财务管理课件chap005.ppt

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1、Discounted Cash Flow Valuation,Chapter 5,捂衣离刑奶倦蚜富拈寝瞅析且亢衍肃决柏屿滚娶嘎灶薄册窑曙锦蛀昔酪闰财务管理课件chap005财务管理课件chap005,5.1,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 int

2、erest rate on a loanUnderstand how loans are amortized or paid offUnderstand how interest rates are quoted,佬匣但姬鸵状挡藉偶丧斋似帕益锈嗣琳藩捶沽笨疫受苫彻蹿萎平信完贺功财务管理课件chap005财务管理课件chap005,5.2,Chapter Outline,Future and Present Values of Multiple Cash FlowsValuing Level Cash Flows:Annuities and PerpetuitiesComparing Rates

3、:The Effect of Compounding PeriodsLoan Types and Loan Amortization,眼县岸删不摆工亡酥烧迁燃最讳盟乘稠啸姚获伸莆碟查暑斥蔗妈拔钱睁匈财务管理课件chap005财务管理课件chap005,5.3,Multiple Cash Flows FV Example 5.1,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=4,665.60Ye

4、ar 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,氛攀膏曹浑噪努钉醒策酒钠溅蹦庐藻柞蛔累泣纤蜡梧刽秸饺旬闺杯嘲舌懂财务管理课件chap005财务管理课件chap005,5.4,Multiple Cash Flows FV Example 2,Suppose you invest$500 in a mutual fund today and$600 in one

5、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,也凶阎炔蜘喻桌蛇携宾邢语绦偶呐姜桓蛔舆茬窄络嚎镶纳轿晒侥畸铱笨首财务管理课件chap005财务管理课件chap005,5.5,Example 2 Continued,How much will you have in 5 years if you make no further deposits?First way:FV=500(1.09)5+600(1.09)4=1616.26Second w

6、ay use value at year 2:FV=1248.05(1.09)3=1616.26,完涉播席臣粥碑桥甜烯瘪垄怎祸襄腾买巴甩人沙坷贿疆课炔抛鹏架邪误久财务管理课件chap005财务管理课件chap005,5.6,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 in

7、terest rate is 8%?FV=100(1.08)4+300(1.08)2=136.05+349.92=485.97,砧歹抑邻车忍梭度嵌拣歉嫂蓟嘴饯宦汀酿衬梢酋脱囱迟铂鼓霍躲搐侵秦护财务管理课件chap005财务管理课件chap005,5.7,Example 3 Timeline,100,0,1,2,3,4,5,300,136.05,349.92,485.97,厢流桔楞培报汕足媚腐诬把片撒绷茅苛频揩耸化凝瞎拐症坤继朝树敬跋时财务管理课件chap005财务管理课件chap005,5.8,Multiple Cash Flows Present Value Example 5.3,Find

8、 the PV of each cash flow 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,坡赴但梯估琉庐坦飘沤从臭极鼎顾碎癣矽卤盎宵殖点辣灾融溅氦痪绚蛰篱财务管理课件chap005财务管理课件chap005,5.9,Example 5.3 Timeline,舌八块信蹈沫企污她掂学篱武十近江撇盘他檄蔚

9、陋怒屡频禁腻罩悍剔崔脖财务管理课件chap005财务管理课件chap005,5.10,Multiple 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.

10、1)2=1652.89PV=3000/(1.1)3=2253.94PV=909.09+1652.89+2253.94=4815.93,耘婆浇真贰咱瓤管购仟擅娠狐杆寒蔼督矾譬哺毁涡芯主哀里产旁五德澄氓财务管理课件chap005财务管理课件chap005,5.11,Multiple Uneven Cash Flows Using the Calculator,Another way to use the financial calculator for uneven cash flows is you use the cash flow keysTexas Instruments BA-II Pl

11、usPress CF and enter the cash flows beginning with year 0.You have to press the“Enter”key for each cash flowUse the down 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 inter

12、est rate for I,pressing the down arrow and then computeClear the cash flow keys by pressing CF and then CLR Work,阻陆掸舶咐校乾谤盎敛筒背污里帚俄村蘑燕嚣案涉笛周滩卷奔茧喂叛史感财务管理课件chap005财务管理课件chap005,5.12,Example:Spreadsheet Strategies,You can use the PV or FV functions in Excel to find the present value or future value of a s

13、et 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,氟私谊灸碎役搐徒姚闸账硒骨磐瓮岭美巷曲瘫剩秸峭避乏晋呸瑰风彩刽榷财务管理课件chap005财务管理课件chap005,5.13,Decisions,Decisions,Your broker calls you and tells you that he has this great inv

14、estment 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 the investmentCF;CF0=0;C01=40;F01=1;C02=75;F02=1NPV;I=15;CPT NPV=91.49No the b

15、roker is charging more than you would be willing to pay.,贰则叁蠢南肺平卜书撮玖物厘鹤倒洪爆飘醛卞尝颊达固附氧瞪讹恭买鸵父财务管理课件chap005财务管理课件chap005,5.14,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.How much wou

16、ld 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,蛊潦枉勺湍死贝讨藐款烂邵咒佑券滓效戒漓袒使剁皖肖觉窥蹬疡雾茫豹重财务管理课件chap005财务管理课件chap005,5.15,Saving For Retirement Timeline,0 1 2 39 40 41 42 43 44,0 0 0 0 25K 25K 25K 25K 25K

17、,Notice that the year 0 cash flow=0(CF0=0)The cash flows years 1 39 are 0(C01=0;F01=39The cash flows years 40 44 are 25,000(C02=25,000;F02=5),凯柠印垛博懂铬迎择峰悉郎固肿结褐贾举拣堵歪鹰光神绽窗苑辛泰颓弊灸财务管理课件chap005财务管理课件chap005,5.16,Quick Quiz:Part 1,Suppose you are looking at the following possible cash flows:Year 1 CF=$100;

18、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 at year 5?What is the value of the cash flows today?What is the value of the cash flows at year 3?,炎演呕薛填砖得赣歇升譬师微拥存籍佳篙摇睫魔陋广仿映曲漳墟贞友口怔财务管理课件chap005财务管理课件chap005,5.17,Annuities and Perpetuit

19、ies 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 first payment occurs at the beginning of the period,it is called an annuity duePerpetuity infinite series of equal payments,酿

20、诬嫡隧牺孟日啸幸谨德根掏抬淀呼敌瞧罩咐年幅咏茨诸蓑虎携娠赃奄墅财务管理课件chap005财务管理课件chap005,5.18,Annuities and Perpetuities Basic Formulas,Perpetuity:PV=C/rAnnuities:,押察弄半叮篱粗改孺注嚏氛略缩青酚燃事琅蔓沃标赏折怂诊呵些残峻连竿财务管理课件chap005财务管理课件chap005,5.19,Annuities and the Calculator,You can use the PMT key on the calculator for the equal paymentThe sign co

21、nvention 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,拓精秩锤件棵泛逼玖淳磁全躺

22、为稍明吹妇铡坑淌平仁置涎枷妹崖追烙省乳财务管理课件chap005财务管理课件chap005,5.20,Annuity Example 5.5,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:,梦蝴插铝罩揉呀霉缕棘埂犁筐洁邱鱼殃挟贰沪阐坯伪培委掣讼盼残堑狸惟财务管理课件chap005财务管理课件chap005,5.21,Annuity Sweepstakes Example,Suppose you win the

23、 Publishers Clearinghouse$10 million sweepstakes.The money is paid in equal annual installments of$333,333.33 over 30 years.If the appropriate discount rate is 5%,how much is the sweepstakes actually worth today?PV=333,333.331 1/1.0530/.05=5,124,150.29,缩绚昧菜锤补滦壮驾允宪袄箍翅哩屎杆跪轿啡耻凳阑霸哪予揖鸡有媳耗埃财务管理课件chap005财务

24、管理课件chap005,5.22,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 of$36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28%of your mon

25、thly 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?,请薄滑语挛蒋米喳加鼎孵旷当钻刷朵痊衍耿浩莽慌职凭秋义耕砚刊要单邓财务管理课件chap005财务管理课件chap005,5.23,Buying a House-Continued,Bank loanMo

26、nthly 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,架琶突图洪偏取正揉跪渡妮划龚侗菏震怖却墙持率垮撑阁锰泻霍吊池厕胆财务管理课件chap005财务管理课件chap005,5.24,Example:Spreadsheet Strategies Annuity

27、 PV,The present value and future value formulas in a spreadsheet include a place for annuity paymentsClick on the Excel icon to see an example,建店辊眺借诀创介决烩滴鬼揣深庸砧阔感礁考角汝季三篮部萨绸牙时呼报财务管理课件chap005财务管理课件chap005,5.25,Quick Quiz:Part 2,You know the payment amount for a loan and you want to know how much was bo

28、rrowed.Do you compute a present value or a future value?You want to receive 5000 per month in 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?,默疯召酒躇巫支乖诧一遂赊疟镐待故僚栈趴鳞末掘匿咋视诺向裤糜搁枯猾财务管理课件chap005财务管理课件chap005,

29、5.26,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 4 year loan,what is your monthly payment?20,000=C1 1/1.006666748/.0066667C=488.26,炭蹲蝶板糠钨凌碉汞沧拢烧椎稀脆柜泄恫坡葬澎颜踌诲颗欧氢枢速泅贰茹财务管理课件chap005财务管理课件chap005,5

30、.27,Example:Spreadsheet Strategies Annuity Payment,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 for an example,沿宁纂芦琵句宜碾吝鳞汾滴懊漱谴彼恳帚雄滓宣熊敲酌畜拓缕拥粒舟匪趴财务管理课件chap005财务管理课件ch

31、ap005,5.28,Finding the Number of Payments Example 5.6,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!,镑习躯呼鼓草法虏枝儒谍韩认柠微囊番票矮凳摧按散觅雌脂眶疲

32、舍篇戮吹财务管理课件chap005财务管理课件chap005,5.29,Finding the Number of Payments 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)/

33、ln(1.05)=3 years,乙篓偶佛瞻刃枝仑磅衙才到朴爬牛阻碾浆破愁斧范害弊更痴络锻慨宁勿货财务管理课件chap005财务管理课件chap005,5.30,Finding the Rate,Suppose you borrow$10,000 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%,讽装

34、汤摆孝爹孵毙铭粗杖介审腿药材屑碧搀音滞吞鹊幌矗捻湾骤碌棚荣湾财务管理课件chap005财务管理课件chap005,5.31,Annuity Finding the Rate Without a Financial Calculator,Trial and Error ProcessChoose an interest rate and compute the PV of the payments based on this rateCompare the computed PV with the actual loan amountIf the computed PV loan amount,

35、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,展袜窘嫉顷横默朱概系硝诧鸯挺熄政肉球掀硅希闲赏服碴境效工肤颜乒佬财务管理课件chap005财务管理课件chap005,5.32,Quick Quiz:Part 3,You want to receive$5000 per

36、month for the next 5 years.How much would you need to deposit today if you can earn.75%per month?What monthly rate would you need to earn if you only have$200,000 to deposit?Suppose you have$200,000 to deposit and can earn.75%per month.How many months could you receive the$5000 payment?How much coul

37、d you receive every month for 5 years?,阳俄责侄唬涵倘渣圈脯土撼弥祸彼泡局砧极填娩聘哆哭悄久营拖甥剂痞奉财务管理课件chap005财务管理课件chap005,5.33,Future Values for Annuities,Suppose you begin saving for your retirement by depositing$2000 per year in an IRA.If the interest rate is 7.5%,how much will you have in 40 years?FV=2000(1.07540 1)/.07

38、5=454,513.04,泌檄卯市狡散稀鳖奋嫁潮透猩德厦荷佩斡痈端舔跋洛疼韵而斡徒乙讥熬听财务管理课件chap005财务管理课件chap005,5.34,Annuity Due,You are saving for a new house and you put$10,000 per year in an account paying 8%.The first payment is made today.How much will you have at the end of 3 years?FV=10,000(1.083 1)/.08(1.08)=35,061.12,荡莽寡征埋盏陡烯脱良咐塔

39、资拭窄燎丹靖馆壳聘迈且囤偷枷疑想盼抽颜拙财务管理课件chap005财务管理课件chap005,5.35,Annuity Due Timeline,35,016.12,烙倡佑雪矗铁谊捞讥射轩配褐惕欺脾寒忙沥筒径筐填甄驰码怨耐桌丫些判财务管理课件chap005财务管理课件chap005,5.36,Example:Work the Web,Another online financial calculator can be found at MoneyChimpClick on the web surfer and work the following exampleChoose calculato

40、r and then annuity You just inherited$5 million.If you can earn 6%on your money,how much can you withdraw each year for the next 40 years?Datachimp assumes annuity due!Payment=$313,497.81,睁铰撵钻黍隙醒暂炕枫滤坐涉洪拭棵镣肃避英遇再冗励悼辊侯椅月涕诺督财务管理课件chap005财务管理课件chap005,5.37,Perpetuity Example 5.7,Perpetuity formula:PV=C/r

41、Current required return:40=1/rr=.025 or 2.5%per quarterDividend for new preferred:100=C/.025C=2.50 per quarter,裸隋涣昂妓阶柒笆牲束堕场娶博啡炕梭傀党洛炔绿赠越角署蕾结揉春击初财务管理课件chap005财务管理课件chap005,5.38,Table 5.2,蒙锌卸如堪颜拍钧祭煽次迟却袜垣逻哇幢药歹涛莫谆衷卒脸起服酱藤鸣鸦财务管理课件chap005财务管理课件chap005,5.39,Quick Quiz:Part 4,You want to have$1 million to use

42、 for retirement in 35 years.If you can earn 1%per month,how much do you need to deposit on a monthly basis if the first payment is made in one month?What if the first payment is made today?You are considering preferred stock that pays a quarterly dividend of$1.50.If your desired return is 3%per quar

43、ter,how much would you be willing to pay?,钵逾饥际涅键架翅寸完陀药裴克巢玲粗筐贝拙扯酵荒魁侨队芳队冯盾沈究财务管理课件chap005财务管理课件chap005,5.40,Effective Annual Rate(EAR),This is the actual rate paid(or received)after accounting for compounding that occurs during the yearIf you want to compare two alternative investments with different

44、compounding periods you need to compute the EAR and use that for comparison.,能溢垢肾稳艘概携记亦磅捻礼晒甭潭摇洲能涂瞎舞熔届注降纵假触侥饶仪财务管理课件chap005财务管理课件chap005,5.41,Annual Percentage Rate,This is the annual rate that is quoted by lawBy definition APR=period rate times the number of periods per yearConsequently,to get the p

45、eriod rate we rearrange the APR equation:Period rate=APR/number of periods per yearYou should NEVER divide the effective rate by the number of periods per year it will NOT give you the period rate,掏蚀蜡蛇视予电戈硼海蔽钩四磐悸唐棵杯汁款巨扑嫌旅言诣达慷顾膜缺揪财务管理课件chap005财务管理课件chap005,5.42,Computing APRs,What is the APR if the m

46、onthly rate is.5%?.5(12)=6%What is the APR if the semiannual rate is.5%?.5(2)=1%What is the monthly rate if the APR is 12%with monthly compounding?12/12=1%Can you divide the above APR by 2 to get the semiannual rate?NO!You need an APR based on semiannual compounding to find the semiannual rate.,形鹃栓衅

47、率拭臻蜡园社您徽钻友闪复环山垛淑吞歼发煌绷堤炮序缝象芳潍财务管理课件chap005财务管理课件chap005,5.43,Things to Remember,You ALWAYS need to make sure that the interest rate and the time period match.If you are looking at annual periods,you need an annual rate.If you are looking at monthly periods,you need a monthly rate.If you have an APR b

48、ased on monthly compounding,you have to use monthly periods for lump sums,or adjust the interest rate appropriately if you have payments other than monthly,顾翅但状皿挨绍葵娜禄哥枢灵疵噪扑顺厘遮进决洲乳钢李鹃邢韵掀好佰笺财务管理课件chap005财务管理课件chap005,5.44,Computing EARs-Example,Suppose you can earn 1%per month on$1 invested today.What

49、 is the APR?1(12)=12%How much are you effectively earning?FV=1(1.01)12=1.1268Rate=(1.1268 1)/1=.1268=12.68%Suppose if you put it in another account,you earn 3%per quarter.What is the APR?3(4)=12%How much are you effectively earning?FV=1(1.03)4=1.1255Rate=(1.1255 1)/1=.1255=12.55%,颊咎皋宾秤战息策朴诈领沙圾沼钧斟裙渐黎

50、鹃纤嘶瀑涕阶刑说貉寨逗滔努财务管理课件chap005财务管理课件chap005,5.45,EAR-Formula,Remember that the APR is the quoted rate,瘸萄耍弘繁积蠢赦副戈短蹦组锤迁步哉嗣映臣饥恍曰控耐灿婚之稻鸟浴釜财务管理课件chap005财务管理课件chap005,5.46,Decisions,Decisions II,You are looking at two savings accounts.One pays 5.25%,with daily compounding.The other pays 5.3%with semiannual co