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)]/0.09}v 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。