Time Value Of Money -Finance
-
date post
20-Oct-2014 -
Category
Economy & Finance
-
view
4.418 -
download
5
description
Transcript of Time Value Of Money -Finance
![Page 1: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/1.jpg)
3-1
THE BASIS OF THE BASIS OF FINANCEFINANCE
Time Value of Time Value of MoneyMoney
Time Value of Time Value of MoneyMoney
© Pearson Education Limited 2004
Fundamentals of Financial Management, 12/eCreated by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI
![Page 2: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/2.jpg)
3-2
After studying this part, After studying this part, you should be able to:you should be able to:
1. 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 used 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 “annuity 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 schedule” for an installment-style loan.
![Page 3: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/3.jpg)
3-3
The Time Value of MoneyThe Time Value of MoneyThe Time Value of MoneyThe Time Value of Money
The Interest Rate Simple Interest Compound Interest Amortizing a Loan Compounding More Than
Once per Year
The Interest Rate Simple Interest Compound Interest Amortizing a Loan Compounding More Than
Once per Year
![Page 4: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/4.jpg)
3-4
Obviously, $10,000 today$10,000 today.
You already recognize that there is TIME VALUE TO MONEYTIME VALUE TO MONEY!!
The Interest RateThe Interest RateThe Interest RateThe Interest Rate
Which would you prefer -- $10,000 $10,000 today today or $10,000 in 5 years$10,000 in 5 years?
![Page 5: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/5.jpg)
3-5
TIMETIME allows you the opportunity to postpone consumption and earn
INTERESTINTEREST.
Why TIME?Why TIME?Why TIME?Why TIME?
Why is TIMETIME such an important element in your decision?
![Page 6: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/6.jpg)
3-6
Types of InterestTypes of InterestTypes of InterestTypes of Interest
Compound InterestCompound Interest
Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent).
Simple InterestSimple Interest
Interest paid (earned) on only the original amount, or principal, borrowed (lent).
![Page 7: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/7.jpg)
3-7
Simple Interest FormulaSimple Interest FormulaSimple Interest FormulaSimple Interest Formula
FormulaFormula SI = P0(i)(n)
SI: Simple Interest
P0: Deposit today (t=0)
i: Interest Rate per Period
n: Number of Time Periods
![Page 8: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/8.jpg)
3-8
SI = P0(i)(n)= $1,000(.07)(2)= $140$140
Simple Interest ExampleSimple Interest ExampleSimple Interest ExampleSimple Interest Example
Assume 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?
![Page 9: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/9.jpg)
3-9
Class work 1:Simple Interest Class work 1:Simple Interest Class work 1:Simple Interest Class work 1:Simple Interest
Assume that you deposit $1,000 in an account earning 9% simple interest for 3 years. What is the accumulated interest at the end of the 3rd year?
![Page 10: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/10.jpg)
3-10
Class work 2:Simple Interest Class work 2:Simple Interest Class work 2:Simple Interest Class work 2:Simple Interest
Assume that you deposit $1,000 in an account earning 12% simple interest for 5 years. What is the accumulated interest at the end of the 5th year?
![Page 11: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/11.jpg)
3-11
Class work 3:Simple Interest Class work 3:Simple Interest Class work 3:Simple Interest Class work 3:Simple Interest
Assume that you deposit $1,000 in an account earning 15% simple interest for 7 years. What is the accumulated interest at the end of the 7th year?
![Page 12: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/12.jpg)
3-12
FVFV = P0 + SI = $1,000 + $140= $1,140$1,140
Future ValueFuture Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate.
Simple Interest (FV)Simple Interest (FV)Simple Interest (FV)Simple Interest (FV)
What is the Future Value Future Value (FVFV) of the deposit?
![Page 13: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/13.jpg)
3-13
The Present Value is simply the $1,000 you originally deposited. That is the value today!
Present ValuePresent Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.
Simple Interest (PV)Simple Interest (PV)Simple Interest (PV)Simple Interest (PV)
What is the Present Value Present Value (PVPV) of the previous problem?
![Page 14: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/14.jpg)
3-14
0
5000
10000
15000
20000
1st Year 10thYear
20thYear
30thYear
Future Value of a Single $1,000 Deposit
10% SimpleInterest
7% CompoundInterest
10% CompoundInterest
Why Compound Interest?Why Compound Interest?Why Compound Interest?Why Compound Interest?
Fu
ture
Va
lue
(U
.S. D
olla
rs)
![Page 15: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/15.jpg)
3-15
Assume that you deposit $1,000$1,000 at a compound interest rate of 7% for
2 years2 years.
Future ValueFuture ValueSingle Deposit (Graphic)Single Deposit (Graphic)Future ValueFuture ValueSingle Deposit (Graphic)Single Deposit (Graphic)
0 1 22
$1,000$1,000
FVFV22
7%
![Page 16: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/16.jpg)
3-16
FVFV11 = PP00 (1+i)1 = $1,000$1,000 (1.07)= $1,070$1,070
Compound Interest
You earned $70 interest on your $1,000 deposit over the first year.
This is the same amount of interest you would earn under simple interest.
Future ValueFuture ValueSingle Deposit (Formula)Single Deposit (Formula)Future ValueFuture ValueSingle Deposit (Formula)Single Deposit (Formula)
![Page 17: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/17.jpg)
3-17
FVFV11 = PP00 (1+i)1 = $1,000$1,000 (1.07) = $1,070$1,070
FVFV22 = FV1 (1+i)1 = PP0 0 (1+i)(1+i) = $1,000$1,000(1.07)(1.07)
= PP00 (1+i)2 = $1,000$1,000(1.07)2
= $1,144.90$1,144.90
You earned an EXTRA $4.90$4.90 in Year 2 with compound over simple interest.
Future ValueFuture ValueSingle Deposit (Formula)Single Deposit (Formula)Future ValueFuture ValueSingle Deposit (Formula)Single Deposit (Formula)
![Page 18: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/18.jpg)
3-18
FVFV11 = P0(1+i)1
FVFV22 = P0(1+i)2
General Future Value Future Value Formula:
FVFVnn = P0 (1+i)n
or FVFVnn = P0 (FVIFFVIFi,n) -- See Table ISee Table I
General Future General Future Value FormulaValue FormulaGeneral Future General Future Value FormulaValue Formula
etc.
![Page 19: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/19.jpg)
3-19
FVIFFVIFi,n is found on Table I
at the end of the book.
Valuation Using Table IValuation Using Table IValuation Using Table IValuation Using Table I
Period 6% 7% 8%1 1.060 1.070 1.0802 1.124 1.145 1.1663 1.191 1.225 1.2604 1.262 1.311 1.3605 1.338 1.403 1.469
![Page 20: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/20.jpg)
3-20
FVFV22 = $1,000 (FVIFFVIF7%,2)= $1,000 (1.145)
= $1,145$1,145 [Due to Rounding]
Using Future Value TablesUsing Future Value TablesUsing Future Value TablesUsing Future Value Tables
Period 6% 7% 8%1 1.060 1.070 1.0802 1.124 1.145 1.1663 1.191 1.225 1.2604 1.262 1.311 1.3605 1.338 1.403 1.469
![Page 21: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/21.jpg)
3-21
TVM on the CalculatorTVM on the Calculator
Use the highlighted row of keys for solving any of the FV, PV, FVA, PVA, FVAD, and PVAD problems
N: Number of periodsI/Y: Interest rate per periodPV: Present valuePMT: Payment per periodFV: Future value
CLR TVM: Clears all of the inputs into the above TVM keys
![Page 22: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/22.jpg)
3-22
Using The TI BAII+ CalculatorUsing The TI BAII+ CalculatorUsing The TI BAII+ CalculatorUsing The TI BAII+ Calculator
N I/Y PV PMT FV
Inputs
Compute
Focus on 3Focus on 3rdrd Row of keys (will be Row of keys (will be displayed in slides as shown above)displayed in slides as shown above)
![Page 23: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/23.jpg)
3-23
Entering the FV ProblemEntering the FV Problem
Press:
2nd CLR TVM
2 N
7 I/Y
-1000 PV
0 PMT
CPT FV
![Page 24: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/24.jpg)
3-24
N: 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)
Solving the FV ProblemSolving the FV ProblemSolving the FV ProblemSolving the FV Problem
N I/Y PV PMT FV
Inputs
Compute
2 7 -1,000 0
1,144.90
![Page 25: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/25.jpg)
3-25
Julie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound annual interest rate of 10% for 5 years5 years.
Story Problem ExampleStory Problem ExampleStory Problem ExampleStory Problem Example
0 1 2 3 4 55
$10,000$10,000
FVFV55
10%
![Page 26: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/26.jpg)
3-26
Calculation based on Table I:FVFV55 = $10,000 (FVIFFVIF10%, 5)
= $10,000 (1.611)= $16,110$16,110 [Due to Rounding]
Story Problem SolutionStory Problem SolutionStory Problem SolutionStory Problem Solution
Calculation based on general formula:FVFVnn = P0 (1+i)n
FVFV55 = $10,000 (1+ 0.10)5
= $16,105.10$16,105.10
![Page 27: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/27.jpg)
3-27
Julie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound annual interest rate of 12% for 5 years5 years.
Class work 4: FVClass work 4: FVClass work 4: FVClass work 4: FV
0 1 2 3 4 55
$10,000$10,000
FVFV55
12%
![Page 28: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/28.jpg)
3-28
Julie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound annual interest rate of 24% for 5 years5 years.
Class work 5: FVClass work 5: FVClass work 5: FVClass work 5: FV
0 1 2 3 4 55
$10,000$10,000
FVFV55
24%
![Page 29: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/29.jpg)
3-29
Julie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound semi-annual interest rate of 24% for 5 years5 years.
Class work 6: FVClass work 6: FVClass work 6: FVClass work 6: FV
0 1 2 3 4 55
$10,000$10,000
FVFV55
24%
![Page 30: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/30.jpg)
3-30
Julie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound (quarterly) interest rate of 24% for 5 years5 years.
Class work 7: FVClass work 7: FVClass work 7: FVClass work 7: FV
0 1 2 3 4 55
$10,000$10,000
FVFV55
24%
![Page 31: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/31.jpg)
3-31
Julie Miller wants to know how large her deposit of $10,000$10,000 today will become at a compound (monthly) interest rate of 24% for 5 years5 years.
Class work 8: FVClass work 8: FVClass work 8: FVClass work 8: FV
0 1 2 3 4 55
$10,000$10,000
FVFV55
24%
![Page 32: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/32.jpg)
3-32
Entering the FV ProblemEntering the FV Problem
Press:
2nd CLR TVM
5 N
10 I/Y
-10000 PV
0 PMT
CPT FV
![Page 33: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/33.jpg)
3-33
The result indicates that a $10,000 investment that earns 10% annually
for 5 years will result in a future value of $16,105.10.
Solving the FV ProblemSolving the FV ProblemSolving the FV ProblemSolving the FV Problem
N I/Y PV PMT FV
Inputs
Compute
5 10 -10,000 0
16,105.10
![Page 34: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/34.jpg)
3-34
We will use the ““Rule-of-72Rule-of-72””..
Double Your Money!!!Double Your Money!!!Double Your Money!!!Double Your Money!!!
Quick! How long does it take to double $5,000 at a compound rate of 12% per
year (approx.)?
![Page 35: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/35.jpg)
3-35
Approx. Years to Double = 7272 / i%
7272 / 12% = 6 Years6 Years[Actual Time is 6.12 Years]
The “Rule-of-72”The “Rule-of-72”The “Rule-of-72”The “Rule-of-72”
Quick! How long does it take to double $5,000 at a compound rate of 12% per
year (approx.)?
![Page 36: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/36.jpg)
3-36
How long does it take to double $5,000 at a compound rate of 10% per
year (approx.)?
How long does it take to double $5,000 at a compound rate of % per
year (approx.)?
Class work 9: Doubling ?Class work 9: Doubling ?Class work 9: Doubling ?Class work 9: Doubling ?
![Page 37: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/37.jpg)
3-37
The 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 years
Solving the Period ProblemSolving the Period ProblemSolving the Period ProblemSolving the Period Problem
N I/Y PV PMT FV
Inputs
Compute
12 -1,000 0 +2,000
6.12 years
![Page 38: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/38.jpg)
3-38
Assume that you need $1,000$1,000 in 2 years.2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually.
0 1 22
$1,000$1,000
7%
PV1PVPV00
Present ValuePresent Value Single Deposit (Graphic)Single Deposit (Graphic)Present ValuePresent Value Single Deposit (Graphic)Single Deposit (Graphic)
![Page 39: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/39.jpg)
3-39
PVPV00 = FVFV22 / (1+i)2 = $1,000$1,000 / (1.07)2 =
FVFV22 / (1+i)2 = $873.44$873.44
Present Value Present Value Single Deposit (Formula)Single Deposit (Formula)Present Value Present Value Single Deposit (Formula)Single Deposit (Formula)
0 1 22
$1,000$1,000
7%
PVPV00
![Page 40: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/40.jpg)
3-40
PVPV00 = FVFV11 / (1+i)1
PVPV00 = FVFV22 / (1+i)2
General Present Value Present Value Formula:
PVPV00 = FVFVnn / (1+i)n
or PVPV00 = FVFVnn (PVIFPVIFi,n) -- See Table IISee Table II
General Present General Present Value FormulaValue FormulaGeneral Present General Present Value FormulaValue Formula
etc.
![Page 41: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/41.jpg)
3-41
PVIFPVIFi,n is found on Table II
at the end of the book.
Valuation Using Table IIValuation Using Table IIValuation Using Table IIValuation Using Table II
Period 6% 7% 8% 1 .943 .935 .926 2 .890 .873 .857 3 .840 .816 .794 4 .792 .763 .735 5 .747 .713 .681
![Page 42: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/42.jpg)
3-42
PVPV22 = $1,000$1,000 (PVIF7%,2)= $1,000$1,000 (.873)
= $873$873 [Due to Rounding]
Using Present Value TablesUsing Present Value TablesUsing Present Value TablesUsing Present Value Tables
Period 6% 7% 8%1 .943 .935 .9262 .890 .873 .8573 .840 .816 .7944 .792 .763 .7355 .747 .713 .681
![Page 43: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/43.jpg)
3-43
N: 2 Periods (enter as 2)
I/Y: 7% interest rate per period (enter as 7 NOT .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 $”)
Solving the PV ProblemSolving the PV ProblemSolving the PV ProblemSolving the PV Problem
N I/Y PV PMT FV
Inputs
Compute
2 7 0 +1,000
-873.44
![Page 44: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/44.jpg)
3-44
Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000$10,000 in 5 years5 years at a discount rate of 10%.
Story Problem Class work 10Story Problem Class work 10Story Problem Class work 10Story Problem Class work 10
0 1 2 3 4 55
$10,000$10,000PVPV00
10%
![Page 45: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/45.jpg)
3-45
Calculation based on general formula: PVPV00 = FVFVnn / (1+i)n
PVPV00 = $10,000$10,000 / (1+ 0.10)5
= $6,209.21$6,209.21
Calculation based on Table I:PVPV00 = $10,000$10,000 (PVIFPVIF10%, 5)
= $10,000$10,000 (.621)= $6,210.00$6,210.00 [Due to Rounding]
Story Problem SolutionStory Problem SolutionStory Problem SolutionStory Problem Solution
![Page 46: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/46.jpg)
3-46
Solving the PV ProblemSolving the PV ProblemSolving the PV ProblemSolving the PV Problem
N I/Y PV PMT FV
Inputs
Compute
5 10 0 +10,000
-6,209.21
The result indicates that a $10,000 future value that will earn 10% annually for 5 years requires a $6,209.21 deposit
today (present value).
![Page 47: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/47.jpg)
3-47
Class work 11: PV of FVClass work 11: PV of FVClass work 11: PV of FVClass work 11: PV of FV
Julie Miller wants to know how large of a deposit to make so that the money will grow to $20,000$20,000 in 5 years5 years at a discount rate of 12%.
0 1 2 3 4 55
$20,000$20,000PVPV00
12%
![Page 48: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/48.jpg)
3-48
Class work 12: PV of FVClass work 12: PV of FVClass work 12: PV of FVClass work 12: PV of FV
Julie Miller wants to know how large of a deposit to make so that the money will grow to $40,000$40,000 in 5 years5 years at a discount rate of 18%.
0 1 2 3 4 55
$40,000$40,000PVPV00
18%
![Page 49: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/49.jpg)
3-49
Class work 13: PV of FVClass work 13: PV of FVClass work 13: PV of FVClass work 13: PV of FV
Julie Miller wants to know how large of a deposit to make so that the money will grow to $60,000$60,000 in 5 years5 years at a discount rate of 20%.
0 1 2 3 4 55
$60,000$60,000PVPV00
20%
![Page 50: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/50.jpg)
3-50
Class work 14: PV of FVClass work 14: PV of FVClass work 14: PV of FVClass work 14: PV of FV
Julie Miller wants to know how large of a deposit to make so that the money will grow to $80,000$80,000 in 5 years5 years at a discount rate of 25%.
0 1 2 3 4 55
$80,000$80,000PVPV00
25%
![Page 51: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/51.jpg)
3-51
Types of AnnuitiesTypes of AnnuitiesTypes of AnnuitiesTypes of Annuities
Ordinary AnnuityOrdinary Annuity: Payments or receipts occur at the end of each period.
Annuity DueAnnuity Due: Payments or receipts occur at the beginning of each period.
An AnnuityAn Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.
![Page 52: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/52.jpg)
3-52
Examples of AnnuitiesExamples of Annuities
Student Loan Payments
Car Loan Payments
Insurance Premiums
Mortgage Payments
Retirement Savings
![Page 53: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/53.jpg)
3-53
Parts of an AnnuityParts of an AnnuityParts of an AnnuityParts of an Annuity
0 1 2 3
$100 $100 $100
(Ordinary Annuity)EndEnd of
Period 1EndEnd of
Period 2
Today EqualEqual Cash Flows Each 1 Period Apart
EndEnd ofPeriod 3
![Page 54: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/54.jpg)
3-54
Parts of an AnnuityParts of an AnnuityParts of an AnnuityParts of an Annuity
0 1 2 3
$100 $100 $100
(Annuity Due)BeginningBeginning of
Period 1BeginningBeginning of
Period 2
Today EqualEqual Cash Flows Each 1 Period Apart
BeginningBeginning ofPeriod 3
![Page 55: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/55.jpg)
3-55
FVAFVAnn = R(1+i)n-1 + R(1+i)n-2 + ... + R(1+i)1 + R(1+i)0
Overview of an Overview of an Ordinary Annuity -- FVAOrdinary Annuity -- FVAOverview of an Overview of an Ordinary Annuity -- FVAOrdinary Annuity -- FVA
R R R
0 1 2 n n n+1
FVAFVAnn
R = Periodic Cash Flow
Cash flows occur at the end of the period
i% . . .
![Page 56: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/56.jpg)
3-56
FVAFVA33 = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0
= $1,145 + $1,070 + $1,000 = $3,215$3,215
Example of anExample of anOrdinary Annuity -- FVAOrdinary Annuity -- FVAExample of anExample of anOrdinary Annuity -- FVAOrdinary Annuity -- FVA
$1,000 $1,000 $1,000
0 1 2 3 3 4
$3,215 = FVA$3,215 = FVA33
7%
$1,070
$1,145
Cash flows occur at the end of the period
![Page 57: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/57.jpg)
3-57
FVAFVA33 = ?
Class work 15 -- FVAClass work 15 -- FVAClass work 15 -- FVAClass work 15 -- FVA
$1,000 $1,000 $1,000
0 1 2 3 3 48%
Cash flows occur at the end of the period
![Page 58: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/58.jpg)
3-58
FVAFVA33 = ?
Class work 16 -- FVAClass work 16 -- FVAClass work 16 -- FVAClass work 16 -- FVA
$1,000 $1,000 $1,000
0 1 2 3 3 49%
Cash flows occur at the end of the period
![Page 59: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/59.jpg)
3-59
FVAFVA33 = ?
Class work 17 -- FVAClass work 17 -- FVAClass work 17 -- FVAClass work 17 -- FVA
$1,000 $1,000 $1,000
0 1 2 3 3 411%
Cash flows occur at the end of the period
![Page 60: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/60.jpg)
3-60
Hint on Annuity ValuationHint on Annuity Valuation
The future value of an ordinary annuity can be viewed as
occurring at the endend of the last cash flow period, whereas the future value of an annuity due can be viewed as occurring at the beginningbeginning of the last cash
flow period.
![Page 61: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/61.jpg)
3-61
FVAFVAnn = R (FVIFAi%,n) FVAFVA33 = $1,000 (FVIFA7%,3)
= $1,000 (3.215) = $3,215$3,215
Valuation Using Table IIIValuation Using Table IIIValuation Using Table IIIValuation Using Table III
Period 6% 7% 8%1 1.000 1.000 1.0002 2.060 2.070 2.0803 3.184 3.215 3.2464 4.375 4.440 4.5065 5.637 5.751 5.867
![Page 62: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/62.jpg)
3-62
N: 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)
Solving the FVA ProblemSolving the FVA ProblemSolving the FVA ProblemSolving the FVA Problem
N I/Y PV PMT FV
Inputs
Compute
3 7 0 -1,000
3,214.90
![Page 63: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/63.jpg)
3-63
FVADFVADnn = R(1+i)n + R(1+i)n-1 + ... + R(1+i)2 +
R(1+i)1 = FVAFVAn n (1+i)
Overview View of anOverview View of anAnnuity Due -- FVADAnnuity Due -- FVADOverview View of anOverview View of anAnnuity Due -- FVADAnnuity Due -- FVAD
R R R R R
0 1 2 3 n-1n-1 n
FVADFVADnn
i% . . .
Cash flows occur at the beginning of the period
![Page 64: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/64.jpg)
3-64
FVADFVAD33 = $1,000(1.07)3 + $1,000(1.07)2 + $1,000(1.07)1
= $1,225 + $1,145 + $1,070 = $3,440$3,440
Example of anExample of anAnnuity Due -- FVADAnnuity Due -- FVADExample of anExample of anAnnuity Due -- FVADAnnuity Due -- FVAD
$1,000 $1,000 $1,000 $1,070
0 1 2 3 3 4
$3,440 = FVAD$3,440 = FVAD33
7%
$1,225
$1,145
Cash flows occur at the beginning of the period
![Page 65: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/65.jpg)
3-65
FVADFVAD33 = ?
Class work 18Class work 18Annuity Due -- FVADAnnuity Due -- FVADClass work 18Class work 18Annuity Due -- FVADAnnuity Due -- FVAD
$1,000 $1,000 $1,000
0 1 2 3 3 48%
Cash flows occur at the beginning of the period
![Page 66: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/66.jpg)
3-66
FVADFVAD33 = ?
Class work 19Class work 19Annuity Due -- FVADAnnuity Due -- FVADClass work 19Class work 19Annuity Due -- FVADAnnuity Due -- FVAD
$1,000 $1,000 $1,000
0 1 2 3 3 49%
Cash flows occur at the beginning of the period
![Page 67: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/67.jpg)
3-67
FVADFVAD33 = ?
Class work 20Class work 20Annuity Due -- FVADAnnuity Due -- FVADClass work 20Class work 20Annuity Due -- FVADAnnuity Due -- FVAD
$1,000 $1,000 $1,000
0 1 2 3 3 411%
Cash flows occur at the beginning of the period
![Page 68: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/68.jpg)
3-68
FVADFVADnn = R (FVIFAi%,n)(1+i)
FVADFVAD33 = $1,000 (FVIFA7%,3)(1.07)= $1,000 (3.215)(1.07) =
$3,440$3,440
Valuation Using Table IIIValuation Using Table IIIValuation Using Table IIIValuation Using Table III
Period 6% 7% 8%1 1.000 1.000 1.0002 2.060 2.070 2.0803 3.184 3.215 3.2464 4.375 4.440 4.5065 5.637 5.751 5.867
![Page 69: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/69.jpg)
3-69
Solving the FVAD ProblemSolving the FVAD ProblemSolving the FVAD ProblemSolving the FVAD Problem
N I/Y PV PMT FV
Inputs
Compute
3 7 0 -1,000
3,439.94
Complete the problem the same as an “ordinary annuity” problem, except you must change the calculator setting
to “BGN” first. Don’t forget to change back!
Step 1: Press 2nd BGN keys
Step 2: Press 2nd SET keys
Step 3: Press 2nd QUIT keys
![Page 70: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/70.jpg)
3-70
PVAPVAnn = R/(1+i)1 + R/(1+i)2
+ ... + R/(1+i)n
Overview of anOverview of anOrdinary Annuity -- PVAOrdinary Annuity -- PVAOverview of anOverview of anOrdinary Annuity -- PVAOrdinary Annuity -- PVA
R R R
0 1 2 n n n+1
PVAPVAnn
R = Periodic Cash Flow
i% . . .
Cash flows occur at the end of the period
![Page 71: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/71.jpg)
3-71
PVAPVA33 = $1,000/(1.07)1 + $1,000/(1.07)2 +
$1,000/(1.07)3
= $934.58 + $873.44 + $816.30 = $2,624.32$2,624.32
Example of anExample of anOrdinary Annuity -- PVAOrdinary Annuity -- PVAExample of anExample of anOrdinary Annuity -- PVAOrdinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 3 3 4
$2,624.32 = PVA$2,624.32 = PVA33
7%
$934.58$873.44 $816.30
Cash flows occur at the end of the period
![Page 72: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/72.jpg)
3-72
PVAPVA33 = ?
Class work 21:Class work 21:Ordinary Annuity -- PVAOrdinary Annuity -- PVAClass work 21:Class work 21:Ordinary Annuity -- PVAOrdinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 3 3 48%
Cash flows occur at the end of the period
![Page 73: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/73.jpg)
3-73
PVAPVA33 = ?
Class work 22:Class work 22:Ordinary Annuity -- PVAOrdinary Annuity -- PVAClass work 22:Class work 22:Ordinary Annuity -- PVAOrdinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 3 3 49%
Cash flows occur at the end of the period
![Page 74: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/74.jpg)
3-74
PVAPVA33 = ?
Class work 23:Class work 23:Ordinary Annuity -- PVAOrdinary Annuity -- PVAClass work 23:Class work 23:Ordinary Annuity -- PVAOrdinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 3 3 411%
Cash flows occur at the end of the period
![Page 75: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/75.jpg)
3-75
Hint on Annuity ValuationHint on Annuity Valuation
The present value of an ordinary annuity can be viewed as
occurring at the beginningbeginning of the first cash flow period, whereas the future value of an annuity
due can be viewed as occurring at the endend of the first cash flow
period.
![Page 76: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/76.jpg)
3-76
PVAPVAnn = R (PVIFAi%,n) PVAPVA33 = $1,000 (PVIFA7%,3)
= $1,000 (2.624) = $2,624$2,624
Valuation Using Table IVValuation Using Table IVValuation Using Table IVValuation Using Table IV
Period 6% 7% 8%1 0.943 0.935 0.9262 1.833 1.808 1.7833 2.673 2.624 2.5774 3.465 3.387 3.3125 4.212 4.100 3.993
![Page 77: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/77.jpg)
3-77
N: 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 relevant in this situation (no ending value)
Solving the PVA ProblemSolving the PVA ProblemSolving the PVA ProblemSolving the PVA Problem
N I/Y PV PMT FV
Inputs
Compute
3 7 -1,000 0
2,624.32
![Page 78: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/78.jpg)
3-78
PVADPVADnn = R/(1+i)0 + R/(1+i)1 + ... + R/(1+i)n-1
= PVAPVAn n (1+i)
Overview of anOverview of anAnnuity Due -- PVADAnnuity Due -- PVADOverview of anOverview of anAnnuity Due -- PVADAnnuity Due -- PVAD
R R R R
0 1 2 n-1n-1 n
PVADPVADnn
R: Periodic Cash Flow
i% . . .
Cash flows occur at the beginning of the period
![Page 79: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/79.jpg)
3-79
PVADPVADnn = $1,000/(1.07)0 + $1,000/(1.07)1 + $1,000/(1.07)2 = $2,808.02$2,808.02
Example of anExample of anAnnuity Due -- PVADAnnuity Due -- PVADExample of anExample of anAnnuity Due -- PVADAnnuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 33 4
$2,808.02 $2,808.02 = PVADPVADnn
7%
$ 934.58$ 873.44
Cash flows occur at the beginning of the period
![Page 80: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/80.jpg)
3-80
PVADPVADnn = ?
Class work 24:Class work 24:Annuity Due -- PVADAnnuity Due -- PVADClass work 24:Class work 24:Annuity Due -- PVADAnnuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 33 48%
Cash flows occur at the beginning of the period
![Page 81: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/81.jpg)
3-81
PVADPVADnn = ?
Class work 25:Class work 25:Annuity Due -- PVADAnnuity Due -- PVADClass work 25:Class work 25:Annuity Due -- PVADAnnuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 33 49%
Cash flows occur at the beginning of the period
![Page 82: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/82.jpg)
3-82
PVADPVADnn = ?
Class work 26:Class work 26:Annuity Due -- PVADAnnuity Due -- PVADClass work 26:Class work 26:Annuity Due -- PVADAnnuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 33 411%
Cash flows occur at the beginning of the period
![Page 83: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/83.jpg)
3-83
PVADPVADnn = R (PVIFAi%,n)(1+i)
PVADPVAD33 = $1,000 (PVIFA7%,3)(1.07) = $1,000 (2.624)(1.07) =
$2,808$2,808
Valuation Using Table IVValuation Using Table IVValuation Using Table IVValuation Using Table IV
Period 6% 7% 8%1 0.943 0.935 0.9262 1.833 1.808 1.7833 2.673 2.624 2.5774 3.465 3.387 3.3125 4.212 4.100 3.993
![Page 84: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/84.jpg)
3-84
Solving the PVAD ProblemSolving the PVAD ProblemSolving the PVAD ProblemSolving the PVAD Problem
N I/Y PV PMT FV
Inputs
Compute
3 7 -1,000 0
2,808.02
Complete the problem the same as an “ordinary annuity” problem, except you must change the calculator setting
to “BGN” first. Don’t forget to change back!
Step 1: Press 2nd BGN keys
Step 2: Press 2nd SET keys
Step 3: Press 2nd QUIT keys
![Page 85: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/85.jpg)
3-85
1. Read problem thoroughly
2. Create a time line
3. Put cash flows and arrows on time line
4. Determine if it is a PV or FV problem
5. Determine if solution involves a single CF, annuity stream(s), or mixed flow
6. Write the formula
7. Solve the problem
8. Check with financial calculator (optional)
Steps to Solve Time Value Steps to Solve Time Value of Money Problemsof Money ProblemsSteps to Solve Time Value Steps to Solve Time Value of Money Problemsof Money Problems
![Page 86: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/86.jpg)
3-86
Julie Miller will receive the set of cash flows below. What is the Present Value Present Value at a discount rate of 10%10%.
Mixed Flows ExampleMixed Flows ExampleMixed Flows ExampleMixed Flows Example
0 1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $100
PVPV00
10%10%
![Page 87: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/87.jpg)
3-87
1. Solve a “piece-at-a-timepiece-at-a-time” by discounting each piecepiece back to
t=0.
2. Solve a “group-at-a-timegroup-at-a-time” by firstbreaking problem into groups of
annuity streams and any single cash flow groups. Then discount each groupgroup back to t=0.
How to Solve?How to Solve?How to Solve?How to Solve?
![Page 88: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/88.jpg)
3-88
““Piece-At-A-Time”Piece-At-A-Time”““Piece-At-A-Time”Piece-At-A-Time”
0 1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $10010%
$545.45$545.45$495.87$495.87$300.53$300.53$273.21$273.21$ 62.09$ 62.09
$1677.15 $1677.15 = = PVPV00 of the Mixed Flowof the Mixed Flow
![Page 89: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/89.jpg)
3-89
““Group-At-A-Time” (#1)Group-At-A-Time” (#1)““Group-At-A-Time” (#1)Group-At-A-Time” (#1)
0 1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $100
10%
$1,041.60$1,041.60$ 573.57$ 573.57$ 62.10$ 62.10
$1,677.27$1,677.27 = = PVPV00 of Mixed Flow of Mixed Flow [Using Tables][Using Tables]
$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) = $62.10
![Page 90: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/90.jpg)
3-90
““Group-At-A-Time” (#2)Group-At-A-Time” (#2)““Group-At-A-Time” (#2)Group-At-A-Time” (#2)
0 1 2 3 4
$400 $400 $400 $400$400 $400 $400 $400
PVPV00 equals
$1677.30.$1677.30.
0 1 2
$200 $200$200 $200
0 1 2 3 4 5
$100$100
$1,268.00$1,268.00
$347.20$347.20
$62.10$62.10
PlusPlus
PlusPlus
![Page 91: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/91.jpg)
3-91
Use the highlighted key for starting the process of solving a mixed cash flow problem
Press the CF key and down arrow key through a few of the keys as you look at the definitions on the next slide
Solving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF RegistrySolving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF Registry
![Page 92: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/92.jpg)
3-92
Defining the calculator variables:For CF0:This is ALWAYS the cash flow 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 whole number (e.g., 1, 2, 20, etc.).
Solving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF RegistrySolving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF Registry
* nn represents the nth cash flow or frequency. Thus, the first cash flow is C01, while the tenth cash flow is C10.
![Page 93: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/93.jpg)
3-93
Solving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF RegistrySolving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF Registry
Steps in the ProcessStep 1: Press CF key
Step 2: Press 2nd CLR Work keys
Step 3: For CF0 Press 0 Enter ↓ keys
Step 4: For C01 Press 600 Enter ↓ keys
Step 5: For F01 Press 2 Enter ↓ keys
Step 6: For C02 Press 400 Enter ↓ keys
Step 7: For F02 Press 2 Enter ↓ keys
![Page 94: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/94.jpg)
3-94
Solving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF RegistrySolving the Mixed Flows Solving the Mixed Flows Problem using CF RegistryProblem using CF Registry
Steps in the Process
Step 8: For C03 Press 100 Enter ↓ keys
Step 9: For F03 Press 1 Enter ↓ keys
Step 10: Press ↓ ↓ keys
Step 11: Press NPV key
Step 12: For I=, Enter 10 Enter ↓ keys
Step 13: Press CPT key
Result: Present Value = $1,677.15
![Page 95: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/95.jpg)
3-95
General Formula:
FVn = PVPV00(1 + [i/m])mn
n: Number of Yearsm: Compounding Periods per
Yeari: Annual Interest RateFVn,m: FV at the end of Year n
PVPV00: PV of the Cash Flow today
Frequency of Frequency of CompoundingCompoundingFrequency of Frequency of CompoundingCompounding
![Page 96: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/96.jpg)
3-96
Julie Miller has $1,000$1,000 to invest for 2 Years at an annual interest rate of
12%.
Annual FV2 = 1,0001,000(1+ [.12/1])(1)(2)
= 1,254.401,254.40
Semi FV2 = 1,0001,000(1+ [.12/2])(2)(2)
= 1,262.481,262.48
Impact of FrequencyImpact of FrequencyImpact of FrequencyImpact of Frequency
![Page 97: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/97.jpg)
3-97
Qrtly FV2 = 1,0001,000(1+ [.12/4])(4)(2)
= 1,266.771,266.77
Monthly FV2 = 1,0001,000(1+ [.12/12])(12)(2)
= 1,269.731,269.73
Daily FV2 = 1,0001,000(1+[.12/365])(365)
(2) = 1,271.201,271.20
Impact of FrequencyImpact of FrequencyImpact of FrequencyImpact of Frequency
![Page 98: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/98.jpg)
3-98
The 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.
Solving the Frequency Solving the Frequency Problem (Quarterly)Problem (Quarterly)Solving the Frequency Solving the Frequency Problem (Quarterly)Problem (Quarterly)
N I/Y PV PMT FV
Inputs
Compute
2(4) 12/4 -1,000 0
1266.77
![Page 99: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/99.jpg)
3-99
Solving the Frequency Solving the Frequency Problem (Quarterly Altern.)Problem (Quarterly Altern.)Solving the Frequency Solving the Frequency Problem (Quarterly Altern.)Problem (Quarterly Altern.)
Press:
2nd P/Y 4 ENTER
2nd QUIT
12 I/Y
-1000 PV
0 PMT
2 2nd xP/Y N
CPT FV
![Page 100: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/100.jpg)
3-100
The 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.
Solving the Frequency Solving the Frequency Problem (Daily)Problem (Daily)Solving the Frequency Solving the Frequency Problem (Daily)Problem (Daily)
N I/Y PV PMT FV
Inputs
Compute
2(365) 12/365 -1,000 0
1271.20
![Page 101: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/101.jpg)
3-101
Solving the Frequency Solving the Frequency Problem (Daily Alternative)Problem (Daily Alternative)Solving the Frequency Solving the Frequency Problem (Daily Alternative)Problem (Daily Alternative)
Press:
2nd P/Y 365 ENTER
2nd QUIT
12 I/Y
-1000 PV
0 PMT
2 2nd xP/Y N
CPT FV
![Page 102: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/102.jpg)
3-102
Effective Annual Interest Rate
The 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 - 1
Effective Annual Effective Annual Interest RateInterest RateEffective Annual Effective Annual Interest RateInterest Rate
![Page 103: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/103.jpg)
3-103
Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is
6% compounded quarterly for 1 year. What is the Effective Annual
Interest Rate (EAREAR)?
EAREAR = ( 1 + 6% / 4 )4 - 1 = 1.0614 - 1 = .0614 or 6.14%!6.14%!
BWs Effective BWs Effective Annual Interest RateAnnual Interest RateBWs Effective BWs Effective Annual Interest RateAnnual Interest Rate
![Page 104: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/104.jpg)
3-104
Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is 8% compounded quarterly for 1 year. What is the Effective Annual
Interest Rate (EAREAR)?
EAREAR = ?
Class work 27: Effective Class work 27: Effective Annual Interest RateAnnual Interest RateClass work 27: Effective Class work 27: Effective Annual Interest RateAnnual Interest Rate
![Page 105: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/105.jpg)
3-105
Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is 8% compounded monthly for 1
year. What is the Effective Annual Interest Rate (EAREAR)?
EAREAR = ?
Class work 28: Effective Class work 28: Effective Annual Interest RateAnnual Interest RateClass work 28: Effective Class work 28: Effective Annual Interest RateAnnual Interest Rate
![Page 106: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/106.jpg)
3-106
Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is 8% compounded weekly for 1
year. What is the Effective Annual Interest Rate (EAREAR)?
EAREAR = ?
Class work 29: Effective Class work 29: Effective Annual Interest RateAnnual Interest RateClass work 29: Effective Class work 29: Effective Annual Interest RateAnnual Interest Rate
![Page 107: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/107.jpg)
3-107
Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate
is 8% compounded daily for 1 year. What is the Effective Annual
Interest Rate (EAREAR)?
EAREAR = ?
Class work 30: Effective Class work 30: Effective Annual Interest RateAnnual Interest RateClass work 30: Effective Class work 30: Effective Annual Interest RateAnnual Interest Rate
![Page 108: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/108.jpg)
3-108
Converting to an EARConverting to an EAR
Press:
2nd I Conv
6 ENTER
↓ ↓
4 ENTER
↑ CPT
2nd QUIT
![Page 109: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/109.jpg)
3-109
1. Calculate the payment per period.
2. Determine the interest in Period t. (Loan Balance at t-1) x (i% / m)
3. Compute principal payment principal payment in Period t.(Payment - Interest from Step 2)
4. Determine ending balance in Period t.(Balance - principal payment principal payment from Step
3)
5. Start again at Step 2 and repeat.
Steps to Amortizing a LoanSteps to Amortizing a LoanSteps to Amortizing a LoanSteps to Amortizing a Loan
![Page 110: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/110.jpg)
3-110
Julie Miller is borrowing $10,000 $10,000 at a compound annual interest rate of 12%.
Amortize the loan if annual payments are made for 5 years.
Step 1: Payment
PVPV00 = R (PVIFA i%,n)
$10,000 $10,000 = R (PVIFA 12%,5)
$10,000$10,000 = R (3.605)
RR = $10,000$10,000 / 3.605 = $2,774$2,774
Amortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan Example
![Page 111: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/111.jpg)
3-111
Amortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan Example
End ofYear
Payment Interest Principal EndingBalance
0 --- --- --- $10,000
1 $2,774 $1,200 $1,574 8,426
2 2,774 1,011 1,763 6,663
3 2,774 800 1,974 4,689
4 2,774 563 2,211 2,478
5 2,775 297 2,478 0
$13,871 $3,871 $10,000
[Last Payment Slightly Higher Due to Rounding]
![Page 112: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/112.jpg)
3-112
The result indicates that a $10,000 loan that costs 12% annually for 5 years and will be completely paid off at that time
will require $2,774.10 annual payments.
Solving for the PaymentSolving for the PaymentSolving for the PaymentSolving for the Payment
N I/Y PV PMT FV
Inputs
Compute
5 12 10,000 0
-2774.10
![Page 113: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/113.jpg)
3-113
Using the Amortization Using the Amortization Functions of the CalculatorFunctions of the Calculator
Press:
2nd Amort
1 ENTER
1 ENTERResults:
BAL = 8,425.90* ↓
PRN = -1,574.10* ↓
INT = -1,200.00* ↓
Year 1 information only
*Note: Compare to 3-82
![Page 114: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/114.jpg)
3-114
Using the Amortization Using the Amortization Functions of the CalculatorFunctions of the Calculator
Press:
2nd Amort
2 ENTER
2 ENTERResults:
BAL = 6,662.91* ↓
PRN = -1,763.99* ↓
INT = -1,011.11* ↓
Year 2 information only
*Note: Compare to 3-82
![Page 115: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/115.jpg)
3-115
Using the Amortization Using the Amortization Functions of the CalculatorFunctions of the Calculator
Press:
2nd Amort
1 ENTER
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)
![Page 116: Time Value Of Money -Finance](https://reader033.fdocuments.us/reader033/viewer/2022061106/54454744afaf9f10098b45ba/html5/thumbnails/116.jpg)
3-116
Usefulness of AmortizationUsefulness of Amortization
2.2. Calculate Debt Outstanding Calculate Debt Outstanding -- The quantity of outstanding debt may be used in financing the day-to-day activities of the firm.
1.1. Determine Interest Expense Determine Interest Expense -- Interest expenses may reduce taxable income of the firm.