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Copyright © 2012 Pearson Prentice Hall.
All rights reserved.
Chapter 5
Time Value of Money
*
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Learning Goals
LG1 Discuss the role of time value in finance, the use of
computational tools, and the basic patterns of cash flow.
LG2 Understand the concepts of future value and present value,
their calculation for single amounts, and the relationship
between them.
LG3 Find the future value and the present value of both an
ordinary annuity and an annuity due, and find the present value
of a perpetuity.
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Learning Goals (cont.)
LG4 Calculate both the future value and the present value of a
mixed stream of cash flows.
LG5 Understand the effect that compounding interest more
frequently than annually has on future value and the effective
annual rate of interest.
LG6 Describe the procedures involved in (1) determining
deposits needed to accumulate a future sum, (2) loan
amortization, (3) finding interest or growth rates, and (4)
finding an unknown number of periods.
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The Role of Time Value in FinanceMost financial decisions
involve costs & benefits that are spread out over time.Time
value of money allows comparison of cash flows from different
periods.Question: Your father has offered to give you some
money and asks that you choose one of the following two
alternatives:$1,000 today, or$1,100 one year from now.What do
you do?
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The Role of Time Value in Finance (cont.)The answer depends
on what rate of interest you could earn on any money you
receive today.For example, if you could deposit the $1,000
today at 12% per year, you would prefer to be paid
today.Alternatively, if you could only earn 5% on deposited
funds, you would be better off if you chose the $1,100 in one
year.
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Future Value versus Present ValueSuppose a firm has an
opportunity to spend $15,000 today on some investment that
will produce $17,000 spread out over the next five years as
follows:
Is this a wise investment?To make the right investment
decision, managers need to compare the cash flows at a single
point in time. YearCash
flow1$3,0002$5,0003$4,0004$3,0005$2,000
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Figure 5.1
Time Line
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Figure 5.2
Compounding and Discounting
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Figure 5.3
Calculator Keys
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Computational Tools (cont.)
Electronic spreadsheets:Like financial calculators, electronic
spreadsheets have built-in routines that simplify time value
calculations. The value for each variable is entered in a cell in
the spreadsheet, and the calculation is programmed using an
equation that links the individual cells. Changing any of the
input variables automatically changes the solution as a result of
the equation linking the cells.
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Basic Patterns of Cash FlowThe 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:
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Future Value of a Single AmountFuture value is the value at a
given future date of an amount placed on deposit today and
earning interest at a specified rate. Found by applying
compound interest over a specified period of time.Compound
interest is interest that is earned on a given deposit and has
become part of the principal at the end of a specified
period.Principal is the amount of money on which interest is
paid.
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Personal Finance Example
If Fred Moreno places $100 in a savings account paying 8%
interest compounded annually, how much will he have at the
end of 1 year?
If Fred were to leave this money in the account for another year,
how much would he have at the end of the second year?
Future value at end of year 2
= $116.64
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Future Value of a Single Amount: The Equation for Future
ValueWe use the following notation for the various inputs:FVn
= future value at the end of period nPV = initial principal, or
present valuer = annual rate of interest paid. (Note: On financial
calculators, I is typically used to represent this rate.)n = number
of periods (typically years) that the money is left on depositThe
general equation for the future value at the end of period n is
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Future Value of a Single Amount: The Equation for Future
Value
Jane Farber places $800 in a savings account paying 6% interest
compounded annually. She wants to know how much money will
be in the account at the end of five years.
This analysis can be depicted on a time line as follows:
823) = $1,070.58
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Personal Finance Example
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Figure 5.4
Future Value Relationship
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Present Value of a Single AmountPresent value is the current
dollar value of a future amount—the amount of money that
would have to be invested today at a given interest rate over a
specified period to equal the future amount.It is based on the
idea that a dollar today is worth more than a dollar
tomorrow.Discounting cash flows is the process of finding
present values; the inverse of compounding interest.The
discount rate is often also referred to as the opportunity cost,
the discount rate, the required return, or the cost of capital.
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Personal Finance Example
Paul Shorter has an opportunity to receive $300 one year from
now. If he can earn 6% on his investments, what is the most he
should pay now for this opportunity?
PV = $300/(1 + 0.06) = $283.02
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Present Value of a Single Amount: The Equation for Present
Value
The present value, PV, of some future amount, FVn, to be
received n periods from now, assuming an interest rate (or
opportunity cost) of r, is calculated as follows:
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Present Value of a Single Amount: The Equation for Future
Value
Pam Valenti wishes to find the present value of $1,700 that will
be received 8 years from now. Pam’s opportunity cost is 8%.
This analysis can be depicted on a time line as follows:
PV = $1,700/(1 + 0.08)8 = $1,700/1.85093 = $918.46
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Personal Finance Example
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Figure 5.5
Present Value Relationship
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Annuities
An annuity is a stream of equal periodic cash flows, over a
specified time period. These cash flows can be inflows of
returns earned on investments or outflows of funds invested to
earn future returns.An ordinary (deferred) annuity is an annuity
for which the cash flow occurs at the end of each periodAn
annuity due is an annuity for which the cash flow occurs at the
beginning of each period.An annuity due will always be greater
than an otherwise equivalent ordinary annuity because interest
will compound for an additional period.
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Personal Finance Example
Fran Abrams is choosing which of two annuities to receive.
Both are 5-year $1,000 annuities; annuity A is an ordinary
annuity, and annuity B is an annuity due. Fran has listed the
cash flows for both annuities as shown in Table 5.1 on the
following slide.
Note that the amount of both annuities total $5,000.
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Table 5.1 Comparison of Ordinary Annuity and Annuity Due
Cash Flows ($1,000, 5 Years)
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Finding the Future Value of an Ordinary AnnuityYou can
calculate the future value of an ordinary annuity that pays an
annual cash flow equal to CF by using the following equation:
As before, in this equation r represents the interest rate and n
represents the number of payments in the annuity (or
equivalently, the number of years over which the annuity is
spread).
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Personal Finance Example
Fran Abrams wishes to determine how much money she will
have at the end of 5 years if he chooses annuity A, the ordinary
annuity and it earns 7% annually. Annuity A is depicted
graphically below:
This analysis can be depicted on a time line as follows:
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Personal Finance Example (cont.)
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Finding the Present Value of an Ordinary AnnuityYou can
calculate the present value of an ordinary annuity that pays an
annual cash flow equal to CF by using the following equation:
As before, in this equation r represents the interest rate and n
represents the number of payments in the annuity (or
equivalently, the number of years over which the annuity is
spread).
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Finding the Present Value of an Ordinary Annuity (cont.)
Braden Company, a small producer of plastic toys, wants to
determine the most it should pay to purchase a particular
annuity. The annuity consists of cash flows of $700 at the end
of each year for 5 years. The required return is 8%.
This analysis can be depicted on a time line as follows:
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Table 5.2 Long Method for Finding the Present Value of an
Ordinary Annuity
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Finding the Present Value of an Ordinary Annuity (cont.)
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Finding the Future Value of an Annuity DueYou can calculate
the present value of an annuity due that pays an annual cash
flow equal to CF by using the following equation:
As before, in this equation r represents the interest rate and n
represents the number of payments in the annuity (or
equivalently, the number of years over which the annuity is
spread).
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Personal Finance Example
Fran Abrams now wishes to calculate the future value of an
annuity due for annuity B in
Table 5.1. Recall that annuity B was a 5 period annuity with the
first annuity beginning immediately.
Note: Before using your calculator to find the future value of an
annuity due, depending on the specific calculator, you must
either switch it to BEGIN mode or use the DUE key.
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Personal Finance Example (cont.)
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Finding the Present Value of an Annuity DueYou can calculate
the present value of an ordinary annuity that pays an annual
cash flow equal to CF by using the following equation:
As before, in this equation r represents the interest rate and n
represents the number of payments in the annuity (or
equivalently, the number of years over which the annuity is
spread).
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Finding the Present Value of an Annuity Due (cont.)
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Matter of Fact
Kansas truck driver, Donald Damon, got the surprise of his life
when he learned he held the winning ticket for the Powerball
lottery drawing held November 11, 2009. The advertised lottery
jackpot was $96.6 million. Damon could have chosen to collect
million = $96.6 million), but instead he elected to accept a lump
sum payment of $48,367,329.08, roughly half the stated jackpot
total.
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Finding the Present Value of a PerpetuityA perpetuity is an
annuity with an infinite life, providing continual annual cash
flow.If a perpetuity pays an annual cash flow of CF, starting
one year from now, the present value of the cash flow stream is
PV = CF ÷ r
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Personal Finance Example
Ross Clark wishes to endow a chair in finance at his alma
mater. The university indicated that it requires $200,000 per
year to support the chair, and the endowment would earn 10%
per year. To determine the amount Ross must give the
university to fund the chair, we must determine the present
value of a $200,000 perpetuity discounted at 10%.
PV = $200,000 ÷ 0.10 = $2,000,000
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Future Value of a Mixed Stream
Shrell Industries, a cabinet manufacturer, expects to receive the
following mixed stream of cash flows over the next 5 years
from one of its small customers.
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Future Value of a Mixed Stream
If the firm expects to earn at least 8% on its investments, how
much will it accumulate by the end of year 5 if it immediately
invests these cash flows when they are received?
This situation is depicted on the following time line.
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Future Value of a Mixed Stream (cont.)
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Present Value of a Mixed Stream
Frey Company, a shoe manufacturer, has been offered an
opportunity to receive the following mixed stream of cash flows
over the next 5 years.
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Present Value of a Mixed Stream
If the firm must earn at least 9% on its investments, what is the
most it should pay for this opportunity?
This situation is depicted on the following time line.
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Present Value of a Mixed Stream (cont.)
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Compounding Interest More Frequently Than
AnnuallyCompounding more frequently than once a year results
in a higher effective interest rate because you are earning on
interest on interest more frequently.As a result, the effective
interest rate is greater than the nominal (annual) interest
rate.Furthermore, the effective rate of interest will increase the
more frequently interest is compounded.
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Table 5.3 Future Value from Investing $100 at 8% Interest
Compounded Semiannually over 24 Months (2 Years)
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Table 5.4 Future Value from Investing $100 at 8% Interest
Compounded Quarterly over 24 Months (2 Years)
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Table 5.5 Future Value from Investing $100 at 8% Interest
Compounded Quarterly over 24 Months (2 Years)
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Compounding Interest More Frequently Than Annually (cont.)
A general equation for compounding more frequently than
annually
Recalculate the example for the Fred Moreno example assuming
(1) semiannual compounding and (2) quarterly compounding.
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Compounding Interest More Frequently Than Annually (cont.)
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Compounding Interest More Frequently Than Annually (cont.)
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Continuous CompoundingContinuous compounding involves the
compounding of interest an infinite number of times per year at
intervals of microseconds.A general equation for continuous
compounding
where e is the exponential function.
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Personal Finance Example
Find the value at the end of 2 years (n = 2) of Fred Moreno’s
$100 deposit (PV = $100) in an account paying 8% annual
interest (r = 0.08) compounded continuously.
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Personal Finance Example (cont.)
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Nominal and Effective Annual Rates of InterestThe nominal
(stated) annual rate is the contractual annual rate of interest
charged by a lender or promised by a borrower.The effective
(true) annual rate (EAR) is the annual rate of interest actually
paid or earned.In general, the effective rate > nominal rate
whenever compounding occurs more than once per year
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Personal Finance Example
Fred Moreno wishes to find the effective annual rate associated
with an 8% nominal annual rate (r = 0.08) when interest is
compounded (1) annually (m = 1); (2) semiannually (m = 2);
and (3) quarterly (m = 4).
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Focus on Ethics
How Fair Is “Check Into Cash”?There are more than 1,100
Check Into Cash centers among an estimated 22,000 payday-
advance lenders in the United States. A payday loan is a small,
unsecured, short-term loan ranging from $100 to $1,000
(depending upon the state) offered by a payday lender. A
borrower who rolled over an initial $100 loan for the maximum
of four times would accumulate a total of $75 in fees all within
a 10-week period.
On an annualized basis, the fees would amount to a whopping
391%.The 391% mentioned above is an annual nominal rate
-week rate (15%) be
compounded to calculate the effective annual interest rate?
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Special Applications of Time Value: Deposits Needed to
Accumulate a Future Sum
The following equation calculates the annual cash payment (CF)
that we’d have to save to achieve a future value (FVn):
Suppose you want to buy a house 5 years from now, and you
estimate that an initial down payment of $30,000 will be
required at that time. To accumulate the $30,000, you will wish
to make equal annual end-of-year deposits into an account
paying annual interest of 6 percent.
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Personal Finance Example
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Special Applications of Time Value: Loan AmortizationLoan
amortization is the determination of the equal periodic loan
payments necessary to provide a lender with a specified interest
return and to repay the loan principal over a specified
period.The loan amortization process involves finding the future
payments, over the term of the loan, whose present value at the
loan interest rate equals the amount of initial principal
borrowed.A loan amortization schedule is a schedule of equal
payments to repay a loan. It shows the allocation of each loan
payment to interest and principal.
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Special Applications of Time Value: Loan Amortization
(cont.)The following equation calculates the equal periodic loan
payments (CF) necessary to provide a lender with a specified
interest return and to repay the loan principal (PV) over a
specified period:
Say you borrow $6,000 at 10 percent and agree to make equal
annual end-of-year payments over 4 years. To find the size of
the payments, the lender determines the amount of a 4-year
annuity discounted at 10 percent that has a present value of
$6,000.
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Personal Finance Example
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Table 5.6 Loan Amortization Schedule
($6,000 Principal, 10% Interest, 4-Year Repayment Period)
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Personal Finance Example (cont.)
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Focus on Practice
New Century Brings Trouble for Subprime MortgagesIn 2006,
some $300 billion worth of adjustable ARMs were reset to
higher rates. In a market with rising home values, a borrower
has the option to refinance their mortgage, using some of the
equity created by the home’s increasing value to reduce the
mortgage payment. But after 2006, home prices started a three-
year slide, so refinancing was not an option for many subprime
borrowers. As a reaction to problems in the subprime area,
lenders tightened lending standards. What effect do you think
this had on the housing market?
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Special Applications of Time Value: Finding Interest or Growth
RatesIt is often necessary to calculate the compound annual
interest or growth rate (that is, the annual rate of change in
values) of a series of cash flows.The following equation is used
to find the interest rate (or growth rate) representing the
increase in value of some investment between two time periods.
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Personal Finance Example
Ray Noble purchased an investment four years ago for $1,250.
Now it is worth $1,520. What compound annual rate of return
has Ray earned on this investment? Plugging the appropriate
values into Equation 5.20, we have:
r = ($1,520 ÷ $1,250)(1/4) – 1 = 0.0501 = 5.01% per year
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Personal Finance Example (cont.)
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Personal Finance Example
Jan Jacobs can borrow $2,000 to be repaid in equal annual end-
of-year amounts of $514.14 for the next 5 years. She wants to
find the interest rate on this loan.
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Personal Finance Example (cont.)
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Special Applications of Time Value: Finding an Unknown
Number of PeriodsSometimes it is necessary to calculate the
number of time periods needed to generate a given amount of
cash flow from an initial amount. This simplest case is when a
person wishes to determine the number of periods, n, it will take
for an initial deposit, PV, to grow to a specified future amount,
FVn, given a stated interest rate, r.
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Personal Finance Example
Ann Bates wishes to determine the number of years it will take
for her initial $1,000 deposit, earning 8% annual interest, to
grow to equal $2,500. Simply stated, at an 8% annual rate of
interest, how many years, n, will it take for Ann’s $1,000, PV,
to grow to $2,500, FVn?
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Personal Finance Example (cont.)
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Personal Finance Example
Bill Smart can borrow $25,000 at an 11% annual interest rate;
equal, annual, end-of-year payments of $4,800 are required. He
wishes to determine how long it will take to fully repay the
loan. In other words, he wishes to determine how many years, n,
it will take to repay the $25,000, 11% loan, PVn, if the
payments of $4,800 are made at the end of each year.
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Personal Finance Example (cont.)
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Review of Learning Goals
LG1 Discuss the role of time value in finance, the use of
computational tools, and the basic patterns of cash
flow.Financial managers and investors use time-value-of-money
techniques when assessing the value of expected cash flow
streams. Alternatives can be assessed by either compounding to
find future value or discounting to find present value. Financial
managers rely primarily on present value techniques. The cash
flow of a firm can be described by its pattern—single amount,
annuity, or mixed stream.
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Review of Learning Goals (cont.)
LG2 Understand the concepts of future value and present value,
their calculation for single amounts, and the relationship
between them.Future value (FV) relies on compound interest to
measure future amounts: The initial principal or deposit in one
period, along with the interest earned on it, becomes the
beginning principal of the following period.The present value
(PV) of a future amount is the amount of money today that is
equivalent to the given future amount, considering the return
that can be earned. Present value is the inverse of future value.
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Review of Learning Goals (cont.)
LG3 Find the future value and the present value of both an
ordinary annuity and an annuity due, and find the present value
of a perpetuity.The future or present value of an ordinary
annuity can be found by using algebraic equations, a financial
calculator, or a spreadsheet program. The value of an annuity
due is always r% greater than the value of an identical annuity.
The present value of a perpetuity—an infinite-lived annuity—is
found using 1 divided by the discount rate to represent the
present value interest factor.
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Review of Learning Goals (cont.)
LG4 Calculate both the future value and the present value of a
mixed stream of cash flows. A mixed stream of cash flows is a
stream of unequal periodic cash flows that reflect no particular
pattern. The future value of a mixed stream of cash flows is the
sum of the future values of each individual cash flow. Similarly,
the present value of a mixed stream of cash flows is the sum of
the present values of the individual cash flows.
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Review of Learning Goals (cont.)
LG5 Understand the effect that compounding interest more
frequently than annually has on future value and the effective
annual rate of interest.Interest can be compounded at intervals
ranging from annually to daily, and even continuously. The
more often interest is compounded, the larger the future amount
that will be accumulated, and the higher the effective, or true,
annual rate (EAR).
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Review of Learning Goals (cont.)
LG6 Describe the procedures involved in (1) determining
deposits needed to accumulate a future sum, (2) loan
amortization, (3) finding interest or growth rates, and (4)
finding an unknown number of periods.(1) The periodic deposit
to accumulate a given future sum can be found by solving the
equation for the future value of an annuity for the annual
payment. (2) A loan can be amortized into equal periodic
payments by solving the equation for the present value of an
annuity for the periodic payment. (3) Interest or growth rates
can be estimated by finding the unknown interest rate in the
equation for the present value of a single amount or an annuity.
(4) An unknown number of periods can be estimated by finding
the unknown number of periods in the equation for the present
value of a single amount or an annuity.
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Chapter Resources on MyFinanceLabChapter CasesGroup
ExercisesCritical Thinking Problems
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.
Table 1: Track Software, Inc. Profit, Dividends, and Retained
Earnings, 2006–2012
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.
Table 2: Track Software, Inc. Income Statement ($000)for the
Year Ended December 31, 2012
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.
Table 3a: Track Software, Inc. Balance Sheet ($000)
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.
Table 3b: Track Software, Inc. Balance Sheet ($000)
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.
Table 4: Track Software, Inc. Statement of Retained Earnings
($000) for the Year Ended December 31, 2012
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.
Table 5: Track Software, Inc. Profit, Dividends, and Retained
Earnings, 2006–2012
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.Upon what financial goal
does Stanley seem to be focusing? Is it the correct goal? Why or
why not?
Could a potential agency problem exist in this firm?
Explain.Calculate the firm’s earnings per share (EPS) for each
year, recognizing that the number of shares of common stock
outstanding has remained unchanged since the firm’s inception.
Comment on the EPS performance in view of your response in
part a.Use the financial data presented to determine Track’s
operating cash flow (OCF) and free cash flow (FCF) in 2012.
Evaluate your findings in light of Track’s current cash flow
difficulties.
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.Analyze the firm’s
financial condition in 2012 as it relates to (1) liquidity, (2)
activity, (3) debt, (4) profitability, and (5) market, using the
financial statements provided in Tables 2 and 3 and the ratio
data included in Table 5. Be sure to evaluate the firm on both a
cross-sectional and a time-series basis.What recommendation
would you make to Stanley regarding hiring a new software
developer? Relate your recommendation here to your responses
in part a.
© 2012 Pearson Prentice Hall. All rights reserved.
© 2012 Pearson Prentice Hall. All rights reserved.
5-*
Integrative Case: Track Software, Inc.Track Software paid
$5,000 in dividends in 2012. Suppose an investor approached
Stanley about buying 100% of his firm. If this investor believed
that by owning the company he could extract $5,000 per year in
cash from the company in perpetuity, what do you think the
investor would be willing to pay for the firm if the required
return on this investment is 10%?Suppose that you believed that
the FCF generated by Track Software in 2012 could continue
forever. You are willing to buy the company in order to receive
this perpetual stream of free cash flow. What are you willing to
pay if you require a 10% return on your investment?
© 2012 Pearson Prentice Hall. All rights reserved.
*
1
ALKATAN
FARAG ALKATAN
English 113 B
Collins, Suzanne. The hunger games. New York: scholastic,
2008: 3-374. Print
The hunger game book is explaining exactly what is the purpose
of these hunger games.it is a story that has been written from
the writer Suzanne Collins. She chooses a female characters
which Katniss to play the role that she assigned her for. Katniss
is a girl from the district 12 and this district was created after
the North America destroyed. There is a city existed after north
of America called “Panem”. It has the capital rich city in the
story and there are 12 poor districts too. As a punishment for
the district 12 after this district tried to coup against the capital
city. The hunger game rules created in this time. The rules is to
choose a boy and a girl to be contributed in this games and their
age must be between 12 and 18 years old. Therefore, they
choose Katniss’s sister firstly as which is very young but
Katniss refuse this decision so she take her sister place to
participate in the game. Meanwhile, the boy was Peeta who also
contribute in the game with Katniss.he was the man who helps
Katniss and her family when they were starving one day. he
gave them a piece of bread because his father is a baker. After
that they took the two players to their assistant who is Haymitch
Abernathy an old winner player of this game in round 50 of the
hunger games. He provides the two players with a useful advise
for the game and how can they recognize the talent of their
rivals to face them. After that the round start and Katniss with
Peeta started the game. Katniss has a partner who she have just
12 years old and she remind her of her sister that she was
supposed to be in her place. Katniss and this little girl start to
fight with each other until one player in the game has killed this
girl. Then Katniss revenge for this girl and killed that player.
Katniss and Peeta were helping each other in the game and they
were representing to the people that they are in love. Therefore,
those who are in charge of this game sit a new rule which is tell
that if the last two player are form the same district they will
win together. That what make Katniss to search for Peeta until
she found him. Then they were the last two players from the
same district so they should be winning the game, but the
people in charge of the game change the rule to force them to
kill each other. Therefore, Katniss and Peeta decide to suicide,
which make them to cancel their rule and announce that the two
players are the winner of the round 74 of this game.
Bridget M. Blodgett and Anastasia Salter. (2013).” Being Effie:
The Hunger Games and War as a Form of Entertainment Media
Consumption.” Retrieved 2013 йил 20-November from
http://web.mit.edu
This article is talking about The hunger game which the movie
that have this idea which comes from the writer Suzanne Collins
while she was watching a TV program and another channel that
shows a war in Iraq. At the same time while she watch this
program, Suzanne Collins came with an idea of Kittness which
is represented in the hunger game movie. The idea was basically
about how the poor people who do not have the power can find
their fortune and fight for the survival. At the second paragraph,
the role of the trans media has been revealed. The media was
contributed in a big role which makes this story became famous
and lovable among the people in the United States. The books of
the film was published in all the united states and has the strong
renown among the people because it is touch our contemporary
world and environment living today. Not only the book make
this story famous but also the movie that was released “the
hunger game” has attract the attention of many other people not
only in the united states but also among the other countries in
the world. The third paragraph, talking about the city Panem as
a global village, which is the village of starting this game. This
village where the players will start the war and killing each
other in order to survive and go back to their home after they
have been choose from those who are in charge of this game.
This is war is a small of the predictable life in the future for our
world. The meaning of this story is shown that by fighting for
survive and finding our rights. The democracy that we are
looking for is the mean cause of this fights and wars between
each other. The story of this movie became popular among the
people because of its sense that touch our real world nowadays
and we see this everyday in the television. Many countries are
fighting for their rights by create a revolution that has the
power to change something in their country for their rights.
Carvalho, C. (2012). Hunger Games (2012). Retrieved 2013 йил
20-November from http://www.imdb.com
Tan, S. S. (2013). Burn with Us: Sacrificing Childhood in The
Hunger Games. Retrieved 2013 йил 20-November from
http://muse.jhu.edu
The Hunger Games trilogy can be used as cultural critique of
the modern world. Just like the stories of Abraham and Jesus’s
role, as the sacrificial body, the Hunger Games indicate the
cultural centrality of the sacrificial son. Such traditions portray
a damaged culture that does not recognize the loss of innocence
and child-self. They portray people’s fears of the future. In the
districts of Panem, childhood is stripped away children turn into
agents of their family’s survival where their families and adults
offer up them up as potential sacrifice. A childhood is
threatened, lost, and unheard. This makes adult survival
dependent on child death. All children lived under this threat of
adult culture and must have recognized their vulnerability.
Katniss became a revolutionary symbolic, accepting her desire
to live though acknowledging the complex desires such as the
desire for others to live, and the desire to define and express
herself. However, she realized she was the protector of her
family and would not endanger their lives by expressing herself.
Her sense of self is characterized by independence, inherent
rebellion and self-sufficiency.
The Hunger Games, like Disneyland, demonstrate a power in
terms of cultural memory and history. This makes people deny
the hyperreality of their own society. Children who are
protected and spared from Games, war and first-hand violence
have been denied a place in the future world. Just like in
Panem, the current world makes the physical process of
maturation dangerous and demands that children be used as a
sacrifice for entertainment. As children, mature into adulthood,
adults are conversely infantilized because adult
disempowerment emerges as a consequence of its own
childhood traumas.
The Hunger Games brandish public punishment, and indeed
violence toward children, as an instrument of political control
and a locus of government supremacy. This resembles modern-
day fascination with youth, where children must appear younger
and thinner, and are made acceptable items of adult desire,
admired for magical innocence and sexualized image. The
simultaneous cultures of sacrificial violence and hysteric
celebration that surround a child’s body carry religious valence.
In the modern world, there Hunger games scenario is reflected
by the commercialization of the adolescent, sexualized body.
Surname 1
Hunger Games
There are many themes brought forth in the Hunger Games such
as love, rebellion, economic inequality, rebellion, sacrifice,
among others. These themes are also evident in the world today
as individuals and societies go through different circumstances
that lead to unavoidable consequences. Every situation that
people go through has a consequence depending on how they
chose to handle their situations. The characters in the hunger
games sacrifice their childhoods and their lives in order to
please a totalitarian government. Just as in real world, people
make sacrifice when under the control of dictators. These
sacrifices lead to tensions that cause uprising and revolution.

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Copyright © 2012 Pearson Prentice Hall. All rights reserve.docx

  • 1. Copyright © 2012 Pearson Prentice Hall. All rights reserved. Chapter 5 Time Value of Money * © 2012 Pearson Prentice Hall. All rights reserved. 5-* Learning Goals LG1 Discuss the role of time value in finance, the use of computational tools, and the basic patterns of cash flow. LG2 Understand the concepts of future value and present value, their calculation for single amounts, and the relationship between them. LG3 Find the future value and the present value of both an ordinary annuity and an annuity due, and find the present value of a perpetuity. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Learning Goals (cont.) LG4 Calculate both the future value and the present value of a mixed stream of cash flows.
  • 2. LG5 Understand the effect that compounding interest more frequently than annually has on future value and the effective annual rate of interest. LG6 Describe the procedures involved in (1) determining deposits needed to accumulate a future sum, (2) loan amortization, (3) finding interest or growth rates, and (4) finding an unknown number of periods. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* The Role of Time Value in FinanceMost financial decisions involve costs & benefits that are spread out over time.Time value of money allows comparison of cash flows from different periods.Question: Your father has offered to give you some money and asks that you choose one of the following two alternatives:$1,000 today, or$1,100 one year from now.What do you do? © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* The Role of Time Value in Finance (cont.)The answer depends on what rate of interest you could earn on any money you receive today.For example, if you could deposit the $1,000 today at 12% per year, you would prefer to be paid today.Alternatively, if you could only earn 5% on deposited funds, you would be better off if you chose the $1,100 in one year. © 2012 Pearson Prentice Hall. All rights reserved.
  • 3. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value versus Present ValueSuppose a firm has an opportunity to spend $15,000 today on some investment that will produce $17,000 spread out over the next five years as follows: Is this a wise investment?To make the right investment decision, managers need to compare the cash flows at a single point in time. YearCash flow1$3,0002$5,0003$4,0004$3,0005$2,000 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Figure 5.1 Time Line © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Figure 5.2 Compounding and Discounting © 2012 Pearson Prentice Hall. All rights reserved.
  • 4. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Figure 5.3 Calculator Keys © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Computational Tools (cont.) Electronic spreadsheets:Like financial calculators, electronic spreadsheets have built-in routines that simplify time value calculations. The value for each variable is entered in a cell in the spreadsheet, and the calculation is programmed using an equation that links the individual cells. Changing any of the input variables automatically changes the solution as a result of the equation linking the cells. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Basic Patterns of Cash FlowThe 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: © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value of a Single AmountFuture value is the value at a
  • 5. given future date of an amount placed on deposit today and earning interest at a specified rate. Found by applying compound interest over a specified period of time.Compound interest is interest that is earned on a given deposit and has become part of the principal at the end of a specified period.Principal is the amount of money on which interest is paid. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example If Fred Moreno places $100 in a savings account paying 8% interest compounded annually, how much will he have at the end of 1 year? If Fred were to leave this money in the account for another year, how much would he have at the end of the second year? Future value at end of year 2 = $116.64 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value of a Single Amount: The Equation for Future ValueWe use the following notation for the various inputs:FVn = future value at the end of period nPV = initial principal, or present valuer = annual rate of interest paid. (Note: On financial calculators, I is typically used to represent this rate.)n = number of periods (typically years) that the money is left on depositThe general equation for the future value at the end of period n is
  • 6. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value of a Single Amount: The Equation for Future Value Jane Farber places $800 in a savings account paying 6% interest compounded annually. She wants to know how much money will be in the account at the end of five years. This analysis can be depicted on a time line as follows: 823) = $1,070.58 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Figure 5.4 Future Value Relationship © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved.
  • 7. 5-* Present Value of a Single AmountPresent value is the current dollar value of a future amount—the amount of money that would have to be invested today at a given interest rate over a specified period to equal the future amount.It is based on the idea that a dollar today is worth more than a dollar tomorrow.Discounting cash flows is the process of finding present values; the inverse of compounding interest.The discount rate is often also referred to as the opportunity cost, the discount rate, the required return, or the cost of capital. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Paul Shorter has an opportunity to receive $300 one year from now. If he can earn 6% on his investments, what is the most he should pay now for this opportunity? PV = $300/(1 + 0.06) = $283.02 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Present Value of a Single Amount: The Equation for Present Value The present value, PV, of some future amount, FVn, to be received n periods from now, assuming an interest rate (or opportunity cost) of r, is calculated as follows: © 2012 Pearson Prentice Hall. All rights reserved.
  • 8. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Present Value of a Single Amount: The Equation for Future Value Pam Valenti wishes to find the present value of $1,700 that will be received 8 years from now. Pam’s opportunity cost is 8%. This analysis can be depicted on a time line as follows: PV = $1,700/(1 + 0.08)8 = $1,700/1.85093 = $918.46 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Figure 5.5 Present Value Relationship © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Annuities An annuity is a stream of equal periodic cash flows, over a
  • 9. specified time period. These cash flows can be inflows of returns earned on investments or outflows of funds invested to earn future returns.An ordinary (deferred) annuity is an annuity for which the cash flow occurs at the end of each periodAn annuity due is an annuity for which the cash flow occurs at the beginning of each period.An annuity due will always be greater than an otherwise equivalent ordinary annuity because interest will compound for an additional period. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Fran Abrams is choosing which of two annuities to receive. Both are 5-year $1,000 annuities; annuity A is an ordinary annuity, and annuity B is an annuity due. Fran has listed the cash flows for both annuities as shown in Table 5.1 on the following slide. Note that the amount of both annuities total $5,000. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Table 5.1 Comparison of Ordinary Annuity and Annuity Due Cash Flows ($1,000, 5 Years) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Future Value of an Ordinary AnnuityYou can
  • 10. calculate the future value of an ordinary annuity that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Fran Abrams wishes to determine how much money she will have at the end of 5 years if he chooses annuity A, the ordinary annuity and it earns 7% annually. Annuity A is depicted graphically below: This analysis can be depicted on a time line as follows: © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Present Value of an Ordinary AnnuityYou can
  • 11. calculate the present value of an ordinary annuity that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Present Value of an Ordinary Annuity (cont.) Braden Company, a small producer of plastic toys, wants to determine the most it should pay to purchase a particular annuity. The annuity consists of cash flows of $700 at the end of each year for 5 years. The required return is 8%. This analysis can be depicted on a time line as follows: © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Table 5.2 Long Method for Finding the Present Value of an Ordinary Annuity © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Present Value of an Ordinary Annuity (cont.)
  • 12. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Future Value of an Annuity DueYou can calculate the present value of an annuity due that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Fran Abrams now wishes to calculate the future value of an annuity due for annuity B in Table 5.1. Recall that annuity B was a 5 period annuity with the first annuity beginning immediately. Note: Before using your calculator to find the future value of an annuity due, depending on the specific calculator, you must either switch it to BEGIN mode or use the DUE key. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-*
  • 13. Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Present Value of an Annuity DueYou can calculate the present value of an ordinary annuity that pays an annual cash flow equal to CF by using the following equation: As before, in this equation r represents the interest rate and n represents the number of payments in the annuity (or equivalently, the number of years over which the annuity is spread). © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Present Value of an Annuity Due (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Matter of Fact Kansas truck driver, Donald Damon, got the surprise of his life when he learned he held the winning ticket for the Powerball lottery drawing held November 11, 2009. The advertised lottery jackpot was $96.6 million. Damon could have chosen to collect million = $96.6 million), but instead he elected to accept a lump
  • 14. sum payment of $48,367,329.08, roughly half the stated jackpot total. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Finding the Present Value of a PerpetuityA perpetuity is an annuity with an infinite life, providing continual annual cash flow.If a perpetuity pays an annual cash flow of CF, starting one year from now, the present value of the cash flow stream is PV = CF ÷ r © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Ross Clark wishes to endow a chair in finance at his alma mater. The university indicated that it requires $200,000 per year to support the chair, and the endowment would earn 10% per year. To determine the amount Ross must give the university to fund the chair, we must determine the present value of a $200,000 perpetuity discounted at 10%. PV = $200,000 ÷ 0.10 = $2,000,000 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value of a Mixed Stream Shrell Industries, a cabinet manufacturer, expects to receive the following mixed stream of cash flows over the next 5 years
  • 15. from one of its small customers. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value of a Mixed Stream If the firm expects to earn at least 8% on its investments, how much will it accumulate by the end of year 5 if it immediately invests these cash flows when they are received? This situation is depicted on the following time line. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Future Value of a Mixed Stream (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Present Value of a Mixed Stream Frey Company, a shoe manufacturer, has been offered an opportunity to receive the following mixed stream of cash flows over the next 5 years. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Present Value of a Mixed Stream
  • 16. If the firm must earn at least 9% on its investments, what is the most it should pay for this opportunity? This situation is depicted on the following time line. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Present Value of a Mixed Stream (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Compounding Interest More Frequently Than AnnuallyCompounding more frequently than once a year results in a higher effective interest rate because you are earning on interest on interest more frequently.As a result, the effective interest rate is greater than the nominal (annual) interest rate.Furthermore, the effective rate of interest will increase the more frequently interest is compounded. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Table 5.3 Future Value from Investing $100 at 8% Interest Compounded Semiannually over 24 Months (2 Years) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved.
  • 17. 5-* Table 5.4 Future Value from Investing $100 at 8% Interest Compounded Quarterly over 24 Months (2 Years) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Table 5.5 Future Value from Investing $100 at 8% Interest Compounded Quarterly over 24 Months (2 Years) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Compounding Interest More Frequently Than Annually (cont.) A general equation for compounding more frequently than annually Recalculate the example for the Fred Moreno example assuming (1) semiannual compounding and (2) quarterly compounding. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Compounding Interest More Frequently Than Annually (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved.
  • 18. 5-* Compounding Interest More Frequently Than Annually (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Continuous CompoundingContinuous compounding involves the compounding of interest an infinite number of times per year at intervals of microseconds.A general equation for continuous compounding where e is the exponential function. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Find the value at the end of 2 years (n = 2) of Fred Moreno’s $100 deposit (PV = $100) in an account paying 8% annual interest (r = 0.08) compounded continuously. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved.
  • 19. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Nominal and Effective Annual Rates of InterestThe nominal (stated) annual rate is the contractual annual rate of interest charged by a lender or promised by a borrower.The effective (true) annual rate (EAR) is the annual rate of interest actually paid or earned.In general, the effective rate > nominal rate whenever compounding occurs more than once per year © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Fred Moreno wishes to find the effective annual rate associated with an 8% nominal annual rate (r = 0.08) when interest is compounded (1) annually (m = 1); (2) semiannually (m = 2); and (3) quarterly (m = 4). © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Focus on Ethics How Fair Is “Check Into Cash”?There are more than 1,100 Check Into Cash centers among an estimated 22,000 payday- advance lenders in the United States. A payday loan is a small, unsecured, short-term loan ranging from $100 to $1,000
  • 20. (depending upon the state) offered by a payday lender. A borrower who rolled over an initial $100 loan for the maximum of four times would accumulate a total of $75 in fees all within a 10-week period. On an annualized basis, the fees would amount to a whopping 391%.The 391% mentioned above is an annual nominal rate -week rate (15%) be compounded to calculate the effective annual interest rate? © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Special Applications of Time Value: Deposits Needed to Accumulate a Future Sum The following equation calculates the annual cash payment (CF) that we’d have to save to achieve a future value (FVn): Suppose you want to buy a house 5 years from now, and you estimate that an initial down payment of $30,000 will be required at that time. To accumulate the $30,000, you will wish to make equal annual end-of-year deposits into an account paying annual interest of 6 percent. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example © 2012 Pearson Prentice Hall. All rights reserved.
  • 21. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Special Applications of Time Value: Loan AmortizationLoan amortization is the determination of the equal periodic loan payments necessary to provide a lender with a specified interest return and to repay the loan principal over a specified period.The loan amortization process involves finding the future payments, over the term of the loan, whose present value at the loan interest rate equals the amount of initial principal borrowed.A loan amortization schedule is a schedule of equal payments to repay a loan. It shows the allocation of each loan payment to interest and principal. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Special Applications of Time Value: Loan Amortization (cont.)The following equation calculates the equal periodic loan payments (CF) necessary to provide a lender with a specified interest return and to repay the loan principal (PV) over a specified period: Say you borrow $6,000 at 10 percent and agree to make equal annual end-of-year payments over 4 years. To find the size of the payments, the lender determines the amount of a 4-year annuity discounted at 10 percent that has a present value of $6,000. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved.
  • 22. 5-* Personal Finance Example © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Table 5.6 Loan Amortization Schedule ($6,000 Principal, 10% Interest, 4-Year Repayment Period) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Focus on Practice New Century Brings Trouble for Subprime MortgagesIn 2006, some $300 billion worth of adjustable ARMs were reset to higher rates. In a market with rising home values, a borrower has the option to refinance their mortgage, using some of the equity created by the home’s increasing value to reduce the mortgage payment. But after 2006, home prices started a three- year slide, so refinancing was not an option for many subprime borrowers. As a reaction to problems in the subprime area, lenders tightened lending standards. What effect do you think this had on the housing market? © 2012 Pearson Prentice Hall. All rights reserved.
  • 23. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Special Applications of Time Value: Finding Interest or Growth RatesIt is often necessary to calculate the compound annual interest or growth rate (that is, the annual rate of change in values) of a series of cash flows.The following equation is used to find the interest rate (or growth rate) representing the increase in value of some investment between two time periods. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Ray Noble purchased an investment four years ago for $1,250. Now it is worth $1,520. What compound annual rate of return has Ray earned on this investment? Plugging the appropriate values into Equation 5.20, we have: r = ($1,520 ÷ $1,250)(1/4) – 1 = 0.0501 = 5.01% per year © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved.
  • 24. 5-* Personal Finance Example Jan Jacobs can borrow $2,000 to be repaid in equal annual end- of-year amounts of $514.14 for the next 5 years. She wants to find the interest rate on this loan. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Special Applications of Time Value: Finding an Unknown Number of PeriodsSometimes it is necessary to calculate the number of time periods needed to generate a given amount of cash flow from an initial amount. This simplest case is when a person wishes to determine the number of periods, n, it will take for an initial deposit, PV, to grow to a specified future amount, FVn, given a stated interest rate, r. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Ann Bates wishes to determine the number of years it will take for her initial $1,000 deposit, earning 8% annual interest, to grow to equal $2,500. Simply stated, at an 8% annual rate of interest, how many years, n, will it take for Ann’s $1,000, PV,
  • 25. to grow to $2,500, FVn? © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example Bill Smart can borrow $25,000 at an 11% annual interest rate; equal, annual, end-of-year payments of $4,800 are required. He wishes to determine how long it will take to fully repay the loan. In other words, he wishes to determine how many years, n, it will take to repay the $25,000, 11% loan, PVn, if the payments of $4,800 are made at the end of each year. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Personal Finance Example (cont.) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Review of Learning Goals LG1 Discuss the role of time value in finance, the use of
  • 26. computational tools, and the basic patterns of cash flow.Financial managers and investors use time-value-of-money techniques when assessing the value of expected cash flow streams. Alternatives can be assessed by either compounding to find future value or discounting to find present value. Financial managers rely primarily on present value techniques. The cash flow of a firm can be described by its pattern—single amount, annuity, or mixed stream. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Review of Learning Goals (cont.) LG2 Understand the concepts of future value and present value, their calculation for single amounts, and the relationship between them.Future value (FV) relies on compound interest to measure future amounts: The initial principal or deposit in one period, along with the interest earned on it, becomes the beginning principal of the following period.The present value (PV) of a future amount is the amount of money today that is equivalent to the given future amount, considering the return that can be earned. Present value is the inverse of future value. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Review of Learning Goals (cont.) LG3 Find the future value and the present value of both an ordinary annuity and an annuity due, and find the present value of a perpetuity.The future or present value of an ordinary annuity can be found by using algebraic equations, a financial calculator, or a spreadsheet program. The value of an annuity
  • 27. due is always r% greater than the value of an identical annuity. The present value of a perpetuity—an infinite-lived annuity—is found using 1 divided by the discount rate to represent the present value interest factor. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Review of Learning Goals (cont.) LG4 Calculate both the future value and the present value of a mixed stream of cash flows. A mixed stream of cash flows is a stream of unequal periodic cash flows that reflect no particular pattern. The future value of a mixed stream of cash flows is the sum of the future values of each individual cash flow. Similarly, the present value of a mixed stream of cash flows is the sum of the present values of the individual cash flows. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Review of Learning Goals (cont.) LG5 Understand the effect that compounding interest more frequently than annually has on future value and the effective annual rate of interest.Interest can be compounded at intervals ranging from annually to daily, and even continuously. The more often interest is compounded, the larger the future amount that will be accumulated, and the higher the effective, or true, annual rate (EAR). © 2012 Pearson Prentice Hall. All rights reserved.
  • 28. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Review of Learning Goals (cont.) LG6 Describe the procedures involved in (1) determining deposits needed to accumulate a future sum, (2) loan amortization, (3) finding interest or growth rates, and (4) finding an unknown number of periods.(1) The periodic deposit to accumulate a given future sum can be found by solving the equation for the future value of an annuity for the annual payment. (2) A loan can be amortized into equal periodic payments by solving the equation for the present value of an annuity for the periodic payment. (3) Interest or growth rates can be estimated by finding the unknown interest rate in the equation for the present value of a single amount or an annuity. (4) An unknown number of periods can be estimated by finding the unknown number of periods in the equation for the present value of a single amount or an annuity. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Chapter Resources on MyFinanceLabChapter CasesGroup ExercisesCritical Thinking Problems © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc. Table 1: Track Software, Inc. Profit, Dividends, and Retained Earnings, 2006–2012 © 2012 Pearson Prentice Hall. All rights reserved.
  • 29. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc. Table 2: Track Software, Inc. Income Statement ($000)for the Year Ended December 31, 2012 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc. Table 3a: Track Software, Inc. Balance Sheet ($000) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc. Table 3b: Track Software, Inc. Balance Sheet ($000) © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc. Table 4: Track Software, Inc. Statement of Retained Earnings ($000) for the Year Ended December 31, 2012 © 2012 Pearson Prentice Hall. All rights reserved.
  • 30. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc. Table 5: Track Software, Inc. Profit, Dividends, and Retained Earnings, 2006–2012 © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc.Upon what financial goal does Stanley seem to be focusing? Is it the correct goal? Why or why not? Could a potential agency problem exist in this firm? Explain.Calculate the firm’s earnings per share (EPS) for each year, recognizing that the number of shares of common stock outstanding has remained unchanged since the firm’s inception. Comment on the EPS performance in view of your response in part a.Use the financial data presented to determine Track’s operating cash flow (OCF) and free cash flow (FCF) in 2012. Evaluate your findings in light of Track’s current cash flow difficulties. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc.Analyze the firm’s financial condition in 2012 as it relates to (1) liquidity, (2) activity, (3) debt, (4) profitability, and (5) market, using the financial statements provided in Tables 2 and 3 and the ratio data included in Table 5. Be sure to evaluate the firm on both a cross-sectional and a time-series basis.What recommendation
  • 31. would you make to Stanley regarding hiring a new software developer? Relate your recommendation here to your responses in part a. © 2012 Pearson Prentice Hall. All rights reserved. © 2012 Pearson Prentice Hall. All rights reserved. 5-* Integrative Case: Track Software, Inc.Track Software paid $5,000 in dividends in 2012. Suppose an investor approached Stanley about buying 100% of his firm. If this investor believed that by owning the company he could extract $5,000 per year in cash from the company in perpetuity, what do you think the investor would be willing to pay for the firm if the required return on this investment is 10%?Suppose that you believed that the FCF generated by Track Software in 2012 could continue forever. You are willing to buy the company in order to receive this perpetual stream of free cash flow. What are you willing to pay if you require a 10% return on your investment? © 2012 Pearson Prentice Hall. All rights reserved. * 1 ALKATAN FARAG ALKATAN English 113 B Collins, Suzanne. The hunger games. New York: scholastic, 2008: 3-374. Print The hunger game book is explaining exactly what is the purpose of these hunger games.it is a story that has been written from
  • 32. the writer Suzanne Collins. She chooses a female characters which Katniss to play the role that she assigned her for. Katniss is a girl from the district 12 and this district was created after the North America destroyed. There is a city existed after north of America called “Panem”. It has the capital rich city in the story and there are 12 poor districts too. As a punishment for the district 12 after this district tried to coup against the capital city. The hunger game rules created in this time. The rules is to choose a boy and a girl to be contributed in this games and their age must be between 12 and 18 years old. Therefore, they choose Katniss’s sister firstly as which is very young but Katniss refuse this decision so she take her sister place to participate in the game. Meanwhile, the boy was Peeta who also contribute in the game with Katniss.he was the man who helps Katniss and her family when they were starving one day. he gave them a piece of bread because his father is a baker. After that they took the two players to their assistant who is Haymitch Abernathy an old winner player of this game in round 50 of the hunger games. He provides the two players with a useful advise for the game and how can they recognize the talent of their rivals to face them. After that the round start and Katniss with Peeta started the game. Katniss has a partner who she have just 12 years old and she remind her of her sister that she was supposed to be in her place. Katniss and this little girl start to fight with each other until one player in the game has killed this girl. Then Katniss revenge for this girl and killed that player. Katniss and Peeta were helping each other in the game and they were representing to the people that they are in love. Therefore, those who are in charge of this game sit a new rule which is tell that if the last two player are form the same district they will win together. That what make Katniss to search for Peeta until she found him. Then they were the last two players from the same district so they should be winning the game, but the people in charge of the game change the rule to force them to kill each other. Therefore, Katniss and Peeta decide to suicide, which make them to cancel their rule and announce that the two
  • 33. players are the winner of the round 74 of this game. Bridget M. Blodgett and Anastasia Salter. (2013).” Being Effie: The Hunger Games and War as a Form of Entertainment Media Consumption.” Retrieved 2013 йил 20-November from http://web.mit.edu This article is talking about The hunger game which the movie that have this idea which comes from the writer Suzanne Collins while she was watching a TV program and another channel that shows a war in Iraq. At the same time while she watch this program, Suzanne Collins came with an idea of Kittness which is represented in the hunger game movie. The idea was basically about how the poor people who do not have the power can find their fortune and fight for the survival. At the second paragraph, the role of the trans media has been revealed. The media was contributed in a big role which makes this story became famous and lovable among the people in the United States. The books of the film was published in all the united states and has the strong renown among the people because it is touch our contemporary world and environment living today. Not only the book make this story famous but also the movie that was released “the hunger game” has attract the attention of many other people not only in the united states but also among the other countries in the world. The third paragraph, talking about the city Panem as a global village, which is the village of starting this game. This village where the players will start the war and killing each other in order to survive and go back to their home after they have been choose from those who are in charge of this game. This is war is a small of the predictable life in the future for our world. The meaning of this story is shown that by fighting for survive and finding our rights. The democracy that we are looking for is the mean cause of this fights and wars between each other. The story of this movie became popular among the people because of its sense that touch our real world nowadays and we see this everyday in the television. Many countries are
  • 34. fighting for their rights by create a revolution that has the power to change something in their country for their rights. Carvalho, C. (2012). Hunger Games (2012). Retrieved 2013 йил 20-November from http://www.imdb.com Tan, S. S. (2013). Burn with Us: Sacrificing Childhood in The Hunger Games. Retrieved 2013 йил 20-November from http://muse.jhu.edu The Hunger Games trilogy can be used as cultural critique of the modern world. Just like the stories of Abraham and Jesus’s role, as the sacrificial body, the Hunger Games indicate the cultural centrality of the sacrificial son. Such traditions portray a damaged culture that does not recognize the loss of innocence and child-self. They portray people’s fears of the future. In the districts of Panem, childhood is stripped away children turn into agents of their family’s survival where their families and adults offer up them up as potential sacrifice. A childhood is threatened, lost, and unheard. This makes adult survival dependent on child death. All children lived under this threat of adult culture and must have recognized their vulnerability. Katniss became a revolutionary symbolic, accepting her desire to live though acknowledging the complex desires such as the desire for others to live, and the desire to define and express herself. However, she realized she was the protector of her family and would not endanger their lives by expressing herself. Her sense of self is characterized by independence, inherent rebellion and self-sufficiency. The Hunger Games, like Disneyland, demonstrate a power in terms of cultural memory and history. This makes people deny the hyperreality of their own society. Children who are protected and spared from Games, war and first-hand violence have been denied a place in the future world. Just like in Panem, the current world makes the physical process of maturation dangerous and demands that children be used as a sacrifice for entertainment. As children, mature into adulthood, adults are conversely infantilized because adult
  • 35. disempowerment emerges as a consequence of its own childhood traumas. The Hunger Games brandish public punishment, and indeed violence toward children, as an instrument of political control and a locus of government supremacy. This resembles modern- day fascination with youth, where children must appear younger and thinner, and are made acceptable items of adult desire, admired for magical innocence and sexualized image. The simultaneous cultures of sacrificial violence and hysteric celebration that surround a child’s body carry religious valence. In the modern world, there Hunger games scenario is reflected by the commercialization of the adolescent, sexualized body. Surname 1 Hunger Games There are many themes brought forth in the Hunger Games such as love, rebellion, economic inequality, rebellion, sacrifice, among others. These themes are also evident in the world today as individuals and societies go through different circumstances that lead to unavoidable consequences. Every situation that people go through has a consequence depending on how they chose to handle their situations. The characters in the hunger games sacrifice their childhoods and their lives in order to please a totalitarian government. Just as in real world, people make sacrifice when under the control of dictators. These sacrifices lead to tensions that cause uprising and revolution.