内容发布更新时间 : 2024/10/20 20:49:58星期一 下面是文章的全部内容请认真阅读。

5 Time value of money Compinding future value FV Discounting present value PV

Interest rate exchange rate between earlier and later money哕簽粪飪棂嬰驿。 ? 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

閘鈐巔挤轡衮麩。 ? For a given time period – the higher the interest rate, the smaller the present value

懑滸织擋暈贸戗。 ? 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?蓮賀辏兑顛辐渎。 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勻贈憚痈鸥鲍厨。 Year 1 CF: 2 N; 8 I/Y; -4000 PV; CPT FV = 4,665、60 FV = 4,000(1、08)2 = 4,665、60渎购賡騁鮫铱绢。 Year 2 CF: 1 N; 8 I/Y; -4000 PV; CPT FV = 4,320 FV = 4,000(1、08) = 4,320鍵紱纖扪氲锰蓠。 Year 3 CF: value = 4,000

Total value in 3 years = 8817、98 + 4665、60 + 4320 + 4000 = 21,803、58妆藍鸪恆鱘娱軋。 Value at year 4: 1 N; 8 I/Y; -21803、58 PV; CPT FV = 23,547、87 气霽装彥覷认頗。

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?绀幀厩楊癘颼崢。 Point out that the question could also be phrased as “How much is this investment worth?”錆疇駝喽頜謹顸。 Calculator:

Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178、57罌灿繭藝違潋辊。 Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318、88傾詢饭鲦糾爛谂。 Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427、07争箫岗颦镤炖陨。 Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = - 508、41鈰骀邇俨勻炜铱。 Total PV = 178、57 + 318、88 + 427、07 + 508、41 = 1,432、93繰妪飲锹繩剑顫。

现金流都发生在年末 e/g后付变先付 相当于原来得数据*（1+r）

? Valuing Level Cash Flows: Annuities and Perpetuities餃灄絎桦潜鶩橢。 ? Annuity年金连续相同得现金流 – finite series of equal payments that occur at

regular intervals曠緩颟鎵叶洼颁。 ? If the first payment occurs at the end of the period, it is called an ordinary

annuity 普通年金歼扫蕴铒苏琐摻。 ? If the first payment occurs at the beginning of the period, it is called an annuity

due 先付年金爛渙创拣琺煩担。 ? Perpetuity – infinite series of equal payments 永续年金只有现值没有终值 期数

无限嘸轟迟们鯰峽绢。 1??? Perpetuity: PV = C / r ?1?(1?r)?PV?C???C?PVIFAr??? Annuities

tr,t优先股有永续年金得特征

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 FVDN?C?FVIFAi,n?(1?r) PVD?C?PVIFAi,n?(1?r)Growing Perpetuity增长年金A growing stream of cash flows with a fixed maturity增长率一定谦轲蟯緘鳳鵝贱。 ????t?(1?r)?1?FV?C?r,t??C?FVIFAr??

PV?PV?CC?(1?g)C?(1?g)t?1????2(1?r)(1?r)(1?r)ttC??(1?g)??A growing stream of cash flows that lasts forever 用来计算股票得价格联呕欽摊壟隐嬙。 C?(1?g)2PV????? (C1?r)(1?r)2(1?r)3PV? r ? g 产品未来所有得价值现在得现值 相当于股票现在得价格不就是交易价格 The expected dividend next year is $1、30, and dividends are expected to grow at 5% forever、 竄驀廠呗誊墮陉。 ??1????r?g??(1?r)?g)C??C?(1???If the discount rate is 10%, what is the value of this promised dividend stream?蛺鹆顧捫谘錐窭。 $1.30PV??$26.00如果现在卖价小于26即可买入

?.05? .10Comparing 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、膃鸥锸数潋篳許。 m比较不同期间得rate不能直接比较 ?Quoted rate?EAR ? ?1 ? ?? 1Annual Percentage Rate（APR）年化报价利率 m??? This is the annual rate that is quoted by law ? By definition APR = period rate times the number of periods per year雛输滟廬尔綬讲。 ? Consequently, to get the period rate we rearrange the APR equation:規猡豬袭櫥駟獄。 ? 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鲧戲紕鋌点栌黪。 1APR ? m ?(1 ? EAR)m - 1?q – 1 ??Continuous Compounding EAR = e??Example: What is the effective annual rate of 7% compounded continuously?偉嬸焖馒赵鉚堑。 EAR = e07 – 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诒窑餃镱漢腡锞。 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卤苋騙骒訣償镭。 This cash flow stream is similar to the cash flows on corporate bonds、 鰥堯頭缍誤网奮。 ? Loan Types and Loan Amortization 每年偿还利息加一部分本金

、

? Make single, fixed payment every period ? 5,000=C*{[1-(1/1、095)]/0、09} ? C=1285、45

7 Interest Rates and Bond Valuation

现金流折现得三个重要信息 现金流 折现率 期限 评估资产价值对资产未来产生得现金流进行估计把所有现金流折现加总得到零时刻得价值 （价值大于价格则买进）从鉬贫价硗担躑。 ? 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 贺织噯鐲貿偬礼。