Chapter 3①The balance sheet②The income statement③The statement of cash flows④tax①The balance sheetEquation: total assets=total liabilities + shareholders’ equityNet working capital(NWC)=current asset – current liabilities是指企业的流动资产总额减Balance sheetCurrent Assets Current Liabilities•Cash & Securities payables•Receivables short-term debt•Inventories ++ long-term liabilitiesFixed Assets +•Tangible Assets shareholders’ equity•Intangible AssetsBook value& market value②the income statementThe income statementSales revenue $135,000Less: cost of sales 108,000Gross profits 27,000Less: Operating expenses 13,500Operating profits 13,500Less: Financing expense 1,350Net profits before taxes 12,150Less: Taxes (15%) 1,823Net profits after taxes $10,327In the income statement below, what was the value of Home Depot’s EBIT in 2009?EBIT = total Revenues －costs －deprecation③the statement of cash flowsExample:Net income for your firm was $10,000 last year. The depreciation expense was $2,500; accounts receivable increased $1,250; accounts payable increased $800; and inventories increased by $2,000.What was the total cash flow from operations for the period?Net income: 10,000Depreciation: 2,500Accounts Receivable: (1,250)Accounts Payable: 800Inventories: (2,000)Cash flow from operations: 10,050Free Cash FlowFree Cash Flow is cash available for distribution to investors after the firm pays for new investments or additions to working capital.Free cash flow = (EBIT – taxes + dep.) - change in net working capital- cap. expenditures④tax: 1.corporate tax2.personal tax一,marginal tax rate二,average tax rateChapter4MuaEvaBook rate of ruturnFinancial ratio (财务比率) and shareholders ’ valueThe Dupont systemprice x shares outstanding)Market value added: Market capitalization minus book value of equty.Market-to-book ratio=equityof value book equity of value market ...................Economic Value Added(EV A)Total capitalization: long-term debt + equityAfter tax operating income = after-tax interest + net incomeEVA :Show the firm’s truly created valueincome earned – income requiredBook Rates of Returnreturn on capital(ROC)资本收益率ROC=after-tax operating income/total capitalizationROC=after-tax operating income/average total capitalizationReturn on asset(ROA)资产收益率ROA=after-tax operating income/total assetsROA=after-tax operating income/average total assetsReturn on equity(ROE)股本回报率，产权回报率ROE=net income/equity因为是operating income 在上章可知operating income 是financial expenses 之前的，故还未减去interest ，故要加after-taxinterset)PPT 中关于ROA ，ROC ，ROE 的练习Financial ratios and shareholders ’ valueEconomic Value Added Operating Income* - [Cost of Capital Total Capitalization]=⨯Shareholder value depends on good investment and financing decisions.Financial Ratios help measure the success and soundness of these decisionsEfficiency RatiosAsset turnover ratio=sales/total assets at start of yearOr=sales/average total assetsReceivables turnover=sales/receivables at start of yearAverage collection period=receivables at start of year/average daily sales=365/receivable turnoverInventory turnover ratio=cost of goods sold/inventory at start of yearAverage days in inventory=inventory at start of year/daily cost of goods sold=365/inventory turnoverProfitability RatiosProfit margin(利润率)=net income/sales(IOPM)Operating profit margin=net income +after-tax interest/sales=after-tax operating income/salesLeverage Ratios杠杆率(debt and equity)Long-term debt ratio=long-term debt/long-term debt+equityLong-term debt equity ratio=long-term debt/equityMeasuring LeverageTotal debt ratio=total liability/total assetsTimes interest earned（利息保障率,利息保障倍数）=EBIT/interest payments用于衡量偿付贷款利息的能力Cash coverage ratio（现金涵盖比率）=EBIT+depreciation/interest paymentsLiquidity Ratios(短期还债能力指标/流动性指标)NWC to total assets ratio(经营运资金比)=net working capital/total assets(Net working capital=current asset – current liabilities) Current ratio(流动比率)=current assets/current liabilities(短期还债能力的一个指标)Quick ratio(速动比率)=cash + marketable securities(有价证券) + receivables/current liabilitiesCash ratio(现金比率)=cash + marketable securities/current liabilitiesThe Dupont systemROA= after-tax operating income/asset=assets sales x sales....income operating tax after -=assets turnover x operating profit margin=leverage ratio x asset turnover x operating profit margin x debt burden股息支付率 再投资率Or call sustainable growth rateChapter 5Future valuePresent valuePv of multiple cash flowsPerpetuitiesAnnutitiesFuture value of annutitiesAnnuities and annuities due EAR & APRAssets Sales Net Income Interest Net Income ROE=x x x Equity Assets Sales Net Income Interest++Dividends Payout Ratio=Earnings Earnings-Dividends Plowback Ratio=Earnings Growth in equity from plowback = Plowback Ratio ROE Earnings - Dividends Earnings Earnings Equity ⨯=⨯Earnings-Dividends = EquityInflationValuing real cash paymentsFuture valueSimple interest: FV simple =initial investment*(1+r*t)Compound interest: FV compound =initial investment*(1+r)tPresent valueDiscount rate: rDiscount factor: DF=t r )1(1+ Present value: PV=FV*t r )1(1+ PV of multiple cash flowsCt=the cash flows in year tExample: Your auto dealer gives you the choice to pay $15,500 cash now or make threepayments: $8,000 now and $4,000 at the end of the following two years. If your cost of money (discount rate) is 8%, which do you prefer?PerpetuitiesPV of perpetuity: PV=C/rExample: In order to create an endowment, which pays $185,000 per year forever, how much money must be set aside today if the rate of interest is 8%?What if the first payment won’t be received until 3 years from today?PV = 2312,500 / (1 + 0.08)3= 1,835,662.5annuities124,0001(1.08)4,0002(1.08)Initial Payment* 8,000.003,703.703,429.36Total PV $15,133.06PV of C PV of C ++=====185,000.08$2,312,500PV ==Present value of an annuity: PV=C*[r 1-t r r )1(1+] The terms within the brackets are collectively called the “annuity factor ”PV of multiple cash flowsFuture value of annuitiesExample: You plan to save $4,000 every year for 20 years and then retire. Given a 10% rate ofAnnuities due(即付年金)（与普通年金（即后付年金）的区别仅在于付款时间的不同，一个n 期的即付年金相当于一个n-1期的普通年金）(期不等于年)PV annuitydue =PV annuity (1+r) FV annuity due =FV annuity(1+r) Example: Suppose you invest $429.59 annually at the beginning of each year at 10% interest. After 50 years, how much would your investment be worth?EAR & APREffective annual interest rate: The period interest rate that is annualized using compound interest.EAR = (1 + monthly rate)12 - 1Annual Percentage Rate: The period interest rate that is annualized using simple interest APR = monthly rate × 12Example : Given a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?Inflation000,550$)10.1()000,500($)1(=⨯=+⨯=AD AD Annuity AD FV FV r FV FV %00.12)12()01.0(%68.121)01.1(12=⨯==-=APR EAR 1+nominal interest rate1+inflation rate 1real interest rate=+Valuing real cash payments♦ Example: You make a loan of $5,000 to Jane who will pay it back in 1 year. The interestrate is 8%, and the inflation rate is 5% now. What is the present value of Jane’s IOU? Show that you get the same answer when (a) discounting the nominal payment at the nominal rate and (b) discounting the real payment at the real rate.♦ (a) 5,000 / (1 + 8%) = $4630(b) 5,000 / (1.05) = $4762 (real dollar)4762 / (1.028) = $4630(2.8% is real interest rate)不能用实际利率去贴现名义现金流Chapter 6bond pricing:example: For a $1000 face value bond with a bid price of 103:05 and an asked price of 103:06, how much would an investor pay for the bond?PV=1)1(r coupon ++2)1(r coupon ++…+t r par coupon )1(++ PV bond =PV coupon +PV parvalue=coupon*(annuity factor)+ par value * (discout factor)Example: What is the value of a 3-year annuity that pays $90 each year and an additional$1,000 at the date of the final repayment? Assume a discount rate of 4%.Warning: bond rate inflation -rate interest nominal rate interest Real ≈()()6103% 103.1875% 321.031875$1,000 $1,031.875of face value ⎛⎫+= ⎪⎝⎭⨯=331(1.04)1$90$1,000.04(1.04)$1,138.75Bond PV --+=⨯+⨯+=()()1(1)where 1and (1)Bond Coupons ParValue Bond t tPV PV PV PV coupon Annuity Factor par value Discount Factor r Annuity Factor rDiscount Factor r -=+=⨯+⨯-+==+The coupon rate IS NOT the discount rate used in the Present Value calculations Example: What is the present value of a 4% coupon bond with face value $1,000 that matures in 3 years? Assume a discount rate of 5%. Bond yields Current yield : annual coupon payments divided by bond priceExample:Suppose you spend $1,150 for a $1,000 face value bond that pays a $60 annual coupon payment for 3 years. What is the bond’s current yield?Yield to maturity:PV=1)1(r coupon ++2)1(r coupon ++…+t r par coupon )1(++ Bond rates of returnRate of return 只算一年的couponYTM vs rate of returnYTM ↑ (↓)(unchange) → the price of bond ↓ (↑) (unchange) → the rate of return for that period less (greater)(equal to) than the yield to maturity.Ytm 通过改变price 去改变p1-p0 从而改变rate of return ，由rate of return 公式得，p1-p0和其成正比，ytm 与change in price 成反比，故ytm 与其成反比Chapter 7Stock marketP/E ratio(本益比): price per share divided by earnings per shareAsk price & bid priceAsk price: the price at which current shareholders are willing to sell their sharesBid price: the price at which investors are willing to buy sharesTerminologyinvestment change price +income Coupon =return of Rate investmentincome total =return of Rate1,market cap. 2.P/E ratio 3.dividend yieldExample: You are considering investing in a firm whose shares are currently selling for $50 per share with 1,000,000 shares outstanding. Expected dividends are $2/share and earnings are $6/share.What is the firm’s Market Cap? P/E Ratio? Dividend Yield?Measure of value1. book value2. liquidation value3.market valueBV= Assets - liabilitiesLV = Assets selling price – LiabilitiesMV = Tangible & intangible assets + Inv. OpportunitiesPrice and intrinsic valueVo 内在价值Example: What is the intrinsic value of a share of stock if expected dividends are $2/shareand the expected price in 1 year is $35/share? Assume a discount rate of 10%.Expected return(ER)Valuing common stocksdividend discount modelconsider three simplying cases1. no growth2. constant growth3. noconstant growth Market Capitalization $501,000,000$50,000,000$50P/E Ratio 8.33$6$2Dividend Yield .044%$50=⨯======HH H r P Div r Div r Div P )1(...)1()1(22110+++++++=1.2.Example: What should the price of a share of stock be if the firm will pay a $4 dividend in 1year 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 returnExample: 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 rateExample: 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?Valuing growth stocksWhere: EPS= Earnings per share PVGO = Present Value of Growth OpportunitiesSuppose 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%.Return on Equity Plowback Rate = :g ROE bearnings dividends where b earnings=⨯⨯-=.10(1.35).065 6.5%g =⨯-==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<r （P199页）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 。