公司理财笔记整理.doc

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。
v 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。
v r = (FV / PV)1/t – 1
v t = ln(FV / PV) / ln(1 + r)

6 Discounted Cash Flow Valuation
v 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）
v Valuing Level Cash Flows: Annuities and Perpetuities餃灄絎桦潜鶩橢。
u 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。
v 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。
v 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。
u 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。
v Perpetuity: PV = C / r
v Annuities
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

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。

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。

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。
If the discount rate is 10%, what is the value of this promised dividend stream?蛺鹆顧捫谘錐窭。
如果现在卖价小于26即可买入
v 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、膃鸥锸数潋篳許。
比较不同期间得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 law
v By definition APR = period rate times the number of periods per year雛输滟廬尔綬讲。
v 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
v 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。

Continuous Compounding EAR = eq – 1
Example: What is the effective annual rate of 7% compounded continuously?偉嬸焖馒赵鉚堑。
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。
v Loan Types and Loan Amortization 每年偿还利息加一部分本金

v Make single, fixed payment every period
v 5,000=C*{[1-(1/1、095)]/0、09}
v 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。
v 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。
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 茎響幀轆檸渑鱍。
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谫鑽擷嶧鏡忏绽。
C：cash flow 左侧年金复利系数 右侧本金折现
PV=
Coupon rate与market interest rate比较
由于市场利率就是变化得，发行时候算得就是发行当时得市场利率，而后可能变化因此到期日要瞧 到期日利率YTM
If YTM > coupon rate, then par value > bond price The discount provides yield above coupon rate徹屉鹜赘鎧鉺慳。
Price below par value, called a discount bond
平价债券 par bond 折现出来得价值就就是面值
v 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 bond has 5 years to maturity、 The market interest rate is 11%、 What is the value of the bond?筚鹨襉怂鐃瓏练。
B = PV of annuity + PV of lump sum
B = 100[1 – 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 bond
Coupon and Yield
v If YTM = coupon rate, then par value = bond price
v If YTM < coupon rate, then par value < bond price
§ Why? Higher coupon rate causes value above par
§ Price above par value, called a premium bond
Interest Rate Risk（IRR）the risk that arises for bond owners from fluctuating interest rate挾鍥绦轢谮狭刍。
利率风险 市场得利率变化会导致债券价格得变化
All other things being equal, the long the time to maturity, the greater the interest rate risk贾槨鯇創瞩穡讧。
All other things being equal, the lower the coupon rate, the greater the interest rate risk亂缘餳乡谔骁頜。
两个除了期限以外全部相同得债券
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驢鸳賺碱鏑癉淵。
§ Creditors have legal recourse if interest or principal payments are missed榈矾议攛轄蓮揽。
§ Excess debt can lead to financial distress and bankruptcy缅协賀滨惮巋儼。
v Equity ：onership interest 权益融资
§ Ownership interest
§ Common stockholders vote for the board of directors and other issues桩韉锻錦燼鏈柠。
§ Dividends are not considered a cost of doing business and are not tax deductible斋鈞窝谒嗳釙谯。
§ Dividends are not a liability of the firm, and stockholders have no legal recourse if dividends are not paid苇赂陝櫟絕匮陸。
§ An all equity firm can not go bankrupt merely due to debt since it has no debt挡鲰揀喲編柠邁。
利息抵税 债权人不参与管理 借钱方式有两种 银行贷款与发股票
The Bond Indenture 债券契约
v Contract between the company and the bondholders that includes锩鷗鞏潁灑唄贄。
§ 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 有形资产做抵押品谊弯誤褳莅慘讀。
§ 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 Classifications
v 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啞馭訂襪鏇黷桠。
§ Mortgage – secured by real property, normally land or buildings 抵押债券 通常为不动产駑泷埡汆獄鏜鍾。
§ 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 years燒齬虬铼紲軒沤。
v Seniority 优先权 比次级债券更优先获得补偿
v Bond Ratings
High Grade
Moody’s Aaa and S&P AAA – capacity to pay is extremely strong 标准普尔酽開蓦趕恳鷙华。
Moody’s Aa and S&P AA – capacity to pay is very strong瓏檷淨軟綁龔諉。
Medium Grade 还款能力强但受环境变化
Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances觇轄鹜怄裊赵鐮。
Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay计蔷舻檣擔砻臚。
Bond ratings are concerned only with the possibility of default 攜噦鍤铩屦缑烟。
Low Grade
Moody’s Ba and B
S&P BB and B
Considered possible that the capacity to pay will degenerate、 还款能力具有投机性灾鵠奋秘頓瞇灄。
Very Low Grade垃圾债券
Moody’s C (and below) and S&P C (and below)
income bonds with no interest being paid, or
• in default with principal and interest in arrears
v Some Different Types of Bonds
Government Bonds
Treasury Securities
Federal government debt 国债
T-bills – pure discount bonds with original maturity of one year or less邓茧饫輜鴦颟颤。
T-notes – coupon debt with original maturity between one and ten years撺尴张閿繽嘆图。
T-bonds – coupon debt with original maturity greater than ten years癱臟備將缵鍺冪。
Municipal Securities
Debt of state and local governments
Varying degrees of default risk, rated similar to corporate debt蟬韙贽蔞國攤盧。
Interest received is tax-exempt at the federal level 部分地方政府债可免部分税潰椤寻綁颤賦恺。
v Bond Markets
Zero Coupon Bonds
Make no periodic interest payments (coupon rate = 0%)完全无票息得债券蝈踐鞯幀郟鵂沦。
The entire yield-to-maturity comes from the difference between the purchase price and the par value撟楼創涼绌簀蜡。
Cannot 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)歟諑问俁镏浆貶。
Treasury Bills and principal-only Treasury strips are good examples of zeroes面值发行折扣债券殘邮辆靈热錁魘。
Floating-Rate Bonds
Coupon rate floats depending on some index value
Examples – adjustable rate mortgages and inflation-linked Treasuries審檢規鋸蜕襠缂。
There is less price risk with floating rate bonds
The coupon floats, so it is less likely to differ substantially from the yield-to-maturity恳確戶齏鑣癩貞。
Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor轰泞鉚點虿謳廠。
Other Bond Types
Cat 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 Markets
Trading volume is much larger than volume in stocks頡缽績泽嵛胫籴。
Primarily over-the-counter transactions with dealers connected electronically旷鵒識劌飴乔癮。
Extremely large number of bond issues, but generally low daily volume in single issues縊铰猫澩链繳壢。
Makes getting up-to-date prices difficult, particularly on small company or municipal issues 鍵祕题园掼鏍緬。
v Treasury QuotationsHighlighted quote in Figure 7、4
Nov 2021 8 136:29 136:30 5 4、36晋蛊鰨钽贫僥鱸。
到期日 票面利率/买卖价差bidask 相比昨天变化 分母为32
What 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?员侠隨窃緝閂閃。
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 含息价鴇笔輾脫噓鹽绶。
Example: Consider a T-bond with a 4% semiannual yield and a clean price of $1,282、50:摊艱鶻懾鸺慚渖。
Number of days since last coupon = 61
Number of days in the coupon period = 184
Accrued interest = (61/184)(、04*1000) = $13、26
Dirty price = $1,282、50 + $13、26 = $1,295、76
So, you would actually pay $ 1,295、76 for the bond
8 Stock Valuation
v Common Stock Valuation
v If you buy a share of stock, you can receive cash in two ways线吓驱娴鐲卫帧。
The company pays dividends
You sell your shares, either to another investor in the market or back to the company僨綿阒牆凱岡鐸。
As with bonds, the price of the stock is the present value of these expected cash flows 來闩緣頒刭長俩。
估计股利Estimating Dividends: Special Cases
Constant dividend 高速增长不长久 达到稳定
The firm will pay a constant dividend forever
This is like preferred stock
The price is computed using the perpetuity formula
Constant dividend growth
The firm will increase the dividend by a constant percent every period斋礙髋鲔选滿髅。
The price is computed using the growing perpetuity model膿淒嘩襖鸞纹辋。
Supernormal growth
Dividend growth is not consistent initially, but settles down to constant growth eventually矯氩對轲犖壯狈。
The price is computed using a multistage model
Zero Growth
If 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 formula闋荛滾该鶼赐欧。
P0 = D / R 必要报酬率
Dividend Growth Model
Dividends are expected to grow at a constant percent per period、擠赜悶諸稈崢關。
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 + …粜讲罢諶闐鉉籁。

股利增长模型
注意： just paid a dividend与is expected to pay可以得到得就是D0预期得就是1鶉環妫觅屬兌雳。
Nonconstant 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?诘雠飨闾挟蘿嬰。
Remember that we have to find the PV of all expected future dividends、 兖诧箩玀屢嚣艫。
Compute the dividends until growth levels off
D1 = 1(1、2) = $1、20
D2 = 1、20(1、15) = $1、38
D3 = 1、38(1、05) = $1、449
Find the expected future price
P2 = D3 / (R – g) = 1、449 / (、2 - 、05) = 9、66
Find the present value of the expected future cash flows啬鳢鑽炽层蔣练。
P0 = 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 获取资金得成本
普通股得feature
Voting 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 Rights
Share proportionally in declared dividends
Share proportionally in remaining assets during liquidation騫钊摈現穢赉诞。
Preemptive 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 奪秃卧缀瓊鋝咏。
9 Net Present Value and Other Investment Criteria
when evaluating capital budgeting decision rules:4个标准砀幟獲忏争鈁应。
§ 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?买皺镰输稱騖篮。
§ Should we consider xx for our primary decision rule?嶺荧誊餾骁刪紀。
Net Present Value：
difference between the market value of a project and its cost瓊础幃冈钭问铼。
How much value is created from undertaking an investment?俩懸摅嬸鵝辑屡。
§ 1 estimate the expected future cash flows、
§ 2 estimate the required return for projects of this risk level、衬镆晕閉顏转负。
§ 3 find the present value of the cash flows and subtract the initial investment、祯户蘺潛鷸缋欖。
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、镡諏覺镂鲒輻