财务管理chapter-02
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Principle Time
Rate
3-13
Simple Interest Formula
Formula SI: P0: SI = P0(i)(n) Simple Interest Deposit today (t=0)
i:
n:
3-14
Interest Rate per Period
Number of Time Periods
Invest $1.00 today at 10% interest . . .
Receive $1.10 one year from today . . .
3-8
There are other reasons why we would rather receive money now.
Uncertainty
3-38
Today . . .
Future . . .
Deduct interest at interest rate “i” for “n” periods.
3-39
Future value of a single cash flow.
3-40
Future Value Single Deposit (Graphic)
3-24
Interest . . .
Interim Value . . .
3-25
Interest . . .
Interim Value . . .
3-26
Interest . . .
Interim Value . . .
3-27
There simply has to be an easier way to do this!
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.
3-21
Compound Interest . . .
For
the first compounding period interest is computed in the same way as simple interest.
3-22
Compound Interest . . .
Compute
Compound
Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent).
3-11
Simple Interest
3-12
Simple Interest
The Power of Compounding
3-32
Compound Interest
Simple Interest $404.93
Difference
$360.00
$44.93
3-33
The Power of Compounding
OK Prof! So, how can I use this stuff?
3-28
Yes there is! Thanks for bringing this up!
3-29
Simply use this formula.
fv n Pv(1 i )
3-30
n
f n P(1 i)
n
3
fn $1,000(1.12) $1,404.93
3-31
$1,000(1.40493)
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.
3-16
Simple Interest (PV)
3-42
Future Value Single Deposit (Formula)
FV1 FV2 = P0 (1+i)1 = $1,000 (1.07) = $1,070
= 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
The It
cost of using money.
is the rental charge for funds, just as rental charges are made for the use of buildings and equipment.
3-7
Time Value of Money . . .
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?
Understand what is meant by "the time value of money." Calculate the future value of an amount invested today, the future value of a stream of equal cash flows (an annuity), and the future value of a stream of mixed cash flows. Calculate the present value of a single future cash flow, the present value of a stream of equal future cash flows, and the present value of a mixed stream of future cash flows. Use the interest factor tables and understand how they provide a short cut to calculating present and future values. Use the tables to find an unknown interest rate or growth rate when the number of time periods and future and 3-4 present values are known.
3-5
Why TIME?
Why is TIME such an important element in your decision? TIME allows you the opportunity to postpone consumption and earn INTEREST.
3-6
Interest - Defined . . .
Chapter 2
Time Value of Money
3-1
3-2
The Time Value of Money
The Interest Rate
Simple Interest
Compound Interest
3-3
After studying Chapter 2, you should be able to:
What
is the Present Value (PV) of the previous problem?
The Present Value is simply the $1,000 you originally deposited. That is the value today!
Present
Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years.
0
7%
1
2
$1,000
FV2
3-41
Future Value Single Deposit (Formula)
FV1 = P0 (1+i)1 = $1,000 (1.07) = $1,070
Inflation
3-9
Computing the Time Value
Simple Interest
Compound Interest
3-10
Types of Interest
Simple
Interest
Interest
paid (earned) on only the original amount, or principal borrowed (lent). Interest
3-36
Future Value Scenarios . . . Present value of a single cash flow.
Present value of an annuity
3-37
Today . . .
Future . . .
Add interest at interest rate “i” for “n” periods.
The Interest Rate
Which would you prefer -- $10,000 today or $10,000 in 5 years?
Obviously, $10,000 today.
You already recognize that there is TIME VALUE TO MONБайду номын сангаасY!!
interest on the original principal plus the interest from step 1.
3-23
Compound Interest . . .
The
process is repeated until the full period of time is reached (here 3 periods).
3-34
Thanks for asking!
There are four time value of money problems,
3-35
Future Value Scenarios . . . Future value of a single cash flow.
Future value of an annuity
3-17
Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.
The Power of Simple Interest
3-18
($50,000,000)(.08/365) = $10,959
3-19
Compound Interest
3-20
Why Compound Interest?
Future Value of a Single $1,000 Deposit
Future Value (U.S. Dollars)
20000 15000 10000 5000 0 1st Year 10th Year 20th Year 30th Year 10% Simple Interest 7% Compound Interest 10% Compound Interest
You earned an EXTRA $4.90 in Year 2 with compound over simple interest. 3-43
General Future Value Formula
FV1 = P0(1+i)1
FV2 = P0(1+i)2
SI
= P0(i)(n) = $1,000(.07)(2) = $140
3-15
Simple Interest (FV)
What
is the Future Value (FV) of the deposit?
FV = P0 + SI = $1,000 + $140 = $1,140
Future
Rate
3-13
Simple Interest Formula
Formula SI: P0: SI = P0(i)(n) Simple Interest Deposit today (t=0)
i:
n:
3-14
Interest Rate per Period
Number of Time Periods
Invest $1.00 today at 10% interest . . .
Receive $1.10 one year from today . . .
3-8
There are other reasons why we would rather receive money now.
Uncertainty
3-38
Today . . .
Future . . .
Deduct interest at interest rate “i” for “n” periods.
3-39
Future value of a single cash flow.
3-40
Future Value Single Deposit (Graphic)
3-24
Interest . . .
Interim Value . . .
3-25
Interest . . .
Interim Value . . .
3-26
Interest . . .
Interim Value . . .
3-27
There simply has to be an easier way to do this!
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.
3-21
Compound Interest . . .
For
the first compounding period interest is computed in the same way as simple interest.
3-22
Compound Interest . . .
Compute
Compound
Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent).
3-11
Simple Interest
3-12
Simple Interest
The Power of Compounding
3-32
Compound Interest
Simple Interest $404.93
Difference
$360.00
$44.93
3-33
The Power of Compounding
OK Prof! So, how can I use this stuff?
3-28
Yes there is! Thanks for bringing this up!
3-29
Simply use this formula.
fv n Pv(1 i )
3-30
n
f n P(1 i)
n
3
fn $1,000(1.12) $1,404.93
3-31
$1,000(1.40493)
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.
3-16
Simple Interest (PV)
3-42
Future Value Single Deposit (Formula)
FV1 FV2 = P0 (1+i)1 = $1,000 (1.07) = $1,070
= 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
The It
cost of using money.
is the rental charge for funds, just as rental charges are made for the use of buildings and equipment.
3-7
Time Value of Money . . .
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?
Understand what is meant by "the time value of money." Calculate the future value of an amount invested today, the future value of a stream of equal cash flows (an annuity), and the future value of a stream of mixed cash flows. Calculate the present value of a single future cash flow, the present value of a stream of equal future cash flows, and the present value of a mixed stream of future cash flows. Use the interest factor tables and understand how they provide a short cut to calculating present and future values. Use the tables to find an unknown interest rate or growth rate when the number of time periods and future and 3-4 present values are known.
3-5
Why TIME?
Why is TIME such an important element in your decision? TIME allows you the opportunity to postpone consumption and earn INTEREST.
3-6
Interest - Defined . . .
Chapter 2
Time Value of Money
3-1
3-2
The Time Value of Money
The Interest Rate
Simple Interest
Compound Interest
3-3
After studying Chapter 2, you should be able to:
What
is the Present Value (PV) of the previous problem?
The Present Value is simply the $1,000 you originally deposited. That is the value today!
Present
Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years.
0
7%
1
2
$1,000
FV2
3-41
Future Value Single Deposit (Formula)
FV1 = P0 (1+i)1 = $1,000 (1.07) = $1,070
Inflation
3-9
Computing the Time Value
Simple Interest
Compound Interest
3-10
Types of Interest
Simple
Interest
Interest
paid (earned) on only the original amount, or principal borrowed (lent). Interest
3-36
Future Value Scenarios . . . Present value of a single cash flow.
Present value of an annuity
3-37
Today . . .
Future . . .
Add interest at interest rate “i” for “n” periods.
The Interest Rate
Which would you prefer -- $10,000 today or $10,000 in 5 years?
Obviously, $10,000 today.
You already recognize that there is TIME VALUE TO MONБайду номын сангаасY!!
interest on the original principal plus the interest from step 1.
3-23
Compound Interest . . .
The
process is repeated until the full period of time is reached (here 3 periods).
3-34
Thanks for asking!
There are four time value of money problems,
3-35
Future Value Scenarios . . . Future value of a single cash flow.
Future value of an annuity
3-17
Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.
The Power of Simple Interest
3-18
($50,000,000)(.08/365) = $10,959
3-19
Compound Interest
3-20
Why Compound Interest?
Future Value of a Single $1,000 Deposit
Future Value (U.S. Dollars)
20000 15000 10000 5000 0 1st Year 10th Year 20th Year 30th Year 10% Simple Interest 7% Compound Interest 10% Compound Interest
You earned an EXTRA $4.90 in Year 2 with compound over simple interest. 3-43
General Future Value Formula
FV1 = P0(1+i)1
FV2 = P0(1+i)2
SI
= P0(i)(n) = $1,000(.07)(2) = $140
3-15
Simple Interest (FV)
What
is the Future Value (FV) of the deposit?
FV = P0 + SI = $1,000 + $140 = $1,140
Future