2022年公司理财笔记整理只是分享.pdf

资料收集于网络，如有侵权请联系网站删除word 可编辑5 Time value of money Compinding future value FV Discounting present value PV Interest rate exchange rate between earlier and later money FV = PV(1 + r)tPV = FV / (1 + r)tr = 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) tpresent 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 Flows You 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) = 4,320 Year 3 CF: value = 4,000 Total value in 3 years = 8817.98 + 4665.60 + 4320 + 4000 = 21,803.58 Value at year 4: 1 N; 8 I/Y; -21803.58 PV; CPT FV = 23,547.87 精品资料 - - - 欢迎下载 - - - - - - - - - - - 欢迎下载 名师归纳 - - - - - - - - - -第 1 页，共 14 页 - - - - - - - - - - 资料收集于网络，如有侵权请联系网站删除word 可编辑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 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 = -178.57 Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318.88 Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427.07 Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = - 508.41 Total 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 ordinary annuity 普通年金If the first payment occurs at the beginning of the period, it is called an annuity due 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trttrtFVIFACrrCFVPVIFACrrCPV,1)1()1(11)1(,rFVIFACFVDniN精品资料 - - - 欢迎下载 - - - - - - - - - - - 欢迎下载 名师归纳 - - - - - - - - - -第 2 页，共 14 页 - - - - - - - - - - 资料收集于网络，如有侵权请联系网站删除word 可编辑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 Compounding Effective 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 will NOT give you the period rate Continuous Compounding EAR = eq 1 Example: 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 bills Interest-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 future This 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(,rPVIFACPVDnittrgCrgCrCPV)1()1()1()1()1(12trggrCPV)1()1(1322)1 ()1()1 ()1()1(rgCrgCrCPVgrCPV1mrateQuoted1EARm00.26$05.10.30.1$PV1-EAR)(1mAPRm1精品资料 - - - 欢迎下载 - - - - - - - - - - - 欢迎下载 名师归纳 - - - - - - - - - -第 3 页，共 14 页 - - - - - - - - - - 资料收集于网络，如有侵权请联系网站删除word 可编辑Make single, fixed payment every period 5,000=C*1-(1/1.095)/0.09 C=1285.45 7 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 Valuation Par 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 par Bond 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 rate Price 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 bond Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the ttr)(1FVrr)(11-1CValueBond精品资料 - - - 欢迎下载 - - - - - - - - - - - 欢迎下载 名师归纳 - - - - - - - - - -第 4 页，共 14 页 - - - - - - - - - - 资料收集于网络，如有侵权请联系网站删除word 可编辑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 sum B = 1001 1/(1.11)5 / .11 + 1,000 / (1.11)5B = 369.59 + 593.45 = 963.04 Coupon rate 大于 market 溢价债券premium bond Coupon and Yield If YTM = coupon rate, then par value = bond price If YTM coupon rate, then par value 1 Cannot be used to rank mutually exclusive projects May be used to rank projects in the presence of capital rationing Payback period Length of time until initial investment is recovered Take the project if it pays back within some specified period Doesn t account for time value of money, and there is an arbitrary cutoff periodDiscounted payback period Length of time until initial investment is recovered on a discounted basis Take the project if it pays back in some specified period There is an arbitrary cutoff period Average Accounting Return Measure of accounting profit relative to book value 精品资料 - - - 欢迎下载 - - - - - - - - - - - 欢迎下载 名师归纳 - - - - - - - - - -第 13 页，共 14 页 - - - - - - - - - - 资料收集于网络，如有侵权请联系网站删除word 可编辑Similar to return on assets measure Take the investment if the AAR exceeds some specified return level Serious problems and should not be used 精品资料 - - - 欢迎下载 - - - - - - - - - - - 欢迎下载 名师归纳 - - - - - - - - - -第 14 页，共 14 页 - - - - - - - - - -