公司理财笔记整理

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)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 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

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 = -178.57 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

1??? Perpetuity: PV = C / r ?1?(1?r)?PV?C???C?PVIFAr??? Annuities

????优先股有永续年金的特征 ?(1?r)?1?FV?C???C?FVIFAr??

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)ttr,tr,t 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

CC?(1?g)C?(1?g)t?1???? PV?(1?r)(1?r)2(1?r)t

t C??(1?g)??PV??1???(1?r)???r?g??? ???A growing stream of cash flows that lasts forever 用来计算股票的价格 CC?(1?g)C?(1?g)2PV????? (1?r)(1?r)2(1?r)3 C r ? g 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?

$1.30PV??$26.00如果现在卖价小于26即可买入

.10?.05

? 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

PV? rate??QuotedEAR ? ?1 ? ?? 1m??mAnnual 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

1APR ? m ?(1 ? EAR)m - 1??? ??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

? 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

1??1-(1?r)tBond Value ? C?r?? ? ??FV??t?(1?r)??

PV=

C：cash flow 左侧年金复利系数 右侧本金折现

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

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 = 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

? If YTM = coupon rate, then par value = bond price ? 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 利率风险 市场的利率变化会导致债券价格的变化

All other things being equal, the long the time to maturity, the greater the interest rate risk All other things being equal, the lower the coupon rate, the greater the interest rate risk

两个除了期限以外全部相同的债券

债券条款：

? 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

? Creditors have legal recourse if interest or principal payments are missed ? Excess debt can lead to financial distress and bankruptcy ? Equity ：onership interest 权益融资

? Ownership interest

? Common stockholders vote for the board of directors and other issues

? Dividends are not considered a cost of doing business and are not tax deductible ? Dividends are not a liability of the firm, and stockholders have no legal recourse

if dividends are not paid

? An all equity firm can not go bankrupt merely due to debt since it has no debt

利息抵税 债权人不参与管理 借钱方式有两种 银行贷款和发股票 The Bond Indenture 债券契约

? Contract between the company and the bondholders that includes

? The basic terms of the bonds 基本条款 ? The total amount of bonds issued 发行总额

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