精品课程PPT公司金融导论第六章(二).ppt

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1、公司理财第六章(B),Discounted Cash Flow Valuation(Formulas),ChapterSix,Key Concepts and Skills,Be able to compute the future value of multiple cash flowsBe able to compute the present value of multiple cash flowsBe able to compute loan paymentsBe able to find the interest rate on a loanUnderstand how loans

2、are amortized or paid offUnderstand how interest rates are quoted,Chapter Outline,Future and Present Values of Multiple Cash FlowsValuing Level Cash Flows:Annuities and PerpetuitiesComparing Rates:The Effect of Compounding PeriodsLoan Types and Loan Amortization,Multiple Cash Flows Future Value Exam

3、ple 6.1,Find the value at year 3 of each cash flow and add them together.Today(year 0):FV=7000(1.08)3=8,817.98Year 1:FV=4,000(1.08)2=4,665.60Year 2:FV=4,000(1.08)=4,320Year 3:value=4,000Total value in 3 years=8817.98+4665.60+4320+4000=21,803.58Value at year 4=21,803.58(1.08)=23,547.87,Multiple Cash

4、Flows FV Example 2,Suppose you invest$500 in a mutual fund today and$600 in one year.If the fund pays 9%annually,how much will you have in two years?FV=500(1.09)2+600(1.09)=1248.05,Multiple Cash Flows Example 2 Continued,How much will you have in 5 years if you make no further deposits?First way:FV=

5、500(1.09)5+600(1.09)4=1616.26Second way use value at year 2:FV=1248.05(1.09)3=1616.26,Multiple Cash Flows FV Example 3,Suppose you plan to deposit$100 into an account in one year and$300 into the account in three years.How much will be in the account in five years if the interest rate is 8%?FV=100(1

6、.08)4+300(1.08)2=136.05+349.92=485.97,Multiple Cash Flows Present Value Example 6.3,Find the PV of each cash flows and add themYear 1 CF:200/(1.12)1=178.57Year 2 CF:400/(1.12)2=318.88Year 3 CF:600/(1.12)3=427.07Year 4 CF:800/(1.12)4=508.41Total PV=178.57+318.88+427.07+508.41=1432.93,Example 6.3 Time

7、line,Multiple Cash Flows Using a Spreadsheet,You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flowsSetting the data up is half the battle if it is set up properly,then you can just copy the formulasClick on the Excel icon for an example,Multiple

8、Cash Flows PV Another Example,You are considering an investment that will pay you$1000 in one year,$2000 in two years and$3000 in three years.If you want to earn 10%on your money,how much would you be willing to pay?PV=1000/(1.1)1=909.09PV=2000/(1.1)2=1652.89PV=3000/(1.1)3=2253.94PV=909.09+1652.89+2

9、253.94=4815.93,Multiple Uneven Cash Flows Usingthe Calculator,Another way to use the financial calculator for uneven cash flows is to use the cash flow keysTexas Instruments BA-II PlusPress CF and enter the cash flows beginning with year 0.You have to press the“Enter”key for each cash flowUse the do

10、wn arrow key to move to the next cash flowThe“F”is the number of times a given cash flow occurs in consecutive yearsUse the NPV key to compute the present value by entering the interest rate for I,pressing the down arrow and then computeClear the cash flow keys by pressing CF and then CLR Work,Decis

11、ions,Decisions,Your broker calls you and tells you that he has this great investment opportunity.If you invest$100 today,you will receive$40 in one year and$75 in two years.If you require a 15%return on investments of this risk,should you take the investment?Use the CF keys to compute the value of t

12、he investmentCF;CF0=0;C01=40;F01=1;C02=75;F02=1NPV;I=15;CPT NPV=91.49No the broker is charging more than you would be willing to pay.,Saving For Retirement,You are offered the opportunity to put some money away for retirement.You will receive five annual payments of$25,000 each beginning in 40 years

13、.How much would you be willing to invest today if you desire an interest rate of 12%?Use cash flow keys:CF;CF0=0;C01=0;F01=39;C02=25000;F02=5;NPV;I=12;CPT NPV=1084.71,Saving For Retirement Timeline,0 1 2 39 40 41 42 43 44,0 0 0 0 25K 25K 25K 25K 25K,Notice that the year 0 cash flow=0(CF0=0)The cash

14、flows years 1 39 are 0(C01=0;F01=39)The cash flows years 40 44 are 25,000(C02=25,000;F02=5),Quick Quiz Part I,Suppose you are looking at the following possible cash flows:Year 1 CF=$100;Years 2 and 3 CFs=$200;Years 4 and 5 CFs=$300.The required discount rate is 7%What is the value of the cash flows

15、at year 5?What is the value of the cash flows today?What is the value of the cash flows at year 3?,Annuities and Perpetuities Defined,Annuity finite series of equal payments that occur at regular intervalsIf the first payment occurs at the end of the period,it is called an ordinary annuityIf the fir

16、st payment occurs at the beginning of the period,it is called an annuity duePerpetuity infinite series of equal payments,Annuities and Perpetuities Basic Formulas,Perpetuity:PV=C/rAnnuities:,Annuities and the Calculator,You can use the PMT key on the calculator for the equal paymentThe sign conventi

17、on still holdsOrdinary annuity versus annuity dueYou can switch your calculator between the two types by using the 2nd BGN 2nd Set on the TI BA-II Plus If you see“BGN”or“Begin”in the display of your calculator,you have it set for an annuity dueMost problems are ordinary annuities,Annuity Example 6.5

18、,You borrow money TODAY so you need to compute the present value.48 N;1 I/Y;-632 PMT;CPT PV=23,999.54($24,000)Formula:,Annuity Sweepstakes Example,Suppose you win the Publishers Clearinghouse$10 million sweepstakes.The money is paid in equal annual installments of$333,333.33 over 30 years.If the app

19、ropriate discount rate is 5%,how much is the sweepstakes actually worth today?PV=333,333.331 1/1.0530/.05=5,124,150.29,Buying a House,You are ready to buy a house and you have$20,000 for a down payment and closing costs.Closing costs are estimated to be 4%of the loan value.You have an annual salary

20、of$36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28%of your monthly income.The interest rate on the loan is 6%per year with monthly compounding(.5%per month)for a 30-year fixed rate loan.How much money will the bank loan you?How much can you offer for the house

21、?,Buying a House-Continued,Bank loanMonthly income=36,000/12=3,000Maximum payment=.28(3,000)=840PV=8401 1/1.005360/.005=140,105Total PriceClosing costs=.04(140,105)=5,604Down payment=20,000 5604=14,396Total Price=140,105+14,396=154,501,Annuities on the Spreadsheet-Example,The present value and futur

22、e value formulas in a spreadsheet include a place for annuity paymentsClick on the Excel icon to see an example,Quick Quiz Part II,You know the payment amount for a loan and you want to know how much was borrowed.Do you compute a present value or a future value?You want to receive 5000 per month in

23、retirement.If you can earn.75%per month and you expect to need the income for 25 years,how much do you need to have in your account at retirement?,Finding the Payment,Suppose you want to borrow$20,000 for a new car.You can borrow at 8%per year,compounded monthly(8/12=.66667%per month).If you take a

24、4 year loan,what is your monthly payment?20,000=C1 1/1.006666748/.0066667C=488.26,Finding the Payment on a Spreadsheet,Another TVM formula that can be found in a spreadsheet is the payment formulaPMT(rate,nper,pv,fv)The same sign convention holds as for the PV and FV formulasClick on the Excel icon

25、for an example,Finding the Number of Payments Example 6.6,Start with the equation and remember your logs.1000=20(1 1/1.015t)/.015.75=1 1/1.015t1/1.015t=.251/.25=1.015tt=ln(1/.25)/ln(1.015)=93.111 months=7.75 yearsAnd this is only if you dont charge anything more on the card!,Finding the Number of Pa

26、yments Another Example,Suppose you borrow$2000 at 5%and you are going to make annual payments of$734.42.How long before you pay off the loan?2000=734.42(1 1/1.05t)/.05.136161869=1 1/1.05t1/1.05t=.8638381311.157624287=1.05tt=ln(1.157624287)/ln(1.05)=3 years,Finding the Rate,Suppose you borrow$10,000

27、from your parents to buy a car.You agree to pay$207.58 per month for 60 months.What is the monthly interest rate?Sign convention matters!60 N10,000 PV-207.58 PMTCPT I/Y=.75%,Annuity Finding the Rate Without aFinancial Calculator,Trial and Error ProcessChoose an interest rate and compute the PV of th

28、e payments based on this rateCompare the computed PV with the actual loan amountIf the computed PV loan amount,then the interest rate is too lowIf the computed PV loan amount,then the interest rate is too highAdjust the rate and repeat the process until the computed PV and the loan amount are equal,

29、快速测验 Part III,你想在接下来的5年中每月收到5000美元,在0.75%的月历率下你今天必须存多少钱?如果你只能存200000美元的话,你必须得到多少月历率?假设在0.75%的月历率下你有200000可以存。你能收到多少个月的每月5000美元的付款？你在以后的5年中每月能收到多少钱？,年金终值,假设你开始每年将2000美元存入你的退休金帐户，在7.5的利率下,40年后你将有多少钱?FV=2000(1.07540 1)/.075=454,513.04,期初年金,你为买一座房子每年将10000美元存在一个8%的帐户中,第一笔存款今天支付,3年后你将有多少钱?FV=10,000(1.083

30、 1)/.08(1.08)=35,061.12,期初年金时间线,35,016.12,永续年金 例 6.7,永续年金公式:PV=C/r当前要求回报率:40=1/rr=.025 或 2.5%每季度新偏好股利:100=C/.025C=2.50每季度,快速测验 Part IV,你希望35年后退休时拥有1000000美元,在1%的月历率下你每月必须存多少钱?如果第一笔存款在一个月后支付。第一笔存款在今天支付呢?你正在考虑一项每季付股利1.50美元的股票,如果你想得到每季3%的回报率,你将支付多少钱?,网络案例练习,另一种在线财务计算器能在 MoneyChimp中找到浏览网页做下面的练习选择计算器和年金

31、你继承了5000000美元,如果你能得到6%的利率,在以后的40年中你每年能收到多少钱?Datachimp 假设是期初年金!付款额=$313,497.81,表 6.2,实际年利率EAR,这是指在一年中发生多次复利计息后你实际付出（或得到）的利率。如果你想比较两种不同复利方式投资的回报，需 要用他们的实际年利率进行比较。,年百分率APR,这是通过法律规定的年利率报价年百分率的定义是APR=一年中每期的利率 该年中的期数因此，为了得到每期的利率，我们可以变形 年百分率的公式 每期的利率=年百分率/该年的期数你千万不能用该年中的期数除以实际利率，这 样你 不会得到每期的利率,计算年百分率APR,如果

32、月利率是0.5%，APR是多少？APR应该是0.5%12=6%如果半年利率是0.5%，APR是多少？APR应该是0.5%2=1%如果APR是12%，每月复利，月利率是多少？应该是12%/12=1%你能把上面的APR除以2得到半年的利率吗？不行！你需要一个以半年复利的APR来计算出半年的利率。,注意事项,你需要记住要始终保证利率和期数相匹配。如果是按年计息，那么你需要一个年利率。如果是按月计息，那么你需要一个月利率。如果你有一个以月复利的APR，你需要用按月计息的利率来计算总数，或者如果你不是以月付款，就需要适当地调节利率来适应,计算EAR举例,假设你今天投资$1每月能够得到1%的利率。APR是

33、多少？1%12=12%你最后实际能得到多少钱呢？FV=1(1.01)12=1.1268 利率=(1.1268-1)/1=0.1268=12.68%假设如果你把它用另一种叙述，你每季度有3%的利率。APR是多少？3%4=12%你最后实际能得到多少钱呢？FV=1(1.03)4=1.1255 利率=(1.1255-1)/1=0.1255=12.55%,EAR的计算公式,记住APR是报价利率,决定,决定II,你正在考虑两种储蓄存款帐户.一种的利率是 5.25%,每日复利.另外的一种利率是 5.3%半年计息一次.你会使用哪个帐户?第一个帐户:实际年利率=(1+.0525/365)365 1=5.39%第

34、二个帐户:实际年利率=(1+.053/2)2 1=5.37%你会选择哪个帐户，为什么呢?,决定,决定 II 继续,.让我们来核对一下选择.假设你每个帐户投资了$100.一年后你会在每个帐户收到多少?第一个帐户:计息365次;日利率是5.25/365=.014383562;现值是$100;资金的终值=105.39第二个帐户:计息两次;利率是5.3/2=2.65;现值是$100，资金的终值=105.37可以看出第一个帐户可以让你得到更多.,从名义年利率来计算实际年利率,如果知道实际年利率你如何计算名义年利率?重新安排实际年利率你可以得到：,名义年利率举例,假设你在考虑一个以月计息的帐户，并且你期望

35、得到的实际年利率是12%.他们必须给出多少的名义年利率?,在名义年利率下计算付款,假设你要买一个新的电脑系统并且商店愿意让你每月分期付款.电脑系统总价值 是$3500.贷款时间是 2 年，以月计息利率是 16.9%，每月需要付款多少?计息次数是24;月 利率为16.9/12=1.408333333;现值是$3500;期初年金为C=172.88 3500=C1 1/1.01408333333)24/.01408333333,终值和以月计息,假设你每个月存$50，名义年利率是 9%,以月计息.35年后你这个帐户中有多少钱?计息次数=420 次利率是9/12=0.75期初年金是$50资金终值=147

36、,089.22,现值和以日计息,你三年后买辆新车需要$15,000.如果你可以存款到一个帐户，名义年利率是5.5%并且以日计息，你今天需要存多少钱?计息次数=1095 次利率为5.5/365=.015068493 终值是15,000 资金的现值=12,718.56,连续复利,一些投资或者贷款是以连续复利计算的。实际年利率=eq 1这里的e 在计算时通常通过ex来表示的特殊功能举例:连续复利计算时7%的实际年利率是多少?实际年利率=e.07 1=.0725 或者7.25%,快速问答 第五部分,什么叫做APR?什么是实际年利率?你将使用哪个利率表示投资和贷款的关系?你需要使用哪个利率表示货币的时间

37、价值？,纯折价贷款 例6.12,国库券是纯折价贷款的一个典型的例子.总的价值在未来的某一时点偿还,没有定期的利息支付.如果一张国库卷承诺一年后偿还 10,000美圆，而市场利率为7%，那么，这张国库券在市场上可以卖多少钱?现值=10,000/1.07=9345.79,纯利息贷款 范例,考虑一个五年期,纯利息贷款利率为7%总资本$10,000.利息每年支付.每笔现金流量是多少?1 4年:利息支付.07(10,000)=7005年:利息+本金=10,700这笔现金流量等价于 它在股票上的现金流，一会儿我们将更加详细的讨论它。,分期偿还贷款固定金额法-范例,考虑一个$50,000,10年期，利率为

38、8%.借款合约中要求借款公司每年偿还$5,000 的借款加上借款余额的利息.点击 Excel 图像看一下分期偿还贷款时间表。,分期偿还贷款金额法-范例,每笔支付 加上利息费用和减少的资本。考虑一个四年，每年支付利息，利率为8%，总资本为5000美圆。每年要支付多少钱?4 N8 I/Y5000 PVCPT PMT=-1509.60点击 Excel 图像看一下分期偿还贷款时间表。,网上练习举例,存在一个网点 可以容易的制作一份分期偿还贷款时间表。上网点击找出 CMB 债权方，看下面的例子你有一笔$25,000的贷款，并且以8%的利率在五年之后偿还.你将支付多少贷款?它的分期偿还贷款时间表是怎么样的?,快速问答 第六部分,什么叫纯折价贷款?纯折价贷款的典型例子是什么?什么叫纯利息贷款?纯利息贷款的典型例子是什么?什么叫分期偿还贷款?分期偿还贷款的典型例子是什么?,