1、3-1 Pearson Education Limited 2004Fundamentals of Financial Management,12/eCreated by:Gregory A.Kuhlemeyer,Ph.D.Carroll College,Waukesha,WI3-21.Understand what is meant by the time value of money.2.Understand the relationship between present and future value.3.Describe how the interest rate can be u
2、sed to adjust the value of cash flows both forward and backward to a single point in time.4.Calculate both the future and present value of:(a)an amount invested today;(b)a stream of equal cash flows(an annuity);and(c)a stream of mixed cash flows.5.Distinguish between an“ordinary annuity”and an“annui
3、ty due.”6.Use interest factor tables and understand how they provide a shortcut to calculating present and future values.7.Use interest factor tables to find an unknown interest rate or growth rate when the number of time periods and future and present values are known.8.Build an“amortization schedu
4、le”for an installment-style loan.3-3u The Interest Rateu Simple Interestu Compound Interestu Amortizing a LoanuCompounding More Than Once per Year3-4Obviously,.You already recognize that there is!Which would you prefer-or?3-5 allows you the opportunity to postpone consumption and earn.Why is such an
5、 important element in your decision?3-6Interest paid(earned)on any previous interest earned,as well as on the principal borrowed(lent).Interest paid(earned)on only the original amount,or principal,borrowed(lent).3-7SI=P0(i)(n)SI:Simple InterestP0:Deposit today(t=0)i:Interest Rate per Periodn:Number
6、of Time Periods3-8uSI=P0(i)(n)=$1,000(.07)(2)=uAssume that you deposit$1,000 in an account earning 7%simple interest for 2 years.What is the accumulated interest at the end of the 2nd year?3-9=P0+SI=$1,000+$140=is the value at some future time of a present amount of money,or a series of payments,eva
7、luated at a given interest rate.uWhat is the()of the deposit?3-10The Present Value is simply the$1,000 you originally deposited.That is the value today!is the current value of a future amount of money,or a series of payments,evaluated at a given interest rate.uWhat is the()of the previous problem?3-
8、11050001000015000200001st Year 10thYear20thYear30thYearFuture Value of a Single$1,000 Deposit10%SimpleInterest7%CompoundInterest10%CompoundInterestFuture Value(U.S.Dollars)3-12Assume that you deposit at a compound interest rate of 7%for.0 1 7%3-13=(1+i)1=(1.07)=Compound InterestYou earned$70 interes
9、t on your$1,000 deposit over the first year.This is the same amount of interest you would earn under simple interest.3-14=(1+i)1=(1.07)=FV1(1+i)1=(1+i)(1+i)=(1.07)(1.07)=(1+i)2=(1.07)2=You earned an EXTRA in Year 2 with compound over simple interest.3-15=P0(1+i)1=P0(1+i)2General Formula:=P0(1+i)n or
10、 =P0(i,n)-etc.3-16i,n is found on Table I at the end of the book.Period6%7%8%11.0601.0701.08021.1241.1451.16631.1911.2251.26041.2621.3111.36051.3381.4031.4693-17=$1,000(7%,2)=$1,000(1.145)=Due to RoundingPeriod6%7%8%11.0601.0701.08021.1241.1451.16631.1911.2251.26041.2621.3111.36051.3381.4031.4693-18
11、uUse the highlighted row of keys for solving any of the FV,PV,FVA,PVA,FVAD,and PVAD problemsN:Number of periodsI/Y:Interest rate per periodPV:Present valuePMT:Payment per periodFV:Future valueCLR TVM:Clears all of the inputs into the above TVM keys3-19NI/YPVPMTFVInputsCompute3-20Press:2nd CLR TVM2 N
12、7 I/Y -1000 PV0 PMT CPT FV3-21N:2 Periods(enter as 2)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:$1,000(enter as negative as you have“less”)PMT:Not relevant in this situation(enter as 0)FV:Compute(Resulting answer is positive)NI/YPVPMTFVInputsCompute 2 7 -1,000 0 1,144.903-22Julie Miller wan
13、ts to know how large her deposit of today will become at a compound annual interest rate of 10%for.0 1 2 3 4 10%3-23uCalculation based on Table I:=$10,000(10%,5)=$10,000(1.611)=Due to RoundinguCalculation based on general formula:=P0(1+i)n =$10,000(1+0.10)5=3-24Press:2nd CLR TVM5 N 10 I/Y -10000 PV0
14、 PMT CPT FV3-25The result indicates that a$10,000 investment that earns 10%annually for 5 years will result in a future value of$16,105.10.NI/YPVPMTFVInputsCompute 5 10 -10,000 0 16,105.103-26We will use the Quick!How long does it take to double$5,000 at a compound rate of 12%per year(approx.)?3-27A
15、pprox.Years to Double=/i%/12%=Actual Time is 6.12 YearsQuick!How long does it take to double$5,000 at a compound rate of 12%per year(approx.)?3-28The result indicates that a$1,000 investment that earns 12%annually will double to$2,000 in 6.12 years.Note:72/12%=approx.6 yearsNI/YPVPMTFVInputsCompute
16、12 -1,000 0 +2,000 6.12 years3-29Assume that you need in Lets examine the process to determine how much you need to deposit today at a discount rate of 7%compounded annually.0 1 7%PV13-30 =/(1+i)2=/(1.07)2 =/(1+i)2=0 1 7%3-31=/(1+i)1=/(1+i)2General Formula:=/(1+i)n or =(i,n)-etc.3-32i,n is found on
17、Table II at the end of the book.Period 6%7%8%1.943.935.926 2.890.873.857 3.840.816.794 4.792.763.735 5.747.713.681 3-33=(PVIF7%,2)=(.873)=Due to RoundingPeriod6%7%8%1.943.935.9262.890.873.8573.840.816.7944.792.763.7355.747.713.6813-34N:2 Periods(enter as 2)I/Y:7%interest rate per period(enter as 7 N
18、OT.07)PV:Compute(Resulting answer is negative“deposit”)PMT:Not relevant in this situation(enter as 0)FV:$1,000(enter as positive as you“receive$”)NI/YPVPMTFVInputsCompute 2 7 0 +1,000 -873.443-35Julie Miller wants to know how large of a deposit to make so that the money will grow to in at a discount
19、 rate of 10%.0 1 2 3 4 10%3-36uCalculation based on general formula:=/(1+i)n =/(1+0.10)5=uCalculation based on Table I:=(10%,5)=(.621)=Due to Rounding3-37NI/YPVPMTFVInputsCompute 5 10 0 +10,000 -6,209.21The result indicates that a$10,000 future value that will earn 10%annually for 5 years requires a
20、$6,209.21 deposit today(present value).3-38:Payments or receipts occur at the end of each period.:Payments or receipts occur at the beginning of each period.represents a series of equal payments(or receipts)occurring over a specified number of equidistant periods.3-39u Student Loan Paymentsu Car Loa
21、n Paymentsu Insurance Premiumsu Mortgage Paymentsu Retirement Savings3-400 1 2 3$100$100$100(Ordinary Annuity)ofPeriod 1 ofPeriod 2Today Cash Flows Each 1 Period Apart ofPeriod 33-410 1 2 3$100$100$100(Annuity Due)ofPeriod 1 ofPeriod 2Today Cash Flows Each 1 Period Apart ofPeriod 33-42=R(1+i)n-1+R(1
22、+i)n-2+.+R(1+i)1+R(1+i)0 R R R0 1 2 n+1R=Periodic Cash FlowCash flows occur at the end of the periodi%.3-43=$1,000(1.07)2+$1,000(1.07)1+$1,000(1.07)0 =$1,145+$1,070+$1,000 =$1,000$1,000$1,0000 1 2 47%$1,070$1,145Cash flows occur at the end of the period3-44The future value of an ordinary annuity can
23、 be viewed as occurring at the of the last cash flow period,whereas the future value of an annuity due can be viewed as occurring at the of the last cash flow period.3-45=R(FVIFAi%,n)=$1,000(FVIFA7%,3)=$1,000(3.215)=Period6%7%8%11.0001.0001.00022.0602.0702.08033.1843.2153.24644.3754.4404.50655.6375.
24、7515.8673-46N:3 Periods(enter as 3 year-end deposits)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:Not relevant in this situation(no beg value)PMT:$1,000(negative as you deposit annually)FV:Compute(Resulting answer is positive)NI/YPVPMTFVInputsCompute 3 7 0 -1,000 3,214.903-47=R(1+i)n+R(1+i)n-
25、1+.+R(1+i)2+R(1+i)1 =(1+i)R R R R R0 1 2 3 ni%.Cash flows occur at the beginning of the period3-48=$1,000(1.07)3+$1,000(1.07)2+$1,000(1.07)1 =$1,225+$1,145+$1,070 =$1,000$1,000$1,000$1,0700 1 2 47%$1,225$1,145Cash flows occur at the beginning of the period3-49=R(FVIFAi%,n)(1+i)=$1,000(FVIFA7%,3)(1.0
26、7)=$1,000(3.215)(1.07)=Period6%7%8%11.0001.0001.00022.0602.0702.08033.1843.2153.24644.3754.4404.50655.6375.7515.8673-50NI/YPVPMTFVInputsCompute 3 7 0 -1,000 3,439.94Complete the problem the same as an“ordinary annuity”problem,except you must change the calculator setting to“BGN”first.Dont forget to
27、change back!Step 1:Press2ndBGNkeysStep 2:Press2ndSETkeysStep 3:Press2ndQUITkeys3-51=R/(1+i)1+R/(1+i)2 +.+R/(1+i)n R R R0 1 2 n+1R=Periodic Cash Flowi%.Cash flows occur at the end of the period3-52=$1,000/(1.07)1+$1,000/(1.07)2+$1,000/(1.07)3 =$934.58+$873.44+$816.30 =$1,000$1,000$1,0000 1 2 47%$934.
28、58$873.44$816.30Cash flows occur at the end of the period3-53The present value of an ordinary annuity can be viewed as occurring at the of the first cash flow period,whereas the future value of an annuity due can be viewed as occurring at the of the first cash flow period.3-54=R(PVIFAi%,n)=$1,000(PV
29、IFA7%,3)=$1,000(2.624)=Period6%7%8%10.9430.9350.92621.8331.8081.78332.6732.6242.57743.4653.3873.31254.2124.1003.9933-55N:3 Periods(enter as 3 year-end deposits)I/Y:7%interest rate per period(enter as 7 NOT.07)PV:Compute(Resulting answer is positive)PMT:$1,000(negative as you deposit annually)FV:Not
30、relevant in this situation(no ending value)NI/YPVPMTFVInputsCompute 3 7 -1,000 0 2,624.323-56=R/(1+i)0+R/(1+i)1+.+R/(1+i)n-1 =(1+i)R R R R0 1 2 nR:Periodic Cash Flowi%.Cash flows occur at the beginning of the period3-57=$1,000/(1.07)0+$1,000/(1.07)1+$1,000/(1.07)2 =$1,000.00$1,000$1,0000 1 2 4=7%$93
31、4.58$873.44Cash flows occur at the beginning of the period3-58=R(PVIFAi%,n)(1+i)=$1,000(PVIFA7%,3)(1.07)=$1,000(2.624)(1.07)=Period6%7%8%10.9430.9350.92621.8331.8081.78332.6732.6242.57743.4653.3873.31254.2124.1003.9933-59NI/YPVPMTFVInputsCompute 3 7 -1,000 0 2,808.02Complete the problem the same as
32、an“ordinary annuity”problem,except you must change the calculator setting to“BGN”first.Dont forget to change back!Step 1:Press2ndBGNkeysStep 2:Press2ndSETkeysStep 3:Press2ndQUITkeys3-601.Read problem thoroughly2.Create a time line3.Put cash flows and arrows on time line4.Determine if it is a PV or F
33、V problem5.Determine if solution involves a single CF,annuity stream(s),or mixed flow6.Solve the problem7.Check with financial calculator(optional)3-61Julie Miller will receive the set of cash flows below.What is the at a discount rate of.0 1 2 3 4 3-621.Solve a“”by discounting each back to t=0.2.So
34、lve a“”by firstbreaking problem into groups of annuity streams and any single cash flow groups.Then discount each back to t=0.3-63 0 1 2 3 4 10%3-64 0 1 2 3 4 10%$600(PVIFA10%,2)=$600(1.736)=$1,041.60$400(PVIFA10%,2)(PVIF10%,2)=$400(1.736)(0.826)=$573.57$100(PVIF10%,5)=$100(0.621)=$62.103-65 0 1 2 3
35、 4 equals 0 1 2 0 1 2 3 4 53-66uUse the highlighted key for starting the process of solving a mixed cash flow problemuPress the CF key and down arrow key through a few of the keys as you look at the definitions on the next slide3-67Defining the calculator variables:For CF0:This is ALWAYS the cash fl
36、ow occurring at time t=0(usually 0 for these problems)For Cnn:*This is the cash flow SIZE of the nth group of cash flows.Note that a“group”may only contain a single cash flow(e.g.,$351.76).For Fnn:*This is the cash flow FREQUENCY of the nth group of cash flows.Note that this is always a positive who
37、le number(e.g.,1,2,20,etc.).*nn represents the nth cash flow or frequency.Thus,the first cash flow is C01,while the tenth cash flow is C10.3-68Steps in the ProcessStep 1:PressCF keyStep 2:Press2ndCLR WorkkeysStep 3:For CF0 Press0Enter keysStep 4:For C01 Press600Enter keysStep 5:For F01 Press2Enter k
38、eysStep 6:For C02 Press400Enter keysStep 7:For F02 Press2Enter keys3-69Steps in the ProcessStep 8:For C03 Press100Enter keysStep 9:For F03 Press1Enter keysStep 10:Press keysStep 11:PressNPV keyStep 12:For I=,Enter10Enter keysStep 13:PressCPT keyResult:Present Value=$1,677.153-70General Formula:FVn=(
39、1+i/m)mnn:Number of Yearsm:Compounding Periods per Yeari:Annual Interest RateFVn,m:FV at the end of Year n:PV of the Cash Flow today3-71Julie Miller has to invest for 2 Years at an annual interest rate of 12%.Annual FV2=(1+.12/1)(1)(2)=Semi FV2=(1+.12/2)(2)(2)=3-72Qrtly FV2=(1+.12/4)(4)(2)=Monthly F
40、V2=(1+.12/12)(12)(2)=Daily FV2=(1+.12/365)(365)(2)=3-73uContinuous compoundingFVn=(1+I/M)nm =(e)in PVn=/(e)in 3-74The result indicates that a$1,000 investment that earns a 12%annual rate compounded quarterly for 2 years will earn a future value of$1,266.77.NI/YPVPMTFVInputsCompute 2(4)12/4 -1,000 0
41、1266.773-75Press:2nd P/Y 4 ENTER 2nd QUIT 12 I/Y-1000 PV 0 PMT22nd xP/Y N CPT FV3-76The result indicates that a$1,000 investment that earns a 12%annual rate compounded daily for 2 years will earn a future value of$1,271.20.NI/YPVPMTFVInputsCompute2(365)12/365 -1,000 0 1271.203-77Press:2nd P/Y 365 EN
42、TER 2nd QUIT 12 I/Y-1000 PV 0 PMT22nd xP/Y N CPT FV3-78Effective Annual Interest RateThe actual rate of interest earned(paid)after adjusting the nominal rate for factors such as the number of compounding periods per year.(1+i/m )m-13-79Basket Wonders(BW)has a$1,000 CD at the bank.The interest rate i
43、s 6%compounded quarterly for 1 year.What is the Effective Annual Interest Rate()?=(1+6%/4)4-1=1.0614-1=.0614 or 3-80Press:2nd I Conv 6ENTER 4ENTER CPT2nd QUIT3-811.Calculate the payment per period.2.Determine the interest in Period t.(Loan Balance at t-1)x(i%/m)3.Computein Period t.(Payment-Interest
44、 from Step 2)4.Determine ending balance in Period t.(Balance-from Step 3)5.Start again at Step 2 and repeat.3-82Julie Miller is borrowing at a compound annual interest rate of 12%.Amortize the loan if annual payments are made for 5 years.Step 1:Payment =R(PVIFA i%,n)=R(PVIFA 12%,5)=R(3.605)=/3.605=3
45、-83End ofYearPaymentInterestPrincipalEndingBalance0-$10,0001$2,774$1,200$1,5748,42622,7741,0111,7636,66332,7748001,9744,68942,7745632,2112,47852,7752972,4780$13,871$3,871$10,000Last Payment Slightly Higher Due to Rounding3-84The result indicates that a$10,000 loan that costs 12%annually for 5 years
46、and will be completely paid off at that time will require$2,774.10 annual payments.NI/YPVPMTFVInputsCompute 5 12 10,000 0 -2774.103-85Press:2nd Amort 1ENTER 1 ENTERResults:BAL=8,425.90*PRN=-1,574.10*INT=-1,200.00*Year 1 information only*Note:Compare to 3-823-86Press:2nd Amort 2ENTER 2 ENTERResults:B
47、AL=6,662.91*PRN=-1,763.99*INT=-1,011.11*Year 2 information only*Note:Compare to 3-823-87Press:2nd Amort 1ENTER 5 ENTERResults:BAL=0.00 PRN=-10,000.00 INT=-3,870.49 Entire 5 Years of loan information(see the total line of 3-82)3-88-The quantity of outstanding debt may be used in financing the day-to-day activities of the firm.-Interest expenses may reduce taxable income of the firm.3-89uTotal price of the apartment=900tuInitial payment=20%*90t=180tuAverage monthly income=12tuRepay periods=30 yearsuInterest rate=4.8%annuallyuWhat is the percentage of your income spending on mortgage?
