1.
2.
Example: What should the price of a share of stock be if the firm will pay a $4 dividend in 1
year that is expected to grow at a constant rate of 5%? Assume a discount rate of 10%.
3.Example:
A firm is expected to pay $2/share in dividends next year. Those dividends are expected to grow by 8% for the next three years and 6% thereafter. If the discount rate is 10%, what is the current price of this security?
Required rates of return
Example: What rate of return should an investor expect on a share of stock with a $2 expected dividend and 8% growth rate that sells today for $60?
Sustainable growth rate
g?Return on Equity ? Plowback Rate = ROE?bearnings?dividends
where:b? earnings Example: Suppose a firm that pays out 35% of earnings as dividends and expects its return on equity to be 10%. What is the expected growth rate?
g?.10?(1?.35)?.065?6.5%
Valuing growth stocks
Where: EPS= Earnings per share PVGO = Present Value of Growth Opportunities
Suppose a stock is selling today for $55/share and there are 10,000,000 shares outstanding. If earnings are projected to be $20,000,000, how much value are investors assigning to growth per share? Assume a discount rate of 10%.
Chapter 8(NPV,EAA,IRR) 第8章（ 重点复习单元）：净现值
及其他投资准则，会算NPV，计算EAA (P191页)，认识其他投评估指标（PP回流期和 IRR内含报酬率）及其判断准则（取大或取小），重点关注NPV与IRR，注意使用IRR指标的前提是IRR 有关投资组合，要知道其大前提是资金是有约束的；单个项目的特征（可分/不可分），可分的单个项目之间的比较与排序用PI（收益指数）值来衡量，不可分的用各自的NPV值来比较衡量，比较的前提是它们的寿命期是一样的，如果不一样的话就用最小共同寿命期法或等价年金法来比较 。 NPV=Co+ Net present value(NPV) Present value of the project cash flows minus initial investments ctc1c2++…+ 2t(1?r)(1?r)(1?r)Co: initial cash flow (often negative) Opportunity cost of capital Long- vs short-lived equipment: equivalent annual annuity(等效年金)(EAA) present value of cash flowsPVCashFlowsEAA =? annuity factor?1?r?(11?r)t?r?? Payback period(投资回收期) Interest rate of return(IRR) Discount rate at which NPV=0 0=Co+ C1C2CT++…+ 2t(1?IRR)(1?IRR)(1?IRR) IRR > cost of capital, then NPV > 0 IRR < cost of capital, then NPV < 0 Other Investment Criteria:Profitability Index NPVProfitability Index? Initial Investment Chapter 9第9章（ 重点复习单元）：应用贴现现金流量分析方法制定决策，识 别贴现新增现金流（忽略沉没成本等），会算现金流量，算运营现金流OCF三种方法，资产折旧有直线和加速折旧。 Incremental cash flow （增量现金流） Incremental cash flow=cash flow with project- cash flow without project Sunk cost沉没成本 Calculationg operation cash flow Total cash flow=cash flows from capital investments + cash flows from changes in working capital + operating cash flows Cash Flow from Operations: Three Methods of Calculation Operating Cash Flow = Revenue - Cash Expenses - Taxes Operating Cash Flow (OCF) = After-tax Profit + Depreciation OCF = (Revenue ? Cash Expenses)?(1?Tax Rate)+(Tax Rate?Depreciation) Example: A project generates revenues of $600,expenses of $300, and depreciation charges of $200 in a particular year. The firm?s tax bracket is 35%. Find the operating cash flow of the project. Method 1: CF = 600 – 300 – 35 = $265 Method 2: CF = (600 - 300 – 200 – 35) + 200 = $265 Method 3: CF = (600 – 300) x (1 – 0.035) + (200 x 0.35) = $265 ( Tax paid = (600 – 300 – 200) x 0.35 = $35 ) Chapter 10第10章：项目分析：敏感分析，场景分析和（重点关注）临界分 析法，计算NPV为零时，销售收入的值。运营杠杆，及其指数DOL， Capital Budgeting: The Decision Process Stage 1: The Capital Budget资本预算 Stage 2: Project Authorization项目授权 What-if Testing Sensitivity Analysis 敏感性分析 Analysis of the effects on project profitability of changes in sales,(or) costs, etc. Profitability Index：未来NCF总现值/原始投资额现值 Scenario Analysis 方案分析 Simulation Analysis Break-Even Analysis 损益平衡分析 Break-even Sales = Fixed Costs Inc. Depr. / (1 - Var. Cost ) 盈亏临界点销售额=固定成本（包括折旧）/每增加1美元销售额所增加的利润 Note: Accounting Break-Even can be expressed in terms of revenue: fixed costs + depreciationBreak-Even level of revenues = additional profit from each additional dollar of salesBreak-Even Point: Finance ? NPV break-even =Accounting profit – Opportunity cost of capital Step 1: PV (Cash Flows) = AnnuityFactor ? YearlyCash Flows ?t1-(1?r)Year 0 where Annuity Factor = rInvestment$5,400?12 1?(1?.08)SalesYears 1-1245?X(36?X)(2,000)(450)9?X?2,450Example: PV(Cash Flows) = .08?[5.4?X?1,020]Var. CostFixed CostsDepreciationPretax Profit 1?(1?.08)?12 Example- ?[5.4?X?1,020]?5,400.08 X?322units Operating leverage Degree of Operating Leverage (DOL) 营运杠杆程度Percentage change in profits given a 1% change in sales. percent change in profits (pre-tax)DOL?percent change in sales fixed costs?1? profitsFixed costs 包括depreciation Example: Optimisic SalesYear 0Years 1-12Base CaseYear 0Years 1-12 Investment-5,400Investment-5,400 Sales18,000Sales16,000Variable Costs(14,400)Variable Costs(12,800) Fixed Costs(2,000)Fixed Costs(2,000) Depreciation(450)Depreciation(450) Pretax profit1,150Pretax profit750Taxes (460)Taxes (300) Profit after tax690Profit after tax450 Operating cash flow1,140Operating cash flow900Net Cash Flow-5,4001,140Net Cash Flow-5,400900 New?Old1,150?750% Change in Profits= ??.5333 Old750 18,000?16,000 % Change in Sales= ?.125016,000 % Change in Profits.5333DOL= ??4.27 % Change in Sales.1250 =1+(2000+450)/750 Step 2: PV (Cash Flows) = Initial InvestmentChapter 11考虑投资组合收益与风险分散，收益期望（可能不考测量风险：方 差与标准差），CAPM资产定价模型，β值组合计算。 Equity Rates of Return Percentage return=(capital gain+dividend)/initial share price Dividend yield=dividend/initial share price Capital gain yield=capital gain/initial share price Example:You purchase shares of GE stock at $15.13 on December 31, 2009. You sell them exactly one year later for $18.29. During this time GE paid $.46 in dividends per share. Ignoring transaction costs, what is your rate of return, dividend yield and capital gain $18.29?$15.13??$.46$.46yield? Percentage Return??23.93%Dividend Yield =?3.04%$15.13$15.13 ?$15.13Capital Gain Yield?$18.29?20.89% $15.13Real rate of return 1 + nominal rate of return 1?real rate of return = 1 + inflation rate Market Index Measure of the investment performance of the overall market. Risk Premium Interest Rate onNormal RiskExample: Expected Market Return=+Treasury BillsPremium 1981: 21.4%=14%+7.4% 2008: 9.6%=2.2%+7.4% Maturity Premium: Extra average return from investing in long- versus short-term Treasury securities. (T-bonds(长期国债) gave slightly higher returns than T-bills（短期国债）. This difference is called the maturity premium) Risk Premium: Expected return in excess of risk-free return as compensation for risk. (The return difference between risk-free Treasury bills and corporate bonds and common stock returns is a risk premium) Measuring Risk(方差和标准差) Variance: Average value of squared deviations from mean. A measure of volatility. Standard Deviation: n?Square root of variance. Also a measure of volatility. ???(Rj?R)2Pj j?1calculating variance and standard deviation (assume a mean of 10) (1)(2)(3) Percent Rate of ReturnDeviation from MeanSquared Deviation +40+30900 +1000 +1000 -20-30900 Variance=average of squared deviations=1800/4=450 Standard deviation=square of root variance=450=21.2% Squared deviation 平方差