公司理财笔记整理.doc

5 Time value of money Compinding future value FVDiscounting present value PVInterest rate exchange rate between earlier and later moneyv FV = PV(1 + r)t v PV = FV / (1 + r)t r = period interest rate, expressed as a decimal t = number of periods Future value interest factor = (1 + r)t 复利终值系数 1/(1+r) t present value factor 现值系数 For a given interest rate the longer the time period, the lower the present value For a given time period the higher the interest rate, the smaller the present valuev r = (FV / PV)1/t 1v t = ln(FV / PV) / ln(1 + r)6 Discounted Cash Flow Valuationv Future and Present Values of Multiple Cash FlowsYou think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in three years? In four years?Today (year 0 CF): 3 N; 8 I/Y; -7,000 PV; CPT FV = 8,817.98 FV = 7000(1.08)3 = 8,817.98Year 1 CF: 2 N; 8 I/Y; -4000 PV; CPT FV = 4,665.60 FV = 4,000(1.08)2 = 4,665.60Year 2 CF: 1 N; 8 I/Y; -4000 PV; CPT FV = 4,320 FV = 4,000(1.08) = 4,320Year 3 CF: value = 4,000Total value in 3 years = 8817.98 + 4665.60 + 4320 + 4000 = 21,803.58Value at year 4: 1 N; 8 I/Y; -21803.58 PV; CPT FV = 23,547.87 You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year and $800 at the end of the next year. You can earn 12 percent on very similar investments. What is the most you should pay for this one?Point out that the question could also be phrased as “How much is this investment worth?”Calculator:Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178.57Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318.88Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427.07Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = - 508.41Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93现金流都发生在年末 e/g后付变先付 相当于原来的数据*（1+r）v Valuing Level Cash Flows: Annuities and Perpetuitiesu Annuity年金连续相同的现金流 finite series of equal payments that occur at regular intervalsv If the first payment occurs at the end of the period, it is called an ordinary annuity 普通年金v If the first payment occurs at the beginning of the period, it is called an annuity due 先付年金u Perpetuity infinite series of equal payments 永续年金只有现值没有终值 期数无限v Perpetuity: PV = C / rv Annuities优先股有永续年金的特征杠杆：自由资金撬动借有资产 美国杠杆高借贷方便FVDN先付 FVIFA 普通Growing Perpetuity增长年金A growing stream of cash flows with a fixed maturity增长率一定A growing stream of cash flows that lasts forever 用来计算股票的价格 产品未来所有的价值现在的现值 相当于股票现在的价格不是交易价格The expected dividend next year is $1.30, and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream?如果现在卖价小于26即可买入v Comparing Rates: The Effect of CompoundingEffective Annual Rate (EAR)This is the actual rate paid (or received) after accounting for compounding that occurs during the year。If you want to compare two alternative investments with different compounding periods, you need to compute the EAR and use that for comparison.比较不同期间的rate不能直接比较Annual Percentage Rate（APR）年化报价利率v This is the annual rate that is quoted by lawv By definition APR = period rate times the number of periods per yearv Consequently, to get the period rate we rearrange the APR equation: Period rate = APR / number of periods per yearv You should NEVER divide the effective rate by the number of periods per year it will NOT give you the period rateContinuous Compounding EAR = eq 1Example: What is the effective annual rate of 7% compounded continuously?EAR = e.07 1 = .0725 or 7.25%Pure Discount Loans The principal amount is repaid at some future date, without any periodic interest payments.纯折现贷款 中间不付息 例如Treasury billsInterest-Only Loan 每年支付利息到期一次性还本金加最后一次利息Pay interest each period and repay the entire principal at some point in the futureThis cash flow stream is similar to the cash flows on corporate bonds. v Loan Types and Loan Amortization 每年偿还利息加一部分本金v Make single, fixed payment every periodv 5,000=C*1-(1/1.095)/0.09v C=1285.457 Interest Rates and Bond Valuation现金流折现的三个重要信息 现金流 折现率 期限 评估资产价值对资产未来产生的现金流进行估计把所有现金流折现加总得到零时刻的价值 （价值大于价格则买进）v Bonds and Bond ValuationPar value (face value) the principal 本金Coupon rate fixed when the bond issued票面利率 发行方许诺支付 Coupon payment par value * coupon rate Maturity date 到期日票面利息Yield or Yield to maturity interest rate required in market on a bond 持有到期收益率 Bond Value = PV of coupons + PV of parBond Value = PV of annuity + PV of lump sum 本金现值As interest rates increase, present values decrease ，bond prices decrease C：cash flow 左侧年金复利系数 右侧本金折现PV=Coupon rate和market interest rate比较 由于市场利率是变化的，发行时候算的是发行当时的市场利率，而后可能变化因此到期日要看 到期日利率YTM If YTM coupon rate, then par value bond price The discount provides yield above coupon ratePrice below par value, called a discount bond平价债券 par bond 折现出来的价值就是面值v Coupon rate小于market折价债券 discount bondConsider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The market interest rate is 11%. What is the value of the bond?B = PV of annuity + PV of lump sumB = 1001 1/(1.11)5 / .11 + 1,000 / (1.11)5 B = 369.59 + 593.45 = 963.04 Coupon rate大于market溢价债券premium bondCoupon and Yieldv If YTM = coupon rate, then par value = bond pricev If YTM coupon rate, then par value bond price Why? Higher coupon rate causes value above par Price above par value, called a premium bondInterest Rate Risk（IRR）the risk that arises for bond owners from fluctuating interest rate利率风险 市场的利率变化会导致债券价格的变化All other things being equal, the long the time to maturity, the greater the interest rate riskAll other things being equal, the lower the coupon rate, the greater the interest rate risk两个除了期限以外全部相同的债券债券条款：v Debt ：hort long term borrowing 债务融资 Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcyv Equity ：onership interest 权益融资 Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm, and stockholders have no legal recourse if dividends are not paid An all equity firm can not go bankrupt merely due to debt since it has no debt利息抵税 债权人不参与管理 借钱方式有两种 银行贷款和发股票The Bond Indenture 债券契约v Contract between the company and the bondholders that includes The basic terms of the bonds 基本条款 The total amount of bonds issued 发行总额 A description of property used as security, if applicable担保说明 有形资产做抵押品 Sinking fund provisions偿债基金条款 Call provisions 赎回条款 Details of protective covenants 保护性条款v 价格受条款影响 有抵押价格高、偿债基金高、没有赎回条款高、有保护条款高Bond Classificationsv Registered记名债券 Bearer Forms 无记名债券 国库券 认券不认人v Security担保性质 Collateral secured by financial securities质押债券 质押物通常为公司普通股 Mortgage secured by real property, normally land or buildings 抵押债券 通常为不动产 Debentures unsecured 信用债券 无担保债券 以企业信用发行 Notes unsecured debt with original maturity less than 10 yearsv Seniority 优先权 比次级债券更优先获得补偿v Bond RatingsHigh GradeMoodys Aaa and S&P AAA capacity to pay is extremely strong 标准普尔Moodys Aa and S&P AA capacity to pay is very strongMedium Grade 还款能力强但受环境变化Moodys A and S&P A capacity to pay is strong, but more susceptible to changes in circumstancesMoodys Baa and S&P BBB capacity to pay is adequate, adverse conditions will have more impact on the firms ability to payBond ratings are concerned only with the possibility of default Low Grade Moodys Ba and BS&P BB and BConsidered possible that the capacity to pay will degenerate. 还款能力具有投机性Very Low Grade垃圾债券Moodys C (and below) and S&P C (and below) income bonds with no interest being paid, or in default with principal and interest in arrearsv Some Different Types of BondsGovernment BondsTreasury SecuritiesFederal government debt 国债T-bills pure discount bonds with original maturity of one year or lessT-notes coupon debt with original maturity between one and ten yearsT-bonds coupon debt with original maturity greater than ten yearsMunicipal SecuritiesDebt of state and local governmentsVarying degrees of default risk, rated similar to corporate debtInterest received is tax-exempt at the federal level 部分地方政府债可免部分税v Bond MarketsZero Coupon BondsMake no periodic interest payments (coupon rate = 0%)完全无票息的债券The entire yield-to-maturity comes from the difference between the purchase price and the par valueCannot sell for more than par value 发行价不能高于面值Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs)Treasury Bills and principal-only Treasury strips are good examples of zeroes面值发行折扣债券Floating-Rate BondsCoupon rate floats depending on some index valueExamples adjustable rate mortgages and inflation-linked TreasuriesThere is less price risk with floating rate bondsThe coupon floats, so it is less likely to differ substantially from the yield-to-maturityCoupons may have a “collar” the rate cannot go above a specified “ceiling” or below a specified “floorOther Bond TypesCat bonds大灾债券Income bonds 收益债券 票息随公司收益波动Convertible bonds 可转换债券可转换为股票Put bonds（call）债券持有者有权要求发行方按照一定价格回购 以保护持有者利益Bond MarketsTrading volume is much larger than volume in stocksPrimarily over-the-counter transactions with dealers connected electronicallyExtremely large number of bond issues, but generally low daily volume in single issuesMakes getting up-to-date prices difficult, particularly on small company or municipal issues v Treasury QuotationsHighlighted quote in Figure 7.4Nov 2021 8 136:29 136:30 5 4.36到期日 票面利率/买卖价差bidask 相比昨天变化 分母为32What is the coupon rate on the bond?When does the bond mature?What is the bid price? What does this mean?What is the ask price? What does this mean?How much did the price change from the previous day?What is the yield based on the ask price?Clean price: quoted price净价/报价Dirty price: price actually paid = quoted price plus accrued interest 含息价Example: Consider a T-bond with a 4% semiannual yield and a clean price of $1,282.50:Number of days since last coupon = 61Number of days in the coupon period = 184Accrued interest = (61/184)(.04*1000) = $13.26Dirty price = $1,282.50 + $13.26 = $1,295.76So, you would actually pay $ 1,295.76 for the bond8 Stock Valuationv Common Stock Valuationv If you buy a share of stock, you can receive cash in two waysThe company pays dividendsYou sell your shares, either to another investor in the market or back to the companyAs with bonds, the price of the stock is the present value of these expected cash flows 估计股利Estimating Dividends: Special CasesConstant dividend 高速增长不长久 达到稳定The firm will pay a constant dividend foreverThis is like preferred stockThe price is computed using the perpetuity formulaConstant dividend growthThe firm will increase the dividend by a constant percent every periodThe price is computed using the growing perpetuity modelSupernormal growthDividend growth is not consistent initially, but settles down to constant growth eventuallyThe price is computed using a multistage model Zero GrowthIf dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formulaP0 = D / R 必要报酬率Dividend Growth ModelDividends are expected to grow at a constant percent per period.P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + 股利增长模型注意： just paid a dividend和is expected to pay可以得到的是D0预期的是1Nonconstant Growth Problem Statement不稳定增长 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. Compute the dividends until growth levels offD1 = 1(1.2) = $1.20D2 = 1.20(1.15) = $1.38D3 = 1.38(1.05) = $1.449Find the expected future priceP2 = D3 / (R g) = 1.449 / (.2 - .05) = 9.66Find the present value of the expected future cash flowsP0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67 股利增长模型求R 对投资者必要报酬率 对企业 获取资金的成本普通股的featureVoting Rights 股东投票权Proxy voting代理投票Classes of stock 我国无 股票分级 一股一票Other RightsShare proportionally in declared dividendsShare proportionally in remaining assets during liquidationPreemptive right first shot at new stock issue to maintain proportional ownership if desired 优先认股 保持比例防止稀释 9 Net Present Value and Other Investment Criteriawhen evaluating capital budgeting decision rules:4个标准 Does xx account for the time value of money? Does xx account for the risk of the cash flows? Does xxprovide an indication about the increase in value? Should we consider xx for our primary decision rule?Net Present Value：difference between the market value of a project and its costHow much value is created from undertaking an investment? 1 estimate the expected future cash flows. 2 estimate the required return for projects of this risk level. 3 find the present value of the cash flows and subtract the initial investment.Decision rule: If the NPV is positive, accept the project NPV正就接受the project is expected to add value to the firm and will therefore increase the wealth of the owners.Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.NPV=-30,000+6,000*1-(1/1.15)8)/0.15+(2000/1.158) =-2,422Payback PeriodHow long does it take to get the initial cost back in a nominal sense?ComputationEstimate the cash flowsSubtract the future cash flows from the initial cost until the initial investment has been recovereddecision Rule Accept if the payback period is less than some preset limit Year 1: 165,000 63,120 = 101,880 still to recover Year 2: 101,880 70,800 = 31,080 still to recover Year 3: 31,080 91,080 = -60,000 project pays back in year 3Advantages and Disadvantages of Payback Easy to understand Adjusts for uncertainty of later cash flows Biased toward liquidity Risk screening deviceDisadvantage Ignores the time value of money Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date Biased against long-term projects, such as research and development, and new projectsNPV(short)=-250+100/1.15+200/1.152=-11.81NPV(long)=-250+100*1-(1/1.154)/0.15=35.50v The Discounted PaybackCompute the present value of each cash flow and then determine how long it takes to pay back on a discounted basisCompare to a specified required periodDecision Rule - Accept the project if it pays back on a discounted basis within the specified time Year 1: 165,000 63,120/1.121 = 108,643 Year 2: 108,643 70,800/1.122 = 52,202 Year 3: 52,202 91,080/1.123 = -12,627 project pays back in year 3评价The answer to the first two questions is yes.The answer to the third question is no because of the arbitrary cut-off date.Since the rule does not indicate whether or not we are creating value for the firm, it should not be the primary decision rule.Advantages and Disadvantages of Discounted Paybackv The Average Accounting Return AAR多种定义Average net income / average book valueNote that the average book value depends on how the asset is depreciated.Need to have a target cutoff rateDecision Rule: Accept the project if the AAR is greater than a preset rateAssume we require an AAR = 25%Average Net Income:(13,620 + 3,300 + 29,100) / 3 = 15,340AAR = 15,340 / 72,000 = .213 = 21.3% rejectv Advantages and Disadvantages of AAR Ad Easy to calculate/Needed information will usually be availableDisadvantages Not a true rate of return; time value of money is ignored Uses an arbitrary benchmark cutoff rate Based on accounting NI and book values, not CF and MVv The Internal Rate of Return (IRR) NPV最好的替代It is often used in practice and is intuitively appealingIt is based entirely on the estimated CF and is independent of interest rates found elsewhereDefinition: IRR is the return that makes the NPV = 0Decision Rule: Accept if the IRR is greater than the required returnThe IRR rule accounts for time value because it is finding the rate of return that equates all of the cash flows on a time value basis.The IRR rule accounts for the risk of the cash flows because you compare it to the required return, which is determined by the risk of the project.The IRR rule provides an indication of value because we will always increase value if we can earn a return greater than our required return.We should consider the IRR rule as our primary decision criteria, but as we will see, it has some problems that the NPV does not have. That is why we end up choosing the NPV as our ultimate decision rule.Advantages Knowing a return is intuitively appealingIt is a simple way to communicate the value of a project to someone who doesnt know all the estimation detailsIf the IRR is high enough, you may not need to estimate a required retu