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NAME:\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t...\t... STUDENT\tID\t#\t...\t...\t...\t...\t... University\tof\tNew\tBrunswick,\tSaint\tJohn Faculty\tof\tBusiness BA\t3425:\tManagerial\tFinance\t[SJ01A\t&\tSJIO] FINAL\tEXAM Total\tPoints:\t100 Duration:\t2\tHours\tand\t30\tMinutes Instructions It's\ta\tCLOSED\tbook\ttest. Formula\tCHEAT\tSHEET\twill\tbe\tprovided. NO\telectronic\tdevices,\tother\tthan\tyour\tcalculator. If you are using calculator, write down your INPUT VARIABLES, otherwise I won't be able to check\tyour\tanswers. Part\tI:\tTrue/False\twith\tExplanation\t[10*3\t=\t30\tpoints] 1. You\thold\ta\twinning\tticket\tfrom\tyour\tprovincial\tlottery.\tIt\tentitles\tthe\tbearer\tto\treceive\tpayments\tof $50,000 at the end of each of the next 20 years. Given what you know about the time value of money,\tyou\tshould\tbe\table\tto\tsell\tthis\tticket\tfor\tno\tless\tthan\t$1\tmillion\tin\tthe\topen\tmarket. 2. Beatrice has a credit card that applies interest every month to her account balance. In this case, Beatrice\tis\tpaying\tan\tinterest\trate\tthat\tis\tgreater\tthan\tthe\tAPR\tshown\ton\ther\tbilling\tstatement. 3. If\tone\tuses\tthe\tconstant\tgrowth\tmodel\tto\tvalue\tstock,\tone\tassumes\tthat\tP1\t=\tP0 (1\t+\tg),\tP2\t=\tP0 (1\t+ g),\tetc. 4. You\tare\tattempting\tto\tvalue\tthe\tshares\tof\ta\tnew,\thigh-technology\tfirm\tin\ta\tdeveloping\tindustry.\tYou would\tMOST\tlikely\tuse\tconstant\tdividend\tgrowth\tmodel. 1 5. If\tthe\tcost\tof\tcapital\tis\tgreater\tthan\tthe\tIRR,\tthe\tproject\tshould\tbe\taccepted. 6. All\telse\tthe\tsame,\tshortening\tthe\tfirm's\tcash\tcycle\twill\tlikely\tincrease\tthe\tfirm's\tprofitability. 7. The primary objective of short-term financial management is to minimize the investment in net working\tcapital. 8. If\tthe\tyield\tcurve\tis\tupward\tsloping,\tthen\tshort-term\tdebt\twill\tbe\texpensive\tthan\tlong-term\tdebt. 9. Disbursement\tfloat\tarises\twhen\tyou\tbasically\treceive\ta\tcheck\tfrom\tyour\tcustomer. 10. The\tbasic\tfactors\tto\tbe\tevaluated\tin\tthe\tcredit\tevaluation\tprocess,\tthe\tfive\tCs\tof\tcredit,\tare\tCapital, collateral,\tcontrol,\tcharacter,\tand\tcapacity. 2 Part\tII:\tQuantitative\tProblems\t[70\tpoints] 1.\tDouglass\tInc.\twants\tto\testablish\tan\temployee\treward\tprogram\twhereby\tthey\tcan\tpay\tfive\temployees $1,000\ta\tyear\teach\tfor\ttwenty\tyears.\tThe\tfirst\tpayment\tis\tto\tbegin\tone\tyear\tfrom\ttoday.\tThe\tcompany expects\tto\tearn\t3.25%\ton\tthe\tfunds\tin\tthis\tprogram.\tHow\tmuch\tdoes\tthe\tcompany\thave\tto\tdeposit\ttoday to\ttotally\tfund\tthis\treward\tprogram?\t[10\tpoints] 2.\tWestover\tRidge\toffers\ta\t9\tpercent\tcoupon\tbond\twith\tsemiannual\tpayments\tand\ta\tyield\tto\tmaturity\tof 11.68 percent. The bonds mature in 16 years. What is the market price per bond if the face value is $1,000?\t[10\tpoints] 3 3.\tHuang\tCompany's\tlast\tdividend\twas\t$1.25.\tThe\tdividend\tgrowth\trate\tis\texpected\tto\tbe\tconstant\tat\t15% for 3 years, after which dividends are expected to grow at a rate of 6% forever. If the firm's required return\t(rs)\tis\t11%,\twhat\tis\tits\tcurrent\tstock\tprice?\t[10\tpoints] 4 4.\tYour\tdivision\tis\tconsidering\ttwo\tinvestment\tprojects,\teach\tof\twhich\trequires\tan\tupfront\texpenditure\tof $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following\tafter-tax\tcash\tflows\t(in\tmillions\tof\tdollars):\t[5*4\t=\t20\tpoints] Year Project\tA Project\tB 1 5 20 2 10 10 3 15 8 4 20 6 a. Calculate\tthe\tpayback\tperiod\tfor\teach\tof\tthe\tprojects. b. Calculate\tthe\tdiscounted\tpayback\tperiod\tfor\teach\tof\tthe\tprojects. c. If the two projects are independent and the cost of capital is 10%, which project or projects should\tthe\tfirm\tundertake? d. If\tthe\ttwo\tprojects\tare\tmutually\texclusive\tand\tthe\tcost\tof\tcapital\tis\t5%,\twhich\tproject\tshould\tthe firm\tundertake? e. Calculate\tthe\tinternal\trate\tof\treturn\tof\teach\tproject?\tWhich\tproject\tshould\tthe\tfirm\tchoose\tand why?\tConsider\tthe\ttwo\tprojects\tare\tmutually\texclusive. 5 5.\tDewey\tCorporation\thas\tthe\tfollowing\tdata,\tin\tthousands.\tAssuming\ta\t365-day\tyear,\twhat\tis\tthe\tfirm's cash\tconversion\tcycle?\t[10\tpoints] Annual\tsales $45,000 Annual\tcost\tof\tgoods\tsold $31,500 Inventory $4,000 Accounts\treceivable $2,000 Accounts\tpayable $2,400 6. Karloff Medical Supply maintains an average inventory of 2,000 human skulls for sale to medical schools\tand\tfilmmakers.\tThe\tcarrying\tcost\tper\tskull\tper\tyear\tis\testimated\tto\tbe\t$5.\tBoris\tplaces\tan\torder for 10,000 skulls on the first of each month and the order cost is $75. Calculate the economic order quantity\t(EOQ.\t[10\tpoints] 6 Cheat Sheet for Formula BA 3425: Managerial Finance Chapter 3: Working with Financial Statements Current Ratio = Current Assets/Current Liabilities Quick Ratio = (Current Assets - Inventories)/Current Liabilities Cash Ratio = Cash & Cash Equivalents/Current Liabilities Debt/Equity Ratio = Total debt/Total equity Long-Term Debt-to-Equity ratio = Long-term debt/ (Long-term debt + Total equity) Debt-to-Asset Ratio = Total Liabilities/Total Assets Times Interest Earned (TIE) = EBIT/Interest Expenses Cash Coverage Ratio = (EBIT + Depreciation)/Interest Expense Inventory Turnover = Cost of sales/ Inventories Receivable Turnover = Revenues/Average Accounts Receivable Total Asset Turnover = Revenues/ Total Assets Return on Invested Capital (ROIC) = Net Income/(Long-term debt + Shareholders' equity) Return on Assets (ROA) = Net Income/Total Assets Return on Equity (ROE) = Net Income/Equity Gross Profit Margin = Gross profit/Sales Operating Profit Margin = Operating profit/Sales Net Profit Margin = Net income/Sales P/E ratio = Price per share/Earnings per share Market-to-book ratio = Market value per share/Book value per share Chapter 5: Time Value of Money FV = PV (1+r)t PV = FV/(1+r)t Chapter 6: Discounted Cash Flow Valuation Perpetuity: PV = C/r PV of Growing Perpetuity PV = C rg PV of Growing Annuity PV = T C1 1 + g 1 r g 1+ r Chapter 7: Interest Rates and Bond Valuation Accrued Interest = Coupon payment X (No. of days from last coupon to settlement date/Number of days in coupon period) PV (bond) = PV(coupon) + PV(face value) Effective annual rate = (1+APR/m)m - 1 Current yield = Annual coupon payment/Current bond price Rate of return = (Coupon income + Price change)/Investment Fisher Equation: (1+Nominal interest rate) = (1+Real interest rate) (1+Inflation rate) FP n Approx.YTM = F+P 2 C = Coupon payment F = Facevalue P = Pr ice C+ n = Years to matuiry m APR EAR = 1+ 1 m 1 EAR m APR = m 1+ 1 m EAR = ex -1 [continuous compounding] APR = ln(1+EAR) [continuous compounding] Chapter 8: Stock Valuation Rate of return = Dividend yield + Capital gain yield Dividend yield = D1/P0 Zero growth case: P0 = D1/r Constant growth case: P0 = D1/(r-g) Supernormal Growth case: D1 D2 Dt Pt + + ...+ + 1 2 t (1+ r) (1+ r) (1+ r) (1+ r)t where P0 = Pt = Dt (1+ g) rg Part II Question 1 Assumptions: Douglas Inc will employ the five employees for the next 20 years with certainty. The expected return on investment is constant over the 20 years. The employee reward program is funded by a once-off payment at inception. The pay-out from the program is constant over 20 years. The amount to deposit today is the sum of the present value of future payments from the program (annuity in arrears). This is calculated as follows using a financial calculator: PMT: $1,000 x 5 = $5,000. N: 20. I/Y: 3.25 FV: $0.00. COMP: PV. Solution The company has to deposit $72,696.73. Part II Question 1 Assumptions: Douglas Inc will employ the five employees for the next 20 years with certainty. The expected return on investment is constant over the 20 years. The employee reward program is funded by a once-off payment at inception. The pay-out from the program is constant over 20 years. The amount to deposit today is the sum of the present value of future payments from the program (annuity in arrears). This is calculated as follows using a financial calculator: PMT: $1,000 x 5 = $5,000. N: 20. I/Y: 3.25 FV: $0.00. COMP: PV. Solution The company has to deposit $72,696.73. Question 2 The market price of the bond is equal to the present value of all future bond proceeds. This is calculated as follows: PMT: Par value x coupon rate coupon frequency = $1,000 x 9% 2 = $45.00. N: Number of payments = Term of bond x coupon frequency = 16 x 2 = 32. I/Y: Periodic (6 months) interest = 11.68 2 = 5.84. FV: $1,000.00. COMP: PV. Solution The market price per bond is $807.86. 13 Return, Risk, and the Security Market Line Chapter Outline Expected Returns and Variances of Individual Assets Expected Returns and Variances of Portfolios Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta Capital Asset Pricing Model (CAPM) Arbitrage Pricing Theory Value investors on risk Risk perception 13-2 Introduction From Chapter 12 (which we didn't cover), we need the following two concepts: 1. There is a reward, on average, for bearing risk (we call it risk premium) 2. Risk premium is larger for riskier investment 13-3 Expected Returns Expected returns are based on the probabilities of possible outcomes. In this context, \"expected\" means average if the process is repeated many times. The \"expected\" return does not even have to be a possible return. n E ( R) pi Ri i 1 13-4 Expected Returns - Example 1 Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? State Probability Stock C Stock T Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ?? 0.02 0.01 13-5 Expected Returns - Example 1 Formula Approach: n E ( R) pi Ri i 1 RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.9% RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7% 13-6 Variance and Standard Deviation Variance and standard deviation measure the volatility of returns (i.e. risk). Variance is the multiplication of squared deviations from the expected return by the probability of each possible outcomes. n 2 pi (Ri E(R))2 i1 Standard deviation is just the square root of variance. n pi (Ri E(R))2 i1 13-7 Variance and Standard Deviation - Example 1 Consider the previous example. What is the variance and standard deviation for each stock? Stock C 2 .3(.15 .099)2 .5(.1 .099)2 .2(.02 .099)2 .002029 .045 Stock T 2 .3(.25 .177)2 .5(.2 .177)2 .2(.01 .177)2 .007441 .0863 13-8 Quick Quiz I Consider the following information: State Probability ABC, Inc. Boom .25 .15 Normal .50 .08 Slowdown .15 .04 Recession .10 -.03 What is the expected return? What is the variance? What is the standard deviation? 13-9 13.2 Portfolios Portfolio is a group of assets such as stocks and bonds held by an investor. An asset's risk and return is important in how it affects the risk and return of the portfolio. The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets. 13-10 Portfolio Weights - Example Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? Stock Amount Invested Weight in the Portfolio ABC $2,000 2000/15000 = .133 DEF $3,000 3000/15000 = .20 GHI $4,000 4000/15000 = .267 JKL $6,000 6000/15000 = .40 13-11 Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio. m E ( RP ) wj E ( Rj ) j 1 13-12 Expected Portfolio Returns - Example If the individual stocks have the following weights (calculated previously) and the expected returns, what is the expected return for the portfolio? Stock Weight in the Portfolio Expected Return ABC .133 19.65 DEF .2 8.96 GHI .267 9.67 JKL .4 8.13 E(RP) = .133(19.65) + .2(8.96) + .267(9.67) + .4(8.13) = 10.24% 13-13 Portfolio Variance Compute the portfolio return for each state: RP w1 R1 w2 R2 ... wmRm Compute the expected portfolio return using the same formula as for an individual asset. Compute the portfolio variance and standard deviation using the same formulas as for an individual asset. 13-14 Portfolio Variance - Example Invest 60% of your money in Asset A and 40% in Asset B. State Probability A B Boom .50 70% 10% Bust .50 -20% 30% What is the expected return and standard deviation for each asset? What is the expected return and standard deviation for the portfolio? 13-15 Individual Asset's Variance - Example Asset A: E(RA) = .5(70) + .5(-20) = 25% Variance(A) = .5(70-25)2 + .5(-20-25)2 = 2,025 Std. Dev.(A) = 2025 = 45% Asset B: E(RB) = .5(10) + .5(30) = 20% Variance(B) = .5(10-20)2 + .5(30-20)2 = 100 Std. Dev.(B) = 100 = 10% 13-16 Portfolio Variance - Example Portfolio return in boom = .6(70) + .4(10) = 46% Portfolio return in bust = .6(-20) + .4(30) = 0% Expected return = .6(25) + .4(20) = 23% Variance of portfolio = .5(46 - 23)2 + .5(0 - 23)2 = 529 Standard deviation = 529 = 23% 13-17 Risk and Diversification Correlation Coefficient (r) Cov(x, y) r x y Covariance (xi x)(yi y) Cov(x, y) N i1 N 13-18 Figure 13.1 - Different Correlation Coefficients 13-19 Figure 13.1 - Different Correlation Coefficients 13-20 Figure 13.1 - Different Correlation Coefficients 13-21 Figure 13.2 - Graphs of Possible Relationships Between Two Stocks 13-22 Quick Quiz II Consider the following information State Probability X Z Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10% What is the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? 13-23 Risk Knight (1921) classifies risk as situations where outcomes are random but the probability distribution governing the outcome is known and therefore expectations (for example, expected returns) can be quantified. Academics measure risk as standard deviation or variance. However, value investors define risk quite differently. 13-24 13.4 Risk: Systematic & Unsystematic Risk The risk of owning an asset comes from surprises - unanticipated events. Some of these events are specific to a particular industry or to a company and some events are more general, affecting everybody in the market. 13-25 Systematic Risk A risk that influences a large number of assets. Because systematic risks are market-wide effects, they are sometimes called market risk. Also known as non-diversifiable risk. Includes such things as changes in GDP, inflation, interest rates, etc. 13-26 Unsystematic Risk A risk factor that affects at most a small number of assets. Because these risks are unique to individual companies or assets, they are sometimes called unique or asset-specific risks. Includes such things as labor strikes, shortages, etc. 13-27 Diversification Diversification is a risk management technique that mixes a wide variety of investments within a portfolio. The rationale is that a portfolio of different kinds of investments will, on average, yield higher returns and pose a lower risk than any individual investment found within the portfolio. There are benefits to diversification whenever the correlation between two stocks is less than perfect (p 1.0, stock is riskier than average. If b 3 means the company is safe; bankruptcy unlikely. 20-21 Quick Quiz If the Z-score cut off for a credit worthy business is 2.7 or higher, would you accept the following client? EBIT total assets 0.12 sales 1.4 total assets retained earnings total assets working capital total assets . =0.4 = 0.12 market equity . 0.9 book debt 20-22 LO4 20.6 Collection Policy Monitoring receivables Keep an eye on average collection period relative to your credit terms Use an aging schedule to determine percentage of payments that are being made late Collection effort Delinquency letter Telephone call Collection agency Legal action 20-23 20.7 Inventory Management LO5 Inventory can be a large percentage of a firm's assets. Costs associated with carrying too much inventory. Costs associated with not carrying enough inventory. Inventory management tries to find the optimal trade-off between carrying too much inventory versus not enough. 20-24 Inventory as a Percentage of Total Current Assets Company 2015 2014 2013 2012 2011 2010 2009 WMT 71.34 73.32 73.08 74.06 70.05 68.11 70.50 48.08 52.46 48.43 48.16 52.29 53.26 62.40 71.53 48.22 48.14 44.13 38.97 38.34 78.77 79.64 89.54 88.31 74.56 82.34 75.66 COST* TGT DG 20-25 Inventory Turnover Ratio Company 2015 2014 2013 2012 2011 2010 2009 WMT 8.08 7.98 10.71 10.98 11.58 12.47 11.71 11.64 13.97 13.39 13.83 13.21 14.38 5.83 6.04 9.28 8.82 8.87 9.10 9.69 4.71 3.76 6.68 7.37 7.38 7.76 7.39 COST* TGT DG 20-26 LO5 Types of Inventory Manufacturing firm Raw material - starting point in production process Work-in-progress Finished goods - products ready to ship or sell Remember that one firm's \"raw material\" may be another company's \"finished good.\" Different types of inventory can vary dramatically in terms of liquidity. 20-27 LO6 Inventory Costs Carrying costs - range from 20-40% of inventory value per year. Storage and tracking Insurance and taxes Losses due to obsolescence, deterioration or theft Opportunity cost of capital Shortage costs Restocking costs Lost sales or lost customers Consider both types of costs and minimize the total cost. 20-28 LO6 20.8 Inventory Management Techniques: ABC Approach Classify inventory by cost, demand and need. Those items that have substantial shortage costs should be maintained in larger quantities than those with lower shortage costs. Generally maintain smaller quantities of expensive items. Maintain a substantial supply of less expensive basic materials. 20-29 LO6 Inventory Management Techniques: Economic Order Quantity (EOQ) Model The EOQ model minimizes the total inventory cost. Total carrying cost = Average inventory x Carrying cost per unit = (Q/2)(CC) Total restocking cost = Fixed cost per order x Number of orders = F(T/Q) Total Cost = Total carrying cost + Total restocking cost = (Q/2)(CC) + F(T/Q) Q * 2TF CC 20-30 LO6 Example: EOQ Model Consider an inventory item that has carrying cost of $1.50 per unit. The fixed order cost is $50 per order and the firm sells 100,000 units per year. What is the economic order quantity? Q* 2(100,000)(50) 2582 1.50 20-31 LO6 Extensions Safety stocks Minimum level of inventory kept on hand Increases carrying costs Reorder points At what inventory level should you place an order? Need to account for delivery time Derived-demand inventories Materials Requirements Planning (MRP) Just-in-Time (JIT) Inventory 20-32 Quick Quiz What are the key issues associated with credit management? What are the cash flows from granting credit? How would you analyze a change in credit policy? How would you analyze whether to grant credit to a new customer? What is ABC inventory management? How do you use the EOQ model to determine optimal inventory levels? 20-33 20.9 Summary and Conclusions Components of credit policy - terms of sale, credit analysis, and collection policy Credit policy analysis - NPV of granting credit depends on five factors Optimal amount of credit that the firm offers depends on the competitive conditions under which it operates NPV is used to analyze a proposed credit policy Decision to grant credit to a given customer depends on the cost relative to the selling price and the possibility of repeat business Collection policy involves monitoring the age of A/R and dealing with past-due accounts 20-34 8 Stock Valuation Prepared by Anne Inglis, Ryerson University Joel Greenblatt on Valuation \"I make a guarantee the first day of class every year that if you're good at valuing companies, the market will agree with you. I just don't guarantee when. It could be a couple weeks or it could be two or three years. And the corollary is simply that, in the vast majority of cases, two or three years is enough time for the market to recognize the value that you see, if you've done good valuation work\" Joel Greenblatt, Adjunct Faculty, Columbia Business School 8-2 Chapter Outline Common Stock Valuation - Discounted Cash Flow (DCF) Approach - Limitations of DCF Approach Common Stock Features Preferred Stock Features Stock Market Reporting Intrinsic Value Appendix A: Corporate Voting 8-3 IBM or Microsoft? Market price: $141.60 Intrinsic value: $166.73 Margin of Safety: 17.75% Market price: $47.00 Intrinsic value: $31.00 Margin of Safety: -51% 8-4 Coach or Este Lauder? Market price: $30.18 Intrinsic value: $66.07 Margin of Safety: 54% Market price: $84.95 Intrinsic value: $44.78 Margin of Safety: -41% 8-5 LO2 Stocks For the Long-Term 8-6 Frequency Distribution of US Equity Total Return, 17902012 Summary Positive years: 164 (74%) Negative years: 59 (26%) 7 8-7 Equities for the Long-Term 8-8 Equities for the Long-Term 8-9 Equities for the Long-Term: Canada 8-10 Monthly Returns Source: Otuteye and Siddiquee (2013a) 8-11 Rolling 1-Year Returns S&P/TSX Total Index 30-Year Govt. Bond Source: Otuteye and Siddiquee (2013a) 8-12 S&P/TSX Total Index Returns Rolling 3-Year Returns Rolling 10-Year Returns Rolling 5-Year Returns Source: Otuteye and Siddiquee (2013a) 8-13 LO1 Common Stock Valuation - 8.1 A share of common stock is more difficult to value in practice than a bond for at least three reasons: 1. Future cash flows are uncertain (both dividend and future stock price) 2. The life of the investment is essentially forever because common stock has no maturity (t) 3. There is no way to easily observe the rate of return that the market requires (r) 8-14 LO1 Common Stock Valuation - One Period D1 P1 P0 1 (1 r) (1 r)1 P0 = Current price of the stock (Present value) P1 = Price in one period D1 = Cash dividend paid at the end of the period r = Required rate of return 8-15 LO1 Common Stock Valuation - One Period Example Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay? 8-16 LO1 Common Stock Valuation - One Period Example Formula approach: 2 14 P0 1 (1 .2) (1 .2)1 13.33 8-17 Common Stock Valuation - One Period Example LO1 Calculator approach [TI BA II Plus Professional]: 16 FV 20 I/Y 1N CPT PV = -13.33 8-18 LO1 Common Stock Valuation - Two Period D1 D2 P2 P0 1 2 (1 r) (1 r) (1 r)2 P0 = Current price of the stock P2 = Price in second period D1 = Cash dividend paid at the end of the first period D2 = Cash dividend paid at the end of the second period r = Required rate of return 8-19 LO1 Common Stock Valuation - Two Period Example Now what if you decide to hold the stock for two years? In addition to the $2 dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay now? 8-20 LO1 Common Stock Valuation - Two Period Example Formula approach: 2 2.10 14.70 (1 .2)1 (1 .2)2 (1 .2)2 13.33 P0 8-21 Common Stock Valuation - Two Period Example LO1 Calculator approach [TI BA II Plus Professional]: CF Registrar CF0 = 0 C01 = 2 F01 = 1 C02 = 16.80 F02 = 1 Press NPV; I = 20 CPT NPV = 13.33 8-22 LO1 Common Stock Valuation - Three Period D1 D2 D3 P3 P0 1 2 3 (1 r) (1 r) (1 r) (1 r)3 P0 = Current price of the stock P3 = Price in third period D1 = Cash dividend paid at the end of the first period D2 = Cash dividend paid at the end of the second period D3 = Cash dividend paid at the end of the third period r = Required rate of return 8-23 LO1 Common Stock Valuation - Three Period Example Finally, what if you decide to hold the stock for three periods? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and a stock price of $15.435. Now how much would you be willing to pay? 8-24 LO1 Common Stock Valuation - Three Period Example Formula approach: 2 2.10 2.205 15.535 P0 1 2 3 (1 .2) (1 .2) (1 .2) (1 .2)3 13.33 8-25 LO1 Common Stock Valuation - Three Period Example Calculator approach [TI BA II Plus Professional]: CF0 = 0 C01 = 2 F01 = 1 C02 = 2.10 F02 = 1 C03 = 17.64 F03 = 1 Press NPV; I = 20 CPT NPV = 13.33 8-26 LO1 Common Stock Valuation: Some Special Cases The three cases we consider are: 1. The dividend has a zero growth rate 2. The dividend grows at a constant rate 3. The dividend grows at a constant rate after some length of time 8-27 LO1 Zero Growth A share of common stock in a company with a constant dividend is much like a share of a preferred stock, and can be valued as a perpetuity. P0 = D/r where D is the dividend and r is the required return 8-28 LO1 Zero Growth: Example Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? P0 = .50 / (.1/4) = $20 8-29 LO1 Constant Growth Suppose we knew that dividend for some company always grows at a steady rate. Call this growth rate g. If we let D0 be the dividend just paid, then the next dividend, D1 = D0 (1+g) The dividend in two periods is, D2 = D1 (1+g) = [D0 (1+g) x (1+g)] = D0 (1+g)2 8-30 LO1 Dividend Growth Model Dividends are expected to grow at a constant percent per period. D1 D2 D3 P0 ... 1 2 3 (1 r) (1 r) (1 r) D0 (1 g)1 D0 (1 g)2 D0 (1 g)3 P0 ... 1 2 3 (1 r) (1 r) (1 r) With a little algebra, this reduces to: D0 (1 g) D1 P0 rg rg 8-31 LO1 Dividend Growth Model - Example 1 Suppose Big D, Inc. just paid a dividend of $0.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? .50(1 .02) (.15 .02) 3.92 P0 8-32 LO1 Dividend Growth Model - Example 2 Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? 2 P0 13.33 .2 .05 8-33 LO1 Dividend Growth Model - Example 3 Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? 4 P0 .16 .06 40 Remember that we already have the dividend expected next year, so we don't multiply the dividend by (1+g). 8-34 LO1 Dividend Growth Model - Example 4 What is the price expected to be in year 4? D5 D1 (1 g)4 P4 rg rg 4(1 .06)4 5.0499 P4 50.49 .16 .06 .10 What is the implied return given the change in price during the four year period? - Formula approach: 50.49 = 40(1+r)4; r = 6% - Calculator approach: 4 N; -40 PV; 50.49; CPT I/Y = 6% The price grows at the same rate as the dividends. 8-35 LO1 Non-Constant Dividend Growth - Example Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends. 8-36 LO1 Non-Constant Dividend Growth - Example Compute the dividends until growth levels of D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future price D3 1.449 P2 9.66 r g .20 .05 Find the present value of the expected future cash 1.20 1.38 9.66 flows. P0 1 2 (1 .20) (1 .20) (1 .20)2 P0 1.00 0.96 6.71 8.67 8-37 LO1 Using the Constant DGM to Find r Start with the constant DGM: D0 (1 g) D1 P0 rg rg byrearrangingthisequation,wecanget D0 (1 g) D1 r g g P0 P0 This shows the components of the required return. 8-38 LO1 Finding the Required Return, r - Example Suppose a firm's stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? D0 (1 g) r g P0 1(1 .05) r .05 15% 10.50 What is the dividend yield? 1(1.05) / 10.50 = 10% What is the capital gains yield? g = 5% 8-39 Dividend Discount Model - Shiller's Findings 1870 Real S&P Composite vs. Ex Post Rational Price Rational Price Year 1980 DJIA Stock Price Index vs. Ex Post Source: Shiller, Robert J (1981). "Do Stock Prices Move Too Much to Be Justified by 8-40 Subsequent Changes in Dividends?" The American Economic Review, pp. 421-436 Limitations of DCF Approach Although some businesses are more stable than others and therefore more predictable, estimating future cash flow for a business is usually a guessing game. Source: Margin of Safety by Seth Klarman (1991) 8-41 Limitations of DCF Approach Will Coca-Cola sell soda next year? Of course. Will it sell more than this year? Pretty definitely, since it has done so every year since 1980. How much more is not so clear. How much the company will earn from selling it is even less clear; factors such as pricing, the sensitivity of demand to changes in price, competitors' actions, and changes in corporate tax rates all may afect profitability. Source: Margin of Safety by Seth Klarman (1991) 8-42 Limitations of DCF Approach Forecasting sales or profits many years into the future is considerably more imprecise, and a great many factors can derail any business forecast. Source: Margin of Safety by Seth Klarman (1991) 8-43 Limitations of DCF Approach There are many investors who make decisions solely on the basis of their own forecasts of future growth. After all, the faster the earnings or cash flow of a business is growing, the greater that business's present value. Source: Margin of Safety by Seth Klarman (1991) 8-44 Limitations of DCF Approach Yet several difficulties confront growth-oriented investors. 1. Such investors frequently demonstrate higher confidence in their ability to predict the future than is warranted. 2. For fast-growing businesses even small diferences in one's estimate of annual growth rates can have a tremendous impact on valuation. 3. With so many investors attempting to buy stock in growth companies, the prices of the consensus choices may reach levels unsupported by fundamentals. Source: Margin of Safety by Seth Klarman (1991) 8-45 Limitations of DCF Approach The other component of present-value analysis, choosing a discount rate, is rarely given sufficient consideration by investors. A discount ra