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NPV and the Time
Value of Money
◗
Construct a cash flow timeline as
the first step in solving problems
◗
Calculate the value of distant
cash flows in the present and of
current cash flows in the future
◗
Value a series of many cash flows
◗
Understand how to compute the
net present value of any set of
cash flows
4
LEARNING OBJECTIVES
notation
◗
Apply shortcuts to value special
sets of regular cash flows called
perpetuities
and
annuities
◗
Compute the number of periods,
cash flow, or rate of return in a
loan or investment
C
cash flow
cash flow at date
n
FV
future value
future value on date
g
growth rate
IRR
internal rate of return
N
date of the last cash flow in
a stream of cash flows
NPV
net present value
P
initial principal or deposit, or
equivalent present value
PV
present value
present value on date
r
interest rate
PV
n
FV
n
C
n
86

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INTERVIEW WITH
Jonathan Jagolinzer, Ameriprise Financial Services
Jonathan Jagolinzer is a financial advisor for Ameriprise Financial Services (formerly American
Express Financial), a Fortune 500 financial planning, asset management, and insurance company.
A 2005 graduate of George Washington University in Washington, DC, Jon majored in economics
and minored in finance.
Jon, who works in Ameriprise’s Vienna, Virginia, office, views himself as personal financial trainer
for his clients. “Much like a personal trainer, I help them set goals, provide guidance to reach their
objectives, and track progress over time,” he says. “Working together, we develop sound financial
planning strategies for investments, funding children’s education, retirement, and estate planning.”
Jon’s specialty is retirement planning, and he has earned his Chartered Retirement Planning
Counselor (CRPC) credential. “My knowledge of time value of money concepts allows me to advise
my clients, many of whom are young and just beginning to accumulate personal assets. Some
want to spend extravagantly, to buy a new television now, and say they will make up the difference
later.” He uses a simple example to illustrate how their dollars can grow over time. “Take just $25
each month—money you’d otherwise spend on movies, new clothes, or fancy coffee drinks—and
put that into an account earning 6% interest a year. At the end of 15 years, your $4500 investment
will have grown to $7270! That $25 may not seem like much today, but the long-term benefits are
quite significant.”
Jon also encourages his clients to invest in tax-deferred retirement funds. “If you contribute
$100 a month to a tax-deferred retirement account that earns 10% a year, at the end of 20 years
you will have over $75,000. If it went into a taxable account and you are in the 28% bracket, it
would grow to less than $54,000 over the same period. Time value and other financial concepts
are, therefore, tools you can use not just on the job but also to make smarter personal financial
decisions today that will bring substantial benefits in the future.”
George Washington
University, 2005
“Time value and
other financial
concepts are,

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