Time-Value-of-Money.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,2013 Cengage Learning.All Rights Reserved.May not be scanned,copied,or duplicated,or posted to a publicly accessible website,in whole or in part.,5-,*,2013 Cengage Learning.All Rights Reserved.May not be scanned,copied,or duplicated,or posted to a publicly accessible website,in whole or in part.,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,3-,*,2013 Cengage Learning.All Rights Reserved.May not be scanned,copied,or duplicated,or posted to a publicly accessible website,in whole or in part.,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,3-,*,Time Value of Money,Future Value,Present Value,Annuities,Rates of Return,Amortization,Chapter 5,5-,1,Time Lines,Show the timing of cash flows.,Tick marks occur at the end of periods,so Time 0 is today;Time 1 is the end of the first period(year,month,etc.)or the beginning of the second period.,5-,2,CF,0,CF,1,CF,3,CF,2,0,1,2,3,I%,Drawing Time Lines,5-,3,100,100,100,0,1,2,3,I%,3-year$100 ordinary annuity,100,0,1,2,I%,$100 lump sum due in 2 years,Drawing Time Lines,5-,4,100,50,75,0,1,2,3,I%,-50,Uneven cash flow stream,What is the future value(FV)of an initial$100 after 3 years,if I/YR=10%?,Finding the FV of a cash flow or series of cash flows is called compounding.,FV can be solved by using the step-by-step,financial calculator,and spreadsheet methods.,5-,5,FV=?,0,1,2,3,10%,100,Solving for FV:The Step-by-Step and Formula Methods,After 1 year:,FV,1,=PV(1+I)=$100(1.10)=$110.00,After 2 years:,FV,2,=PV(1+I),2,=$100(1.10),2,=$121.00,After 3 years:,FV,3,=PV(1+I),3,=$100(1.10),3,=$133.10,After N years(general case):,FV,N,=PV(1+I),N,5-,6,Solving for FV:Calculator and Excel Methods,Solves the general FV equation.,Requires 4 inputs into calculator,and will solve for the fifth.(Set to P/YR=1 and END mode.),Excel:=FV(rate,nper,pmt,pv,type),5-,7,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,0,10,-100,133.10,Solving for PV:Calculator and Excel Methods,Solves the general FV equation for PV.,Exactly like solving for FV,except we have different input information and are solving for a different variable.,Excel:=PV(rate,nper,pmt,fv,type),5-,10,100,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,0,10,-75.13,100,Solving for I:What annual interest rate would cause$100 to grow to$125.97 in 3 years?,Solves the general FV equation for I/YR.,Hard to solve without a financial calculator or spreadsheet.,Excel:=RATE(nper,pmt,pv,fv,type,guess),5-,11,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,0,8,-100,125.97,Solving for N:If sales grow at 20%per year,how long before sales double?,Solves the general FV equation for N.,Hard to solve without a financial calculator or spreadsheet.,EXCEL:=NPER(rate,pmt,pv,fv,type),5-,12,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3.8,0,20,-1,2,What is the difference between an ordinary annuity and an annuity due?,5-,13,Ordinary Annuity,PMT,PMT,PMT,0,1,2,3,I%,PMT,PMT,0,1,2,3,I%,PMT,Annuity Due,Solving for FV:3-Year Ordinary Annuity of$100 at 10%,$100 payments occur at the end of each period,but there is no PV.,Excel:=FV(rate,nper,pmt,pv,type),Here type=0.,5-,14,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,-100,10,0,331,Solving for PV:3-year Ordinary Annuity of$100 at 10%,$100 payments still occur at the end of each period,but now there is no FV.,Excel:=PV(rate,nper,pmt,fv,type),Here type=0.,5-,15,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,100,10,-248.69,0,Solving for FV:3-Year Annuity Due of$100 at 10%,Now,$100 payments occur at the beginning of each period.,FVA,due,=FVA,ord,(1+I)=$331(1.10)=$364.10,Alternatively,set calculator to“BEGIN”mode and solve for the FV of the annuity:,Excel:=FV(rate,nper,pmt,pv,type),Here type=1.,5-,16,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,-100,10,0,364.10,BEGIN,Solving for PV:3-Year Annuity Due of$100 at 10%,Again,$100 payments occur at the beginning of each period.,PVA,due,=PVA,ord,(1+I)=$248.69(1.10)=$273.55,Alternatively,set calculator to“BEGIN”mode and solve for the PV of the annuity:,Excel:=PV(rate,nper,pmt,fv,type),Here type=1.,5-,17,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,100,10,-273.55,0,BEGIN,What is the present value of a 5-year$100 ordinary annuity at 10%?,Be sure your financial calculator is set back to END mode and solve for PV:,N=5,I/YR=10,PMT=-100,FV=0.,PV=$379.08.,5-,18,What if it were a 10-year annuity?A 25-year annuity?A perpetuity?,10-year annuity,N=10,I/YR=10,PMT=-100,FV=0;solve for PV=$614.46.,25-year annuity,N=25,I/YR=10,PMT=-100,FV=0;solve for PV=$907.70.,Perpetuity,PV=PMT/I=$100/0.1=$1,000.,5-,19,The Power of Compound Interest,A 20-year-old student wants to save$3 a day for her retirement.Every day she places$3 in a drawer.At the end of the year,she invests the accumulated savings($1,095)in a brokerage account with an expected annual return of 12%.,How much money will she have when she is 65 years old?,5-,20,Solving for FV:If she begins saving today,how much will she have when she is 65?,If she sticks to her plan,she will have$1,487,261.89 when she is 65.,Excel:=FV(.12,45,-1095,0,0),5-,21,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,45,-1095,12,0,1,487,262,Solving for FV:If you dont start saving until you are 40 years old,how much will you have at 65?,If a 40-year-old investor begins saving today,and sticks to the plan,he or she will have$146,000.59 at age 65.This is$1.3 million less than if starting at age 20.,Lesson:It pays to start saving early.,Excel:=FV(.12,25,-1095,0,0),5-,22,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,25,-1095,12,0,146,001,Solving for PMT:How much must the 40-year old deposit annually to catch the 20-year old?,To find the required annual contribution,enter the number of years until retirement and the final goal of$1,487,261.89,and solve for PMT.,Excel:=PMT(rate,nper,pv,fv,type),=PMT(.12,25,0,1487262,0),5-,23,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,25,12,0,-11,154.42,1487262,What is the PV of this uneven cash flow stream?,5-,24,0,100,1,300,2,300,3,10%,-50,4,90.91,247.93,225.39,-34.15,530.08 =PV,Solving for PV:Uneven Cash Flow Stream,Input cash flows in the calculators“CFLO”register:,CF,0,=0,CF,1,=100,CF,2,=300,CF,3,=300,CF,4,=-50,Enter I/YR=10,press NPV button to get NPV=$530.087.(Here NPV=PV.),5-,25,Will the FV of a lump sum be larger or smaller if compounded more often,holding the stated I%constant?,LARGER,as the more frequently compounding occurs,interest is earned on interest more often.,5-,26,Annually:FV,3,=$100(1.10),3,=$133.10,0,1,2,3,10%,100,133.10,Semiannually:FV,6,=$100(1.05),6,=$134.01,0,1,2,3,5%,4,5,6,134.01,1,2,3,0,100,Classification of Interest Rates,Nominal rate(I,NOM,):also called the quoted or stated rate.An annual rate that ignores compounding effects.,I,NOM,is stated in contracts.Periods must also be given,e.g.8%quarterly or 8%daily interest.,Periodic rate(I,PER,):amount of interest charged each period,e.g.monthly or quarterly.,I,PER,=I,NOM,/M,where M is the number of compounding periods per year.M=4 for quarterly and M=12 for monthly compounding.,5-,27,Classification of Interest Rates,Effective(or equivalent)annual rate(EAR=EFF%):the annual rate of interest actually being earned,considering compounding.,EFF%for 10%semiannual interest,EFF%=(1+I,NOM,/M),M,1,=(1+0.10/2),2,1=10.25%,Excel:=EFFECT(nominal_rate,npery),=EFFECT(.10,2),Should be indifferent between receiving 10.25%annual interest and receiving 10%interest,compounded semiannually.,5-,28,Why is it important to consider effective rates of return?,Investments with different compounding intervals provide different effective returns.,To compare investments with different compounding intervals,you must look at their effective returns(EFF%or EAR).,5-,29,Why is it important to consider effective rates of return?,See how the effective return varies between investments with the same nominal rate,but different compounding intervals.,EAR,ANNUAL,10.00%,EAR,SEMIANNUALLY,10.25%,EAR,QUARTERLY,10.38%,EAR,MONTHLY,10.47%,EAR,DAILY(365),10.52%,5-,30,When is each rate used?,I,NOM,:Written into contracts,quoted by banks and brokers.Not used in calculations or shown on time lines.,I,PER,:Used in calculations and shown on time lines.If M=1,I,NOM,=I,PER,=EAR.,EAR:Used to compare returns on investments with different payments per year.Used in calculations when annuity payments dont match compounding periods.,5-,31,What is the FV of$100 after 3 years under 10%semiannual compounding?Quarterly compounding?,5-,32,Can the effective rate ever be equal to the nominal rate?,Yes,but only if annual compounding is used,i.e.,if M=1.,If M 1,EFF%will always be greater than the nominal rate.,5-,33,Whats the FV of a 3-year$100 annuity,if the quoted interest rate is 10%,compounded semiannually?,Payments occur annually,but compounding occurs every 6 months.,Cannot use normal annuity valuation techniques.,5-,34,0,1,100,2,3,5%,4,5,100,100,6,Method 1:Compound Each Cash Flow,5-,35,FV,3,=$100(1.05),4,+$100(1.05),2,+$100,FV,3,=$331.80,110.25,121.55,331.80,0,1,100,2,3,5%,4,5,100,6,100,Method 2:Financial Calculator or Excel,Find the EAR and treat as an annuity.,EAR=(1+0.10/2),2,1=10.25%.,Excel:=FV(.1025,3,-100,0,0),5-,36,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,-100,10.25,0,331.80,Find the PV of This 3-Year Ordinary Annuity,Could solve by discounting each cash flow,or,Use the EAR and treat as an annuity to solve for PV.,Excel:=PV(.1025,3,100,0,0),5-,37,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,100,10.25,-247.59,0,Loan Amortization,Amortization tables are widely used for home mortgages,auto loans,business loans,retirement plans,etc.,Financial calculators and spreadsheets are great for setting up amortization tables.,EXAMPLE:Construct an amortization schedule for a$1,000,10%annual rate loan with 3 equal payments.,5-,38,Step 1:Find the Required Annual Payment,All input information is already given,just remember that the FV=0 because the reason for amortizing the loan and making payments is to retire the loan.,Excel:=PMT(.10,3,-1000,0,0),5-,39,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,-1000,402.11,0,Step 2:Find the Interest Paid in Year 1,The borrower will owe interest upon the initial balance at the end of the first year.Interest to be paid in the first year can be found by multiplying the beginning balance by the interest rate.,INT,t,=Beg bal,t,(I),INT,1,=$1,000(0.10)=$100,5-,40,Step 3:Find the Principal Repaid in Year 1,If a payment of$402.11 was made at the end of the first year and$100 was paid toward interest,the remaining value must represent the amount of principal repaid.,PRIN=PMT INT,=$402.11$100=$302.11,5-,41,Step 4:Find the Ending Balance after Year 1,To find the balance at the end of the period,subtract the amount paid toward principal from the beginning balance.,END BAL=BEG BAL PRIN,=$1,000$302.11,=$697.89,5-,42,Constructing an Amortization Table:Repeat Steps 1-4 Until End of Loan,Interest paid declines with each payment as the balance declines.What are the tax implications of this?,5-,43,YEAR,BEG BAL,PMT,INT,PRIN,END BAL,1,$1,000,$,402,$100,$,302,$698,2,698,402,70,332,366,3,366,402,3,6,366,0,TOTAL,$1,206,$206,$1,000,Illustrating an Amortized Payment:Where does the money go?,Constant payments,Declining interest payments,Declining balance,5-,44,$,0,1,2,3,402.11,Interest,302.11,Principal Payments,