Date post: | 30-Dec-2015 |
Category: |
Documents |
Upload: | jonas-cunningham |
View: | 51 times |
Download: | 0 times |
Time Value of Money Tutorial
Prepared byRonald Moy
Tobin College of BusinessSt. John’s University
Solving Time Value of Money Problems
• To solve a time value of money problem, you need to ask yourself a number of questions in order to determine which formula you will be using.
Let’s Begin*
* Please view as a slideshow
Type of Cash Flow
• Is the amount one lump sum of money?
Yes No
Present or Future Value
• Are you trying to determine what something is worth in the future or what some future amount is worth today?
Worth Today Worth in the Future
Previous slideBeginning of tutorial
Annuity or Multiple Cash Flow
• Will you be paying (or receiving) an equal sum of money made at equal intervals?
Yes No
Previous slideBeginning of tutorial
Ordinary Annuity or Annuity Due?
• Is the first cash flow at the beginning of the period or at the end of the period?
Beginning End
Previous slide Beginning of tutorial
Present or Future Value
• You are finding the value of multiple cash flows. Are you looking for the value of these cash flows in the future or the value today?
Value in the Future Value Today
Previous slide Beginning of tutorial
Future Value of Multiple Cash Flows
• The future value of multiple cash flows is
Previous slide ExampleBeginning of tutorial
)()3(3
)2(2
)1(1 )1(...)1()1()1( tt
tttt rCrCrCrCFV
Annuity Due
• You are dealing with an annuity due. Are you looking for the value of the annuity in the future or what the annuity is worth today?
Worth in the Future Worth Today
Previous slide Beginning of tutorial
Present Value of Multiple Cash Flows
• You are finding the present value of multiple cash flows
Previous slide ExampleBeginning of tutorial
tt
33
221
)r1(
C...
)r1(
C
)r1(
C
)r1(
CPV
Ordinary Annuity
• You are dealing with an ordinary annuity. Are you looking for the value of the annuity in the future or what the annuity is worth today?
Worth in the Future Worth Today
Previous slide Beginning of tutorial
Present Value of Ordinary Annuity• You are looking for the present value of an
ordinary annuity. The present value of an annuity formula is,
Previous slide ExampleBeginning of tutorial
r)r1(
11
CPVt
Present Value of Annuity Due• You are looking for the present value of an
annuity due. The present value of an annuity formula is,
Previous slide ExampleBeginning of tutorial
r1r)r1(
11
CPVt
Future Value of Ordinary Annuity
• You are looking for the future value of an ordinary annuity. The formula for the future value of an annuity is
Previous slide ExampleBeginning of tutorial
r
1)r1(CFV
t
Future Value of Annuity Due
• You are looking for the future value of an annuity due. The formula for the future value of an annuity is
Previous slide ExampleBeginning of tutorial
r1r
1)r1(CFV
t
Present Value of a Lump Sum• You are looking for the present value of a lump
sum. The present value for a lump sum is
Previous slidePresent value example
Beginning of tutorial
t)r1(
FVPV
Future Value of a Lump Sum
• You are looking for the future value of a lump sum. The future value of a lump sum is,
Previous slide Future Value exampleBeginning of tutorial
t)r1(PVFV
Future Value a Lump Sum Example
• Find the future value in 10 years of $100 received today, if the interest rate is 8%.
Previous slide FV CalculatorBeginning of tutorial Timeline example
89.215$)08.1(100$FV 10
Future Value Time Line
• Previous slide Beginning of tutorial
19
0 1 2 3 4 10
$215.89 $100
. . .
Present Value of a Lump Sum Example
• Find the present value of $1,000 received 5 years from today if the interest rate is 9%.
Previous slide Calculator exampleBeginning of tutorial Timeline example
93.649$)09.1(
000,1$PV
5
Present Value Time Line
Previous slide Beginning of tutorial
0 1 2 3 4 5
$1,000
$649.93
Present Value of an Ordinary Annuity
• You can afford to make monthly car payments of $500 per month for 48 months. If the interest rate is 12% (1% per month). How much can you afford to spend on a car? Assume that the first car payment will be made in one month.
Previous slide Calculator exampleBeginning of tutorial
98.986,18$01.)01.1(1
1500$PV
48
Present Value of an Annuity Due Example
• You can afford to make monthly car payments of $500 per month for 48 months. If the interest rate is 12% (1% per month). How much can you afford to spend on a car? Assume that the first car payment will be made today.
Previous slide Calculator exampleBeginning of tutorial
85.176,19$)01.1(01.)01.1(1
1500$PV
48
Future Value of an Ordinary Annuity Example
• Suppose you want to start saving next year for your retirement. You save $1,000 per year for the next 40 years. If the interest rate is 10%, how much will you have in your account after you make the last deposit?
Previous slide Calculator exampleBeginning tutorial
56.592,442$10.
1)10.1(000,1$FV
40
Future Value of an Annuity Due Example
• Suppose you want to start saving today for your retirement. You save $1,000 per year for the next 40 years. If the interest rate is 10%, how much will you have in your account after you make the last deposit?
Previous slide Calculator exampleBeginning of tutorial
82.851,486$)10.1(10.
1)10.1(000,1$FV
40
Present Value of Multiple Cash Flows Example
• You are considering an investment that will pay you $1,000 in one year, $2,000 in two years and $3,000 in three years. If you want to earn 10% on your money, how much would you be willing to pay?
Previous slide Calculator exampleBeginning of tutorial Timeline example
93.815,4$)10.1(
000,3$
)10.1(
000,2$
)10.1(
000,1$PV
32
PV Time Line – Multiple Cash Flows
Previous slide Beginning of tutorial27
0 1 2 3 4
1,000 2,000 3,000909.09
1,652.89
2,253.94
4,815.92
Future Value of Multiple Cash Flows Example
• Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years?
Previous slide Timeline exampleBeginning of tutorial
05.248,1$)09.1(600$)09.1(500$ 2 FV
FV Time Line – Multiple Cash Flows
Previous slideBeginning of
tutorial
29
$500
0 1 2 3 4 5
$600
$654.00
$594.05
$1,248.05
PV Calculator• Calculator solution
Previous slide Beginning of tutorial
N I/Y PMT PV FV
5 9 1000
CPT PV 649.93
FV Calculator• Calculator solution
Previous slide Beginning of tutorial
N I/Y PMT PV FV
10 8 -100
CPT FV 215.89
Calc Ex. PV Ordinary Annuity• Calculator solution• Make sure calculator is set for “END”
– Set by 2nd BGN 2nd Enter
Previous slide Beginning of tutorial
N I/Y PMT PV FV
48 1 500
CPT PV 18,986.98
Calc Ex PV Annuity Due
• Calculator solution• Make sure calculator is set for “BEG”
– Set by 2nd BGN 2nd Enter
Previous slide Beginning of tutorial
N I/Y PMT PV FV
48 1 500
CPT PV 19,176.85
Calc Ex FV Ordinary Annuity
• Calculator solution• Make sure calculator is set for “END”
– Set by 2nd BGN 2nd Enter
Previous slide Beginning of tutorial
N I/Y PMT PV FV
40 10 1000
CPT FV 442,592.56
FV Annuity Due• Calculator solution• Make sure calculator is set for “BEG”
– Set by 2nd BGN 2nd Enter
Previous slide Beginning of tutorial
N I/Y PMT PV FV
40 10 1000
CPT FV 486,851.82
PV Multiple Cash Flows
• In this case, you will use the Cash Flow Worksheet on the calculator.– CF– CF0 – CF01 1000 Enter– F01 – CF02 2000 Enter– F02 – CF03 3000 Enter – F03 – NPV 10 Enter– CPT 4,815.93 Previous slide Beginning of tutorial