公司理财笔记整理

5 Time value of moneyCompinding future value FVDiscounting present value PVInterest rate exchange rate between earlier and later money❖FV = PV（1 + r)t❖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 value ❖r = (FV / PV）1/t– 1❖t = ln（FV / PV) / ln(1 + r)6 Discounted Cash Flow Valuation❖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。

98 Year 1 CF：2 N; 8 I/Y；—4000 PV；CPT FV = 4,665。

60 FV = 4,000(1.08)2 = 4，665。

60 Year 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。

87You 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 tha t 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)❖ Valuing Level Cash Flows ： Annuities and Perpetuities◆ Annuity 年金连续相同的现金流 – finite series of equal payments that occur at regular intervals❖ If the first payment occurs at the end of the period ， it is called an ordinaryannuity 普通年金❖ If the first payment occurs at the beginning of the period, it is called an annuitydue 先付年金◆ Perpetuity – infinite series of equal payments 永续年金只有现值没有终值 期数无限❖ Perpetuity ： PV = C / r ❖ 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 tr t t r t FVIFA C r r C FV PVIFA C r r C PV ,,1)1()1(11⨯=⎥⎦⎤⎢⎣⎡-+=⨯=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡+-=)1(,r FVIFA C FVD n i N +⨯⨯=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❖ 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比较不同期间的rate 不能直接比较Annual Percentage Rate(APR ）年化报价利率❖ This is the annual rate that is quoted by law❖ By definition APR = period rate times the number of periods per year❖ Consequently, to get the period rate we rearrange the APR equation ：▪ Period rate = APR / number of periods per year ❖ You should NEVER divide the effective rate by the number of periods per year – it willNOT give you the period rateContinuous Compounding EAR = e q – 1Example ： What is the effective annual rate of 7％ compounded continuously?EAR = e .07 – 1 = 。

0725 or 7。

25％Pure Discount LoansThe 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 。

❖ Loan Types and Loan Amortization 每年偿还利息加一部分本金)1(,r PVIFA C PVD n i +⨯⨯=tt r g C r g C r C PV )1()1()1()1()1(12++⨯++++⨯++=- ⎥⎥⎦⎤⎢⎢⎣⎡⎪⎪⎭⎫ ⎝⎛++--=t r g g r C PV )1()1(1 +++⨯+++⨯++=322)1()1()1()1()1(r g C r g C r C PV g r CPV -=00.26$05.10.30.1$=-=PV ⎥⎦⎤⎢⎣⎡+=1 - EAR) (1 m APR m 1❖ Make single ， fixed payment every period❖ 5，000=C*｛[1-（1/1.095）］/0。

09}❖ 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）❖ 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 rateMaturity 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 decreaseC: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YTMIf 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❖ Coupon rate 小于market 折价债券 discount bondt tr)(1FV r r)(11-1C V alue Bond ++⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡+=Consider 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。