财务管理课件chap004.ppt

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1、Introduction to Valuation:The Time Value of Money,Chapter 4,鼠静蚌英脱僧且塑杉者荔灸玖芳埃借割弦冷肺叼负挑滞爪蒜栓抨凝羞拓奏财务管理课件chap004财务管理课件chap004,4.1,Key Concepts and Skills,Be able to compute the future value of an investment made todayBe able to compute the present value of cash to be received at some future dateBe able to

2、compute the return on an investment,吃卑踪望吝酝钎北靡层酞吮坝奏谅短陨铱既潘温颇顿狞有青亭淆荫端桑抹财务管理课件chap004财务管理课件chap004,4.2,Chapter Outline,Future Value and CompoundingPresent Value and DiscountingMore on Present and Future Values,氖瓢枫姚鬃致沤捌阿轩蜗腆沈绿邯绣严义擦铣梢爽成抡宴淋钢舰锑目蛊象财务管理课件chap004财务管理课件chap004,4.3,Basic Definitions,Present Value

3、 earlier money on a time lineFuture Value later money on a time lineInterest rate“exchange rate”between earlier money and later moneyDiscount rateCost of capitalOpportunity cost of capitalRequired return,卸膜良踞观欢腺系栗纫时暮娥澳兴址晚捡匀丛挎孔华斧咏粤虾杠朔邑积谊财务管理课件chap004财务管理课件chap004,4.4,Future Values,Suppose you invest$

4、1000 for one year at 5%per year.What is the future value in one year?Interest=1000(.05)=50Value in one year=principal+interest=1000+50=1050Future Value(FV)=1000(1+.05)=1050Suppose you leave the money in for another year.How much will you have two years from now?FV=1000(1.05)(1.05)=1000(1.05)2=1102.5

5、0,师摸圾箭惜跌嚣爪弱醚炮峦青多乓喝于缘榷喧左沏祷诣轨峙美功洽扣诬凉财务管理课件chap004财务管理课件chap004,4.5,Future Values:General Formula,FV=PV(1+r)tFV=future valuePV=present valuer=period interest rate,expressed as a decimalT=number of periodsFuture value interest factor=(1+r)t,秀卑遍屡秤馁辩骄星梨启赵攫韶殉访媒陨贯掏咀见休帮帅忻搞迢闲胁凋企财务管理课件chap004财务管理课件chap004,4.6,

6、Effects of Compounding,Simple interest Compound interestConsider the previous exampleFV with simple interest=1000+50+50=1100FV with compound interest=1102.50The extra 2.50 comes from the interest of.05(50)=2.50 earned on the first interest payment,蒋存阳抄塌奎躯湾央娱款蛾叁舒佑轿比冗藕阻总烁煎巾熄韭株靡拙叼沽寒财务管理课件chap004财务管理课件c

7、hap004,4.7,Figure 4.1,敷蚤童个程抛湿释裤机据伯骸笆砸斡严绸植惋议堑劈辞祭唬护居祥腻甸爸财务管理课件chap004财务管理课件chap004,4.8,Figure 4.2,烃捅办拇炙醋别冉于粗瑰轨嫡渤恕拴危脑国酪穴诧针铭冻岩墒烬西笔尉狞财务管理课件chap004财务管理课件chap004,4.9,Calculator Keys,Texas Instruments BA-II PlusFV=future valuePV=present valueI/Y=period interest rateP/Y must equal 1 for the I/Y to be the per

8、iod rateInterest is entered as a percent,not a decimalN=number of periodsRemember to clear the registers(CLR TVM)after each problemOther calculators are similar in format,弱瞻睛氛些五钓麦曙朱伏姆诈食诞妻烙扇习落与膨拌咯夜非克州俱购俊肋财务管理课件chap004财务管理课件chap004,4.10,Future Values Example 2,Suppose you invest the$1000 from the prev

9、ious example for 5 years.How much would you have?FV=1000(1.05)5=1276.28The effect of compounding is small for a small number of periods,but increases as the number of periods increases.(Simple interest would have a future value of$1250,for a difference of$26.28.),丑阎绿继惟留纽窗勿俄倒懦要蓬诧桅酵搓昼坏妄疡听缀涌迂浅筹据搪障丽财务管理

10、课件chap004财务管理课件chap004,4.11,Future Values Example 3,Suppose you had a relative deposit$10 at 5.5%interest 200 years ago.How much would the investment be worth today?FV=10(1.055)200=447,189.84What is the effect of compounding?Simple interest=10+200(10)(.055)=210.55Compounding added$446,979.29 to the

11、value of the investment,侥僻至涪霹帛吝买锤真直颅亢两冰桓器帕流接打鞭带泪佛灌七织匀肃增鬃财务管理课件chap004财务管理课件chap004,4.12,Future Value as a General Growth Formula,Suppose your company expects to increase unit sales of widgets by 15%per year for the next 5 years.If you currently sell 3 million widgets in one year,how many widgets do

12、you expect to sell in 5 years?FV=3,000,000(1.15)5=6,034,072,暑茄淡敛郧嫂奠笆溢党粟琐帜馈惯沙由谆爵钮喀萎彬艾栏邪详豫掂崎淌止财务管理课件chap004财务管理课件chap004,4.13,Quick Quiz:Part 1,What is the difference between simple interest and compound interest?Suppose you have$500 to invest and you believe that you can earn 8%per year over the next

13、 15 years.How much would you have at the end of 15 years using compound interest?How much would you have using simple interest?,努稼护诚靖张赁贡套紧织蝴讫波粘俭眶紧陵蓄夺碑淖镐娄祈室棠衣奔注票财务管理课件chap004财务管理课件chap004,4.14,Present Values,How much do I have to invest today to have some amount in the future?FV=PV(1+r)tRearrange to

14、solve for PV=FV/(1+r)tWhen we talk about discounting,we mean finding the present value of some future amount.When we talk about the“value”of something,we are talking about the present value unless we specifically indicate that we want the future value.,咋坝祭枉涡秃船笼慰若上葛符报脱旬凋柑漆拉驾卑猩烘豫胚类派爷玖驾犯财务管理课件chap004财务

15、管理课件chap004,4.15,PV One Period Example,Suppose you need$10,000 in one year for the down payment on a new car.If you can earn 7%annually,how much do you need to invest today?PV=10,000/(1.07)1=9345.79Calculator1 N7 I/Y10,000 FVCPT PV=-9345.79,守倒渣括酝讫沥辩探夺装退缄热溅朽码牡箕样商网凑组促伞孟晃意宅峻婉财务管理课件chap004财务管理课件chap004,

16、4.16,Present Values Example 2,You want to begin saving for you daughters college education and you estimate that she will need$150,000 in 17 years.If you feel confident that you can earn 8%per year,how much do you need to invest today?PV=150,000/(1.08)17=40,540.34,仙搞袖除辅陷以要窘屈姨廓您多介晋承举示尖俄肘坠纷兴狼瑶烤矮否湃噬财务管

17、理课件chap004财务管理课件chap004,4.17,Present Values Example 3,Your parents set up a trust fund for you 10 years ago that is now worth$19,671.51.If the fund earned 7%per year,how much did your parents invest?PV=19,671.51/(1.07)10=10,000,宛坡饭隶遵肖腻锤呜殷绝穿处窃刺电堆债田吭奥六仿谢佐雏崎岔吞含术找财务管理课件chap004财务管理课件chap004,4.18,PV Impor

18、tant Relationship I,For a given interest rate the longer the time period,the lower the present valueWhat is the present value of$500 to be received in 5 years?10 years?The discount rate is 10%5 years:PV=500/(1.1)5=310.4610 years:PV=500/(1.1)10=192.77,桅隐消砒肪摇谋早壕票静菲颅栏呛耀刘翻庙盲蜡畏驭颊菩衣界蹲彝呸呕决财务管理课件chap004财务管理

19、课件chap004,4.19,PV Important Relationship II,For a given time period the higher the interest rate,the smaller the present valueWhat is the present value of$500 received in 5 years if the interest rate is 10%?15%?Rate=10%:PV=500/(1.1)5=310.46Rate=15%;PV=500/(1.15)5=248.58,羚琴族菏醒蔚历门旭帅姥梧唾骸伙铆旭袭娩脐股蓬佐饿篆厌腔镍遵

20、遗墓洱财务管理课件chap004财务管理课件chap004,4.20,Quick Quiz:Part 2,What is the relationship between present value and future value?Suppose you need$15,000 in 3 years.If you can earn 6%annually,how much do you need to invest today?If you could invest the money at 8%,would you have to invest more or less than at 6%

21、?How much?,属霓蓬落露毖岭借须煎令符蘑矩测禽挑坏笨换调鸥凌抱奖颊刷溜嗽笛麦书财务管理课件chap004财务管理课件chap004,4.21,Figure 4.3,微孝溅缠纲桶饲依勃拔侗量艘峡扎窝屁橱姿全钓讥贪剂层枯互凶俏柬哄惫财务管理课件chap004财务管理课件chap004,4.22,The Basic PV Equation-Refresher,PV=FV/(1+r)tThere are four parts to this equationPV,FV,r and tIf we know any three,we can solve for the fourthIf you a

22、re using a financial calculator,be sure and remember the sign convention or you will receive an error when solving for r or t,汕姓默掏蘑茄基溺旨刽竣这率盼烽懈鸿趣窒贫琉册厉喷蹦疟申扣芦揣欠绘财务管理课件chap004财务管理课件chap004,4.23,Discount Rate,Often we will want to know what the implied interest rate is in an investmentRearrange the basic

23、 PV equation and solve for rFV=PV(1+r)tr=(FV/PV)1/t 1If you are using formulas,you will want to make use of both the yx and the 1/x keys,妨河轿贤廷劣止阂躁马馆韧君岂课纱凭猫盛涝铅鳞津蚀阎俄贤恼完堵赠彻财务管理课件chap004财务管理课件chap004,4.24,Discount Rate Example 1,You are looking at an investment that will pay$1200 in 5 years if you inves

24、t$1000 today.What is the implied rate of interest?r=(1200/1000)1/5 1=.03714=3.714%Calculator the sign convention matters!N=5PV=-1000(you pay 1000 today)FV=1200(you receive 1200 in 5 years)CPT I/Y=3.714%,径洲纬音决拱羹迪悸绊碱扩续紧薛奢植宫印凛毯馏沽炬舌闭蘸赵象佯妖步财务管理课件chap004财务管理课件chap004,4.25,Discount Rate Example 2,Suppose y

25、ou are offered an investment that will allow you to double your money in 6 years.You have$10,000 to invest.What is the implied rate of interest?r=(20,000/10,000)1/6 1=.122462=12.25%,避涝读元祸腰柞遂谅碍阻埔掘敦也积赫下袍诬规窟劣栅弗之工椎臭坊肪公财务管理课件chap004财务管理课件chap004,4.26,Discount Rate Example 3,Suppose you have a 1-year old

26、son and you want to provide$75,000 in 17 years towards his college education.You currently have$5000 to invest.What interest rate must you earn to have the$75,000 when you need it?r=(75,000/5,000)1/17 1=.172688=17.27%,绅躺独喉扰庸吏稠原卷弓投普惠捞流募辟蜒芋檄硼靛巡信茎丈酉次邑臂凯财务管理课件chap004财务管理课件chap004,4.27,Quick Quiz:Part 3,

27、What are some situations where you might want to compute the implied interest rate?Suppose you are offered the following investment choices:You can invest$500 today and receive$600 in 5 years.The investment is considered low risk.You can invest the$500 in a bank account paying 4%.What is the implied

28、 interest rate for the first choice and which investment should you choose?,鹤发廷瓤彰触吭姨期拱报蹄广饥敦绣府冗道棕层芍遏豆芭环汪怀椅韦素读财务管理课件chap004财务管理课件chap004,4.28,Finding the Number of Periods,Start with basic equation and solve for t(remember your logs)FV=PV(1+r)tt=ln(FV/PV)/ln(1+r)You can use the financial keys on the c

29、alculator as well,just remember the sign convention.,婆逊詹级熔晨怜怕脓族贾拙胰线弃瘴呕伴谗硷播全喧弯杖密瞧炳肯垦哭兽财务管理课件chap004财务管理课件chap004,4.29,Number of Periods Example 1,You want to purchase a new car and you are willing to pay$20,000.If you can invest at 10%per year and you currently have$15,000,how long will it be before

30、you have enough money to pay cash for the car?t=ln(20,000/15,000)/ln(1.1)=3.02 years,拯潍盐啄合豹酋仇桐绚雌拽烙昧驶询颓颖咒娇利纤筷猿俊饮下闭纵司踪忘财务管理课件chap004财务管理课件chap004,4.30,Number of Periods Example 2,Suppose you want to buy a new house.You currently have$15,000 and you figure you need to have a 10%down payment plus an add

31、itional 5%in closing costs.If the type of house you want costs about$150,000 and you can earn 7.5%per year,how long will it be before you have enough money for the down payment and closing costs?,速习堕慧童坦阵啮狮坍录迎骸恐澎燎葵来蹲瓢刁由涕惭资芽找菲剔援垮躇财务管理课件chap004财务管理课件chap004,4.31,Example 2 Continued,How much do you need

32、 to have in the future?Down payment=.1(150,000)=15,000Closing costs=.05(150,000 15,000)=6,750Total needed=15,000+6,750=21,750Compute the number of periodsPV=-15,000FV=21,750I/Y=7.5CPT N=5.14 yearsUsing the formulat=ln(21,750/15,000)/ln(1.075)=5.14 years,碳狱戮惟脑白捞廖镇千肢埋微眯巳纹销糖莹鞭惕衅嫩案溉敢耽鬃肖杆蟹扩财务管理课件chap004财

33、务管理课件chap004,4.32,Example:Spreadsheet Strategies,Use the following formulas for TVM calculationsFV(rate,nper,pmt,pv)PV(rate,nper,pmt,fv)RATE(nper,pmt,pv,fv)NPER(rate,pmt,pv,fv)The formula icon is very useful when you cant remember the exact formulaClick on the Excel icon to open a spreadsheet contai

34、ning four different examples.,汛蓉靳咀闽礁遗扔杆撼片剐幌轿峨亚应剐配蔼届赌陶统谊软嘛算转硷润棱财务管理课件chap004财务管理课件chap004,4.33,Work the Web Example,Many financial calculators are available onlineClick on the web surfer to go to Cignas web site and work the following example:You need$40,000 in 15 years.If you can earn 9.8%interest,h

35、ow much do you need to invest today?You should get$9,841,谗眷东淄涟议竹袖委扰罚芝疽氖坎耐克缄辐辫溪炕遵同毁彩氦磨挚儡窃垂财务管理课件chap004财务管理课件chap004,4.34,Table 4.4,誓垦脾硼瘩签舌蔡掀惦处噶崭旭呐陡赚荣牡苹驳计寥兰蝴巡烤蒂顶平羔藉财务管理课件chap004财务管理课件chap004,4.35,Quick Quiz:Part 4,When might you want to compute the number of periods?Suppose you want to buy some new furniture for your family room.You currently have$500 and the furniture you want costs$600.If you can earn 6%,how long will you have to wait if you dont add any additional money?,乌纤危闰续静花警案桓父宏蜘丘邑淹惧若言贸欣檀孰肩甩磷织乙健棉凌胺财务管理课件chap004财务管理课件chap004,