Chapter 3 : Chapter 3 Time Value of Money © 2001 Prentice-Hall, Inc.
Fundamentals of Financial Management, 11/e
Created by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI
The Time Value of Money : The Time Value of Money The Interest Rate
Simple Interest
Compound Interest
Amortizing a Loan
The Interest Rate : Obviously, $10,000 today.
You already recognize that there is TIME VALUE TO MONEY!! The Interest Rate Which would you prefer -- $10,000 today or $10,000 in 5 years?
Why TIME? : TIME allows you the opportunity to postpone consumption and earn INTEREST.
Why TIME? Why is TIME such an important element in your decision?
Types of Interest : Types of Interest Compound Interest
Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Simple Interest
Interest paid (earned) on only the original amount, or principal borrowed (lent).
Simple Interest Formula : Simple Interest Formula Formula SI = P0(i)(n)
SI: Simple Interest
P0: Deposit today (t=0)
i: Interest Rate per Period
n: Number of Time Periods
Simple Interest Example : SI = P0(i)(n) = $1,000(.07)(2) = $140 Simple 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?
Simple Interest (FV) : FV = P0 + SI = $1,000 + $140 = $1,140
Future 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) What is the Future Value (FV) of the deposit?
Simple Interest (PV) : The Present Value is simply the $1,000 you originally deposited. That is the value today!
Present 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) What is the Present Value (PV) of the previous problem?
Why Compound Interest? : Why Compound Interest? Future Value (U.S. Dollars)
Future Value Single Deposit (Graphic) : Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years. Future Value Single Deposit (Graphic) 0 1 2 $1,000 FV2 7%
Future Value Single Deposit (Formula) : FV1 = P0 (1+i)1 = $1,000 (1.07) = $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 Value Single Deposit (Formula)
Slide13 : FV1 = P0 (1+i)1 = $1,000 (1.07) = $1,070
FV2 = FV1 (1+i)1 = P0 (1+i)(1+i) = $1,000(1.07)(1.07) = P0 (1+i)2 = $1,000(1.07)2 = $1,144.90
You earned an EXTRA $4.90 in Year 2 with compound over simple interest. Future Value
Single Deposit (Formula)
General Future Value Formula : FV1 = P0(1+i)1
FV2 = P0(1+i)2
General Future Value Formula:
FVn = P0 (1+i)n
or FVn = P0 (FVIFi,n) -- See Table I General Future Value Formula etc.
Valuation Using Table I : FVIFi,n is found on Table I at the end of the book or on the card insert. Valuation Using Table I
Using Future Value Tables : FV2 = $1,000 (FVIF7%,2) = $1,000 (1.145) = $1,145 [Due to Rounding] Using Future Value Tables
TVM on the Calculator : TVM 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 periods
I/Y: Interest rate per period
PV: Present value
PMT: Payment per period
FV: Future value
CLR TVM: Clears all of the inputs into the above TVM keys
Using The TI BAII+ Calculator : Using The TI BAII+ Calculator N I/Y PV PMT FV Inputs Compute Focus on 3rd row of keys (will be displayed in slides as shown above)
Entering the FV Problem : Entering the FV Problem Press:
2nd CLR TVM
2 N
7 I/Y
-1000 PV
0 PMT
CPT FV
Solving the FV Problem : 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 Problem N I/Y PV PMT FV Inputs Compute 2 7 -1,000 0 1,144.90
Story Problem Example : Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years. Story Problem Example 0 1 2 3 4 5 $10,000 FV5 10%
Story Problem Solution : Calculation based on Table I: FV5 = $10,000 (FVIF10%, 5) = $10,000 (1.611) = $16,110 [Due to Rounding] Story Problem Solution Calculation based on general formula: FVn = P0 (1+i)n FV5 = $10,000 (1+ 0.10)5 = $16,105.10
Entering the FV Problem : Entering the FV Problem Press:
2nd CLR TVM
5 N
10 I/Y
-10000 PV
0 PMT
CPT FV
Solving the FV Problem : 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 Problem N I/Y PV PMT FV Inputs Compute 5 10 -10,000 0 16,105.10
Double Your Money!!! : We will use the “Rule-of-72”. Double Your Money!!! Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?
The “Rule-of-72” : Approx. Years to Double = 72 / i%
72 / 12% = 6 Years
[Actual Time is 6.12 Years] The “Rule-of-72” Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)?
Solving the Period Problem : 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 Problem N I/Y PV PMT FV Inputs Compute 12 -1,000 0 +2,000 6.12 years
Present Value Single Deposit (Graphic) : Assume that you need $1,000 in 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 2 $1,000 7% PV1 PV0 Present Value Single Deposit (Graphic)
Present Value Single Deposit (Formula) : PV0 = FV2 / (1+i)2 = $1,000 / (1.07)2 = FV2 / (1+i)2 = $873.44 Present Value Single Deposit (Formula) 0 1 2 $1,000 7% PV0
General Present Value Formula : PV0 = FV1 / (1+i)1
PV0 = FV2 / (1+i)2
General Present Value Formula:
PV0 = FVn / (1+i)n
or PV0 = FVn (PVIFi,n) -- See Table II General Present Value Formula etc.