Transcript Financial Management for Entrepreneurs

Chapter 4,5
Time Value of Money
Learning Goals
1. Understand the concept of future value, their
calculation for a single amount, and the
relationship of present to future cash flow.
2. Find the future value and present value of both
an ordinary annuity and an annuity due, and
the present value of a perpetuity.
Learning Goals
4. Calculate the present value of a mixed stream of cash
flows.*
5. Understand the effect that compounding more
frequently than annually has on future value and the
effective annual interest rate.
The Role of Time Value in Finance
• Most financial decisions involve costs & benefits that
are spread out over time.
• Time value of money allows comparison of cash flows
from different periods.
Question?
Would it be better for a company to invest
$100,000 in a product that would return a total of
$200,000 after one year, or one that would return
$220,000 after two years?
The Role of Time Value in Finance
• Most financial decisions involve costs & benefits that
are spread out over time.
• Time value of money allows comparison of cash flows
from different periods.
Answer!
It depends on the interest rate!
Basic Concepts
• Future Value: compounding or growth over time
• Present Value: discounting to today’s value
• Single cash flows & series of cash flows can be
considered
• Time lines are used to illustrate these relationships
Computational Aids
• Use the Equations
• Use the Financial Tables
• Use Financial Calculators
• Use Spreadsheets
Computational Aids
Time Line
Computational Aids
Financial Calculators
Basic Patterns of Cash Flow
• The cash inflows and outflows of a firm can be
described by its general pattern.
• The three basic patterns include a single amount, an
annuity, or a mixed stream:
Simple Interest
With simple interest, you don’t earn interest on
interest.
• Year 1: 5% of $100
=
$5 + $100 = $105
• Year 2: 5% of $100
=
$5 + $105 = $110
• Year 3: 5% of $100
=
$5 + $110 = $115
• Year 4: 5% of $100
=
$5 + $115 = $120
• Year 5: 5% of $100
=
$5 + $120 = $125
Compound Interest
With compound interest, a depositor earns interest
on interest!
• Year 1: 5% of $100.00 = $5.00 + $100.00 = $105.00
• Year 2: 5% of $105.00 = $5.25 + $105.00 = $110.25
• Year 3: 5% of $110.25 = $5 .51+ $110.25 = $115.76
• Year 4: 5% of $115.76 = $5.79 + $115.76 = $121.55
• Year 5: 5% of $121.55 = $6.08 + $121.55 = $127.63
Time Value Terms
• PV0 =
present value or beginning amount
• k
interest rate
=
• FVn =
future value at end of “n” periods
• n
=
number of compounding periods
• A
=
an annuity (series of equal payments or
receipts)
Four Basic Models
• FVn = PV0(1+k)n = PV(FVIFk,n)
• PV0 = FVn[1/(1+k)n] = FV(PVIFk,n)
Future Value Example
Algebraically and Using FVIF Tables
You deposit $2,000 today at 6%
interest. How much will you have in 5
years?
$2,000 x (1.06)5 =
$2,000 x 1.3382 = $2,676.40
Nominal & Effective Rates
• The nominal interest rate is the stated or contractual
rate of interest charged by a lender or promised by a
borrower.
• The effective interest rate is the rate actually paid or
earned.
• In general, the effective rate > nominal rate whenever
compounding occurs more than once per year
EAR = (1 + k/m) m -1
Nominal & Effective Rates
• For example, what is the effective rate of interest on
your credit card if the nominal rate is 18% per year,
compounded monthly?
EAR = (1 + .18/12) 12 -1
EAR = 19.56%
Present Value
• Present value is the current dollar value of a future
amount of money.
• It is based on the idea that a dollar today is worth
more than a dollar tomorrow.
• It is the amount today that must be invested at a given
rate to reach a future amount.
• Calculating present value is also known as
discounting.
• The discount rate is often also referred to as the
opportunity cost, the discount rate, the required return,
and the cost of capital.
Present Value Example
Algebraically and Using PVIF Tables
How much must you deposit today in order to
have $2,000 in 5 years if you can earn 6%
interest on your deposit?
$2,000 x [1/(1.06)5] = $2,000 x 0.74758
$1,494.52
=
Present Value of a Perpetuity
• A perpetuity is a special kind of annuity.
• With a perpetuity, the periodic annuity or cash flow
stream continues forever.
PV = Annuity/k
• For example, how much would I have to deposit today
in order to withdraw $1,000 each year forever if I can
earn 8% on my deposit?
PV = $1,000/.08 = $12,500
Future Value of an Ordinary Annuity
Using the FVIFA Tables
• Annuity = Equal Annual Series of Cash Flows
• Example: How much will your deposits grow to if you
deposit $100 at the end of each year at 5% interest for
three years.
FVA = 100(FVIFA,5%,3) = $315.25
Year 1 $100 deposited at end of year
=
$100.00
Year 2 $100 x .05 = $5.00 + $100 + $100
=
$205.00
Year 3 $205 x .05 = $10.25 + $205 + $100
=
$315.25
Future Value of an Ordinary Annuity
Using Calculator/Excel
• Annuity = Equal Annual Series of Cash Flows
• Example: How much will your deposits grow to if you
deposit $100 at the end of each year at 5% interest for
three years.
PMT
k
n
FV?
$
100
5.0%
3
$ 315.25
Excel Function
=FV (interest, periods, pmt, PV)
=FV (.06, 5,100, )
Present Value of an Ordinary Annuity
Using PVIFA Tables
• Annuity = Equal Annual Series of Cash Flows
• Example: How much could you borrow if you could
afford annual payments of $2,000 (which includes
both principal and interest) at the end of each year for
three years at 10% interest?
PVA = 2,000(PVIFA,10%,3) = $4,973.70
Present Value of an Ordinary Annuity
Using Excel
• Annuity = Equal Annual Series of Cash Flows
• Example: How much could you borrow if you could
afford annual payments of $2,000 (which includes
both principal and interest) at the end of each year for
three years at 10% interest?
PMT
I
n
PV?
$
2,000
10.0%
3
$4,973.70
Excel Function
=PV (interest, periods, pmt, FV)
=PV (.10, 3, 2000, )
Present Value of a Mixed Stream
Using Tables
• A mixed stream of cash flows reflects no particular
pattern
• Find the present value of the following mixed stream
assuming a required return of 9%.
Year Cash Flow
PVIF9%,N
PV
1
400
0.917
$ 366.80
2
800
0.842
$ 673.60
3
500
0.772
$ 386.00
4
400
0.708
$ 283.20
5
300
0.650
$ 195.00
PV
$1,904.60