of ownership was as follows: The Series B preferred shares were new shares of stock being sold by RealNetworks. At the price the new shares were sold for, Glaser’s shares were worth $9.2 million and represented 83.6% of the outstanding shares. Pre-Money Valuation: • At the issuance of new equity, the value of the firm’s prior shares outstanding at the price in the funding round. $9.2 million in the RealNetworks example. Post-Money Valuation: • At the issue of new equity, the value of the whole firm (old plus new shares) at the price at which the new equity sold. $11.0 million in the RealNetworks example. Over the next few years, RealNetworks raised three more rounds of outside equity in addition to the Series B funding round. Venture Capital Financing Terms: • Liquidation Preference • Seniority • Participation Rights • Anti-Dilution Protection o Down Round • Board Membership Exiting an Investment in a Private Company Exit Strategy: It details how investors will eventually realize the return from their investment. In July 1997, the post-money valuation of existing preferred stock was $8.99 per share. However, because RealNetworks was still a private company, investors could not liquidate their investment by selling their stock in the public stock markets. 77 Initial Public Offering (IPO) The process of selling stock to the public for the first time. Advantages and Disadvantages of Going Public Advantages: • Greater liquidity: Private equity investors get the ability to diversify. • Better access to capital: Public companies typically have access to much larger amounts of capital through the public markets. Disadvantages: • The equity holders become more widely dispersed. This makes it difficult to monitor management. • The firm must satisfy all of the requirements of public companies. SEC filings, Sarbanes-Oxley, etc. Types of Offerings Underwriter: An investment banking firm that manages a security issuance and designs its structure. Primary Offering: New shares available in a public offering that raise new capital. Secondary Offering: Shares sold by existing shareholders in an equity offering. Best-Efforts, Firm Commitment, and Auction IPOs Best-Efforts Basis: • For smaller IPOs, a situation in which the underwriter does not guarantee that the stock will be sold, but instead tries to sell the stock for the best possible price. Often such deals have an all-or-none clause: either all of the shares are sold on the IPO, or the deal is called off. Firm Commitment: • An agreement between an underwriter and an issuing firm in which the underwriter guarantees that it will sell all of the stock at the offer price. Auction IPO: • A method of selling new issues directly to the public. Rather than setting a price itself and then allocating shares to buyers, the underwriter in an auction IPO takes bids from investors and then sets the price that clears the market. Example: Ashton, Inc., is selling 900,000 shares of stock in an auction IPO. At the end of the bidding period, Ashton’s investment bank has received the following bids. What will the offer price of the shares be? 78 The Mechanics of an IPO • Underwriters and the Syndicate: o Lead Underwriter: The primary investment banking firm responsible for managing a security issuance o Syndicate: A group of underwriters who jointly underwrite and distribute a security issuance • SEC Filings o Registration Statement: A legal document that provides financial and other information about a company to investors prior to a security issuance o Preliminary Prospectus (Red Herring): Part of the registration statement prepared by a company prior to an IPO that is circulated to investors before the stock is offered o Final Prospectus: Part of the final registration statement prepared by a company prior to an IPO that contains all the details of the offering, including the number of shares offered and the offer price • Valuation o There are two ways to value a company: § Compute the present value of the estimated future cash flows. § Estimate the value by examining comparables (recent IPOs). o Road Show: During an IPO, when a company’s senior management and its underwriters travel around promoting the company and explaining their rationale for an offer price to the underwriters’ largest customers, mainly institutional investors such as mutual funds and pension funds. o Book Building: A process used by underwriters for coming up with an offer price based on customers’ expressions of interest. Example: RAXHouse is a private company considering going public. RAXHouse has assets of $585 million and liabilities of $415 million. The firm’s cashflow from operations was $137 million for the previous year. After the IPO, RAXHouse will have 118 million shares outstanding. The industry average cash flow per share multiple is 3.0, and the average book value per share is 2.3. Based on these multiples, estimate the IPO price for RAXHouse. 79 • Pricing the Deal and Managing Risk o Spread: The fee a company pays to its underwriters that is a percentage of the issue price of a share of stock. § For RealNetworks, the final offer price was $12.50 per share, and the company paid the underwriters a spread of $0.875 per share, exactly 7% of the issue price. Because this was a firm commitment deal, the underwriters bought the stock from RealNetworks for $11.625per share and then resold it to their customers for $12.50 per share. ($12.50 – $0.875 = $11.625) o When an underwriter provides a firm commitment, it is potentially exposing itself to the risk that the banking firm might have to sell the shares at less than the offer price and take a loss. § However, researchshows that 75% of IPOs experience an increase in share price on the first day (only 9% experience a decrease). o Over-Allotment Allocation (Greenshoe Provision) § In an IPO, an option that allows the underwriter to issue more stock, usually amounting to 15% of the original offer size, at the IPO offer price. o RealNetworks IPO had a greenshoe provision. § The prospectus specified that 3 million shares would be offered at $12.50 per share. In addition, the greenshoe provision allowed for the issue of an additional 450,000 shares at $12.50 per share. o Underwriters initially market both the initial allotment and the allotment in the greenshoe provision by short selling the greenshoe allotment. § If the issue is a success, the underwriter exercises the greenshoe option, thereby covering its short position. § If the issue is not a success, the underwriter covers the short position by repurchasing the greenshoe allotment in the aftermarket, thereby supporting the price. o Lockup: A restrictionthat prevents existing shareholders from selling their shares for some period, usually 180 days, after an IPO IPO Puzzles Underpricing: Generally, underwriters set the issue price so that the average first-day return is positive. As mentioned previously, research has found that 75% of first-day returns are positive. The average first day return in the United States is 17%. The underwriters benefit from the underpricing because it allows them to manage their risk. The pre-IPO shareholders bear the cost of underpricing. In effect, these owners are selling stock in their firm for less than they could get in the aftermarket. Although IPO returns are attractive, all investors cannot earn these returns. When an IPO goes well, the demand for the stock exceeds the supply. Thus, the allocation of shares for each investor is rationed. When an IPO does not go well, demand at the issue price is weak, so all initial orders are filled completely. Thus, the typical investor will have their investment in “good” IPOs rationed while fully investing in “bad” IPOs. Winner’s Curse: Refers to a situation in competitive bidding when the high bidder, by virtue of being the high bidder, has very likely overestimated the value of the item being bid on. You “win” (get all the shares you requested) when demand for the shares by others is low and the IPO is more likely to perform poorly. 80 Cyclicality The number of issues is highly cyclical. When times are good, the market is flooded with new issues; when times are bad, the number of issues dries up. Costs of an IPO A typical spread is 7% of the issue price. By most standards, this fee is large, especially considering the additional cost to the firm associated with underpricing. It is puzzling that there seems to be a lack of sensitivity of fees to issue size. One possible explanation is that by charging lower fees, an underwriter may risk signaling that it is not the same quality as its higher priced competitors. Relative Costs of Issuing Securities Long-Run Underperformance Although shares of IPOs generally perform very well immediately following the public offering, it has been shown that newly listed firms subsequently appear to perform relatively poorly over the following three to five years after their IPOs. The Seasoned Equity Offering (SEO) SEO is when a public company offers new shares for sale. Public firms use SEOs to raise additional equity. When a firm issues stock using an SEO, it follows many of the same steps as for an IPO. The main difference is that a market price for the stock already exists, so the price setting process is not necessary. Although not as costly as IPOs, seasoned offerings are still expensive. Underwriting fees amount to 5% of the proceeds of the issue. Rights offers have lower costs than cash offers. The Mechanics of an SEO • Primary Shares: New shares issued by a company in an equity offering • Secondary Shares: Shares sold by existing shareholders in an equity offering • Tombstones: A newspaper advertisement in which an underwriter advertises a security issuance There are two types of seasoned equity offerings: • Cash Offer: A type of SEO in which a firm offers the new shares to investors at large • Rights Offer: A type of SEO in which a firm offers the new shares only to existing shareholders. Rights offers protect existing shareholders from underpricing. 81 Price Reaction Researchers have found that, on average, the market greets the news of an SEO with a price decline. This is consistent with the adverse selection. SW12: Debt Financing Public Debt The Prospectus: Indenture: A public bond issue is similar to a stock issue. Included in a prospectus, it is a formal contract between a bond issuer and a trust company. The trust company represents the bondholders and makes sure that the terms of the indenture are enforced. In the case of default, the trust company represents the interests of the bond holders. Corporate bonds almost always pay coupons semiannually, although a few corporations have issued zero-coupon bonds. Most corporate bonds have maturities of 30 years or less. The face value or principal amount of a bond is denominated in standard increments, most often $1000. The face value does not always correspond to the actual money raised because of underwriting fees and/or if the bond is issued at a discount. Original Issue Discount Bond describes a bond that is issued at a discount. Types of Corporate Debt Unsecured Debt: A type of corporate debt that, in the event of bankruptcy, gives bondholders a claim to only the assets of the firm that are not already pledged as collateral on other debt. Notes: A type of unsecured corporate debt. Notes typically are coupon bonds with maturities shorter than 10 years. Debentures: A type of unsecured corporate debt. Debentures typically have longer maturities than notes. Secured Debt: A type of corporate debt in which specific assets are pledged as collateral. Mortgage Bonds: A type of secured corporate debt. Real property is pledged as collateral that bondholders have a direct claim to in the event of bankruptcy. All classes of securities are paid from the same cash flow source. Asset-Backed Bonds: A type of secured corporate debt. Specific assets are pledged as collateral that bondholders have a direct claim to in the event of bankruptcy. Can be secured by any kind of asset. 82 Seniority Seniority is a bondholder’s priority in claiming assets not already securing other debt. Most debenture issues contain clauses restricting the company from issuing new debt with equal or higher priority than existing debt. Subordinated Debentures: Debt that, in the event of a default, has a lower priority claim to the firm’s assets than other outstanding debt. Question: Why do bonds with lower seniority have higher yields than equivalent bonds with higher seniority? Bonds with Lower Seniority have higher yields because they are riskier. Investors need a higher reward because of the higher risk. Bond Markets Types of Bond markets: • International Bonds o Domestic Bonds § Bonds issued by a local entity and traded in a local market but purchased by foreigners. (No exchange risk) § They are denominated in the local currency. o Foreign Bonds § Bonds issued by a foreign company in a local market and intended for local investors. (Exchange risk) § They are denominated in the local currency. International Risk Yankee Bonds: Foreign bonds in the United States. Samurai Bonds: Foreign bonds in Japan Bulldogs: Foreign bonds in the United Kingdom Eurobonds: International bonds that are not denominated in the local currency of the country in which they are issued. Global Bonds: Bonds that are offered for sale in several different markets simultaneously. Global bonds can be offered for sale in the same currency as the country of issuance (unlike Eurobonds). Debt Private Debt Private debt is debt that is not publicly traded. It has the advantage that it avoids the cost of registration but has the disadvantage of being illiquid. Term Loans: A bank loan that lasts for a specific term. • Syndicated Bank Loan: A single loan that is funded by a group of banks rather than just a single bank. • Revolving Line of Credit: A credit commitment for a specific time period, typically two to three years, which a company can use as needed. Private Placements: A bond issue that is sold to a small group of investors rather than the general public. Because a private placement does not need to be registered, it is less costly to issue than public debt. 83 Sovereign Debt Sovereign Debt is debt issued by national governments. U.S. Treasury securities represents the single largest sector of the U.S. bond market. The U.S. Treasury issues: • Treasury Bills: Pure discount bonds with maturities up to 26 weeks • Treasury Notes: Semiannual coupon bonds with maturities of 2 to 10 years • Treasury Bonds: Semiannual coupon bonds with maturities longer than 10 years. o Long Bonds: Bonds issued by the U.S. Treasury with the longest outstanding maturities (currently 30 years) TIPS (Treasury-Inflation-Protected Securities): An inflation-indexed bond issued by the U.S. Treasury with maturities of 5, 10, and 20 years. They are standard fixed-rate coupon bonds with one difference: • The outstanding principal is adjusted for inflation. Municipal Bonds Municipal Bonds (Munis): Bonds issued by state and local governments. They are not taxable at the federal level (and sometimes at the state and local level as well). Sometimes referred to as tax-exempt bonds. Most pay semi-annual interest at one of the following rates: • Fixed Rate: Has the same coupon over the life of the bond • Floating Rate: The coupon of the bond is adjusted periodically. Asset-Backed Securities Asset-Backed Securities are securities made up of other financial securities. Security’s cash flows come from the cash flows of the underlying financial securities that “back” it. • Asset Securitization: The process of creating an asset-backed security. • Mortgage-Backed Security o Largest sector of the asset-backed security market o Backed by home mortgages o Largest issuers are U.S. government agencies and sponsored enterprises, such as the Government National Mortgage Association (GNMA) • Private organizations, such as banks, also issue asset-backed securities. o Backed by home mortgages, auto loans, credit card receivables, and other consumer loans • Collateralized Debt Obligation (CDO) o A re-securitization of other asset-backed securities o Often divided into tranches that are assigned different repayment priority Bond Covenants Covenants: Restrictive clauses in a bond contract that limit the issuers from undercutting their ability to repay the bonds. For example, covenants may: • Restrict the ability of management to pay dividends • Restrict the level of further indebtedness • Specify that the issuer must maintain a minimum amount of working capital 84 Callable Bonds Callable Bonds are bonds that contain a call provision that allows the issuer to repurchase the bonds at a predetermined price. A call feature allows the issuer of the bond the right (but not the obligation) to retire all outstanding bonds on (or after) a specific date (the call date), for the call price. The call price is generally set at or above, and expressed as a percentage of, the bond’s face value. A firm may choose to call a bond issue if interest rates have fallen. The issuer can lower its borrowing costs by exercising the call on the callable bond and then immediately refinancing the issue at a lower rate. Note: If rates rise after a bond is originally issued, there is no need to refinance. Holders of callable bonds understand that the issuer will exercise the call option only when the coupon rate of the bond exceeds the prevailing market rate. If a bond is called, investors must reinvest the proceeds when market rates are lower than the coupon rate they are currently receiving. This makes callable bonds relatively less attractive to bondholders than identical non-callable bonds. A callable bond will trade at a lower price (and therefore a higher yield) than an otherwise equivalent noncallable bond. Prices of Callable and Non-Callable Bonds on the Call Date Call Provisions Prior to the Call Date: • When market yields are high relative to the bond coupon, investors anticipate that the likelihood of exercising the call is low and the bond price is similar to an otherwise identical non-callable bond. • When market yields are low relative to the bond coupon, investors anticipate that the bond will likely be called, so its price is close to the price of a noncallable bond that matures on the call date. 85 Sinking Fund Sinking Fund is a method of repaying a bond in which a company makes regular payments into a fund administered by a trustee over the life of the bond. These payments are then used to repurchase bonds. This allows the firm to retire some of the outstanding debt without affecting the cash flows of the remaining bonds. • If the bonds are trading at a discount, the company will repurchase the bonds in the market. • If the bonds are trading above its face value, the bonds are repurchased at par. Which bonds are repurchased is decided by a lottery. Balloon Payment: A large payment that must be made on the maturity date of a bond. Some sinking funds require equal payments over the life of the bond. In other cases, the sinking fund payments are not sufficient to retire the entire issue and the company must make a balloon payment. Convertible Provisions Convertible Bond: A corporate bond with a provision that gives the bondholder an option to convert each bond owned into a fixed number of shares of common stock. Conversion Ratio: The number of shares received upon conversion of a convertible bond, usually stated per $1000 of face value. Conversion Price: The face value of a convertible bond divided by the number of shares received if the bond is converted. Example: Assume you have a convertible bond with a $1000 face value and a conversion ratio of 15. If you convert the bond into stock, you will receive 15 shares. If you do not convert, you will receive $1000. By converting you essentially “pay” $1000 for 15 shares, implying a price per share of $66.67. If the price of the stock exceeds $66.67, you will choose to convert; otherwise, you will take the cash. Often companies issue convertible bonds that are callable. With these bonds, if the issuer calls them, the holder can choose to convert rather than let the bonds be called. Convertible Bond Value Warrant Warrant is a call option written by the company itself on new stock. When a holder of a warrant exercises it and thereby purchases stock, the company delivers this stock by issuing new stock. Convertible debt carries a lower interest rate because it has an embedded warrant. 86 SW13: Working Capital Management Overview of Working Capital Most projects require the firm to invest in net working capital. The main components of net working capital are cash, inventory, receivables, and payables. πππΆ = πΆπ’πππππ‘ π΄π π ππ‘π − πΆπ’πππππ‘ πΏπππππππ‘πππ The Cash Cycle The Cash Cycle describes the length of time between when a firm pays cash to purchase its initial inventory and when it receives cash from the sale of the output produced from that inventory. Cash Conversion Cycle (CCC) is a measure of the cash cycle: Large CCC = Inefficiency Low / negative CCC = efficient Operating Cycle is the average length of time between when a firm originally purchases its inventory and when it receives the cash back from selling its product. Most firms buy their inventory on credit, which reduces the amount of time between the cash investment and the receipt of cash from that investment. Working Capital in Various Industries (2018) 87 Firm Value and Working Capital Any reduction in working capital requirements generates a positive free cash flow that the firm can distribute immediately to shareholders. Thus, efficiently managing working capital will maximize firm value. Example: Jackson Enterprises is considering a new project that will cost $10,000,000. The project will require an investment today of $1,500,000for net working capital. The firm will recover the investment in net working capital when the project ends in 10 years. The discount rate for this type of cash flow is 5.6% per year. What is the present value of the cost of working capital for the project? Trade Credit Terms Trade Credit: Net 30: The credit that the firm extends to its customers. Payment is not due until 30 days from the date of the invoice. Note: The number of days may vary, such as Net 15 or Net 60. 2/10 Net 30: If the buyer pays within 10 days, they will receive a 2% discount, otherwise the full amount is due in 30 days. Firms offer discounts to encourage customers to pay early. However, the discount also represents a cost to the selling firm. Note: The discount and number of days may vary, such as 1/10 Net 20 or 2/10 Net 45. Trade Credit and Market Frictions Cost of Trade Credit: Assume a firm sells a product for $100 and offers its customer terms of 2 /10, net 30. The customer doesn’t have to pay anything for the first 10 days, so it effectively has a zero interest loan for this period. If the customer takes advantage of the discount and pays within the 10-day discount period, the customer pays only $98 for the product. Rather than pay within 10 days, the customer has the option to use the $98 for an additional 20 days. The interest rate for the 20-day term of the loan is: $2 = 2.04% $98 With a 365-day year, this rate over 20 days corresponds to an effective annual rate of: By not taking the discount, the firm is effectively paying 44.6% annually to finance the purchase. If the firm can obtain a bank loan at a lower interest rate, it would be better off borrowing at the lower rate on day 10 and using the cash proceeds of the loan to take advantage of the discount offered by the supplier. The firm would then repay the bank loan on day 30. 88 Example: Your firm purchases goods from its supplier on terms of 2/10, net 45. What is the effective annual cost to your firm if it chooses not to take advantage of the trade discount offered? Benefits of Trade Credit: • Trade credit is simple and convenient to use, and it therefore has lower transaction costs than alternative sources of funds. • It is a flexible source of funds and can be used as needed. • It is sometimes the only source of funding available to a firm. Trade Credit Versus Standard Loans: Why offer trade credit? • Providing financing at below-market rates is an indirect way to lower prices for only certain customers. For example, automobile manufacturer’s often offer low cost financing, but only for the most qualified buyers. • Because a supplier may have an ongoing business relationship with its customer, it may have more information about the credit quality of the customer than a bank. • If the buyer defaults, the supplier may be able to seize the inventory as collateral. Managing Float Collection Float: The amount of time it takes for a firm to be able to use funds after a customer has paid for its goods. It consists of: • Mail Float: How long it takes a firm to receive a customer's payment check after the customer has mailed it • Processing Float: How long it takes a firm to process a customer’s payment check and deposit it in the bank • Availability Float: How long it takes a bank to give a firm credit for customer payments the firm has deposited in the bank Receivables Management Determining the Credit Policy: 1. Establishing Credit Standards a. Determine who will qualify for credit. 2. Establishing Credit Terms a. Determine the “net” period and if a discount will be offered. 3. Establishing a Collection Policy a. Determine course of action to take if a customer does not pay as agreed. Monitoring Accounts Receivable Accounts Receivable Days: The accounts receivable days is the average number of days that it takes a firm to collect on its sales. A firm can compare the accounts receivable days to the credit terms. • For example, if the credit terms specify “net 30” and the accounts receivable days outstanding is 45 days, the firm can conclude that its customers are paying 15 days late, on average. A firm can look at the trend in accounts receivable days. 89 Aging Schedules Aging Schedules categorize a firm’s accounts by the number of days they have been on the firm’s books. It can be prepared using either the number of accounts or the dollar amount of the accounts receivable outstanding. Example: Marley Corporation bills its accounts on terms of 2/10, Net 30. The firm’s accounts receivable are collected as follows: The company currently has $780,000in accounts outstanding. If Marley’s average daily credit sales is $22,000, what is the company’s accounts receivable days? Prepare an accounts receivable aging table for the company. Is the accounts receivable days a true representation of the accounts receivable collection experience? Payment Pattern: Provides information on the percentage of monthly sales that the firm collects in each month after the sale. For example, a firm may observe that 10% of its sales are usually collected in the month of the sale, 40% in the month following the sale, 25% two months after the sale, 20% three months after the sale, and 5% four months after the sale. Management can then watch for deviations from this pattern. Payables Management A firm should borrow using accounts payable only if trade credit is the least expensive source of funding. The cost of the trade credit depends on the credit terms. • The higher the discount percentage offered, the greater the cost of forgoing the discount. • The shorter the loan period, the greater the cost of forgoing the discount. A firm should always pay on the latest day allowed. 90 Determining Accounts Payable Days Outstanding A firm should monitor its accounts payable to ensure that it is making its payments at an optimal time. Calculate the accounts payable days outstanding and compare it to the credit terms. • If the accounts payable outstanding is 45 days and the terms are 2/10, net 30, the firm can conclude that it generally pays late and may be risking supplier difficulties. • If the accounts payable days outstanding is 20 days, the firm is paying too early. It could be earning another 10 days’ interest on its money. Stretching Accounts Payable Stretching the Accounts Payable is when a firm ignores a payment due period and pays later. For example: • Given Net 30 terms, a firm may pay on day 45. • Given 2/10 Net 30 terms, a firm may pay on day 12 and still take the 2% discount. Suppliers may react to a firm whose payments are always late by imposing late fees or terms of cash on delivery (COD) or cash before delivery (CBD). Example: Your firm’s supplier offers 1/10, Net 30 terms. What is the effective annual cost of credit if you pay on day 30? What if your firm does not pay the supplier until day 50? Effective Annual Cost: $ )0/J ()#V$#) $ )0/J (/#V$#) π·ππ¦ 30: ¦1 + 55§ − 1 = 20.13% π·ππ¦ 50: ¦1 + 55§ − 1 = 9.6% The more advantage taken from supplier, the better for us. Inventory Management Benefits of Holding Inventory: • Prevent stock-outs • Seasonality in demand Costs of Holding Inventory: • Acquisition costs • Order costs • Carrying costs Minimizing these costs involves trade-offs. Just-in-Time (JIT) Inventory Management: When a firm acquires inventory precisely when needed so that its inventory balance is always zero, or very close to it. JIT is often used to reduce carrying costs as much as possible. Cash Management Motivation for Holding Cash: • Transactions Balance: The amount of casha firm needs to be able to pay its bills • Precautionary Balance: The amount of cash a firm holds to counter the uncertainty surrounding its future cash needs • Compensating Balance: An amount a firm’s bank may require the firm to maintain in an account at the bank as compensation for services the bank may perform 91 Alternative Investments Thus far, it has been assumed that the firm will invest any cash in short-term securities. A firm may choose from a variety of short-term securities that differ with regard to their default risk and liquidity risk. Money Market Investment Options 92
