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,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,6-,*,CHAPTER 6,Time Value of Money,Future value,Present value,Annuities,Rates of return,Amortization,CHAPTER 6Time Value of MoneyF,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.,CF,0,CF,1,CF,3,CF,2,0,1,2,3,i%,Time linesShow the timing of c,2,Drawing time lines:$100 lump sum due in 2 years;3-year$100 ordinary annuity,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:$100 lump,3,Drawing time lines:Uneven cash flow stream;CF,0,=-$50,CF,1,=$100,CF,2,=$75,and CF,3,=$50,100,50,75,0,1,2,3,i%,-50,Uneven cash flow stream,Drawing time lines:Uneven cas,4,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 when compound interest is applied is called compounding.,FV can be solved by using the arithmetic,financial calculator,and spreadsheet methods.,FV=?,0,1,2,3,10%,100,What is the future value(FV),5,Solving for FV:The arithmetic method,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,Solving for FV:The arithmetic,6,Solving for FV:The calculator method,Solves the general FV equation.,Requires 4 inputs into calculator,and will solve for the fifth.(Set to P/YR=1 and END mode.),INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,0,133.10,-100,Solving for FV:The calculator,7,PV=?,100,What is the present value(PV)of$100 due in 3 years,if I/YR=10%?,Finding the PV of a cash flow or series of cash flows when compound interest is applied is called discounting(the reverse of compounding).,The PV shows the value of cash flows in terms of todays purchasing power.,0,1,2,3,10%,PV=?100What is the present v,8,Solving for PV:The arithmetic method,Solve the general FV equation for PV:,PV=FV,n,/(1+i),n,PV=FV,3,/(1+i),3,=$100/(1.10),3,=$75.13,Solving for PV:The arithmetic,9,Solving for PV:The calculator method,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.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,0,100,-75.13,Solving for PV:The calculator,10,Solving for N:If sales grow at 20%per year,how long before sales double?,Solves the general FV equation for N.,Same as previous problems,but now solving for N.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3.8,20,0,2,-1,Solving for N:If sales grow a,11,What is the difference between an ordinary annuity and an annuity due?,Ordinary Annuity,PMT,PMT,PMT,0,1,2,3,i%,PMT,PMT,0,1,2,3,i%,PMT,Annuity Due,What is the difference between,12,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.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,-100,331,0,Solving for FV:3-year ordinar,13,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.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,100,0,-248.69,Solving for PV:3-year ordinar,14,Solving for FV:3-year annuity due of$100 at 10%,Now,$100 payments occur at the beginning of each period.,Set calculator to“BEGIN”mode.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,-100,364.10,0,Solving for FV:3-year annuity,15,Solving for PV:3 year annuity due of$100 at 10%,Again,$100 payments occur at the beginning of each period.,Set calculator to“BEGIN”mode.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,10,100,0,-273.55,Solving for PV:3 year annuity,16,What is the PV of this uneven cash flow stream?,0,100,1,300,2,300,3,10%,-50,4,90.91,247.93,225.39,-34.15,530.08 =PV,What is the PV of this uneven,17,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=$530.09.(Here NPV=PV.),Solving for PV:Uneven cash fl,18,Solving for I:What interest rate would cause$100 to grow to$125.97 in 3 years?,Solves the general FV equation for I.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,3,8,0,125.97,-100,Solving for I:What interest r,19,The Power of Compound Interest,A 20-year-old student wants to start saving for retirement.She plans to save$3 a day.Every day,she puts$3 in her drawer.At the end of the year,she invests the accumulated savings($1,095)in an online stock account.The stock account has an expected annual return of 12%.,How much money will she have when she is 65 years old?,The Power of Compound Interest,20,Solving for FV:Savings problem,If she begins saving today,and sticks to her plan,she will have$1,487,261.89 when she is 65.,INPUTS,OUTPUT,N,I/YR,PMT,PV,FV,45,12,-1095,1,487,262,0,Solving for FV:Savings proble,21,Solving for FV:Savings problem,if you wait until you are 40 years old
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