In a previous article, we introduced the CFA Institute
Investment Foundation Program (Read
more here). It is a free program
designed for anyone who wants to enter or advance within the investment
management industry, including IT, operations, accounting, administration, and
marketing. Candidates who successfully
pass the online exam earn the CFA Institute Investment Foundations Certificate.
There are total of 20 Chapters in 7 modules, covering all
the essential topics in finance, economics, ethics and regulations. This series of articles will highlight the
core knowledge of each chapter.
Chapter 8 provides an overview of quantitative concepts. The
learning outcome of chapter 8 is as follows:
·
Define the concept of interest;
·
Compare simple and compound interest;
·
Define present value, future value, and discount
rate;
·
Describe how time and discount rate affect
present and future values;
·
Explain the relevance of net present value in
valuing financial investments;
·
Describe applications of time value of money;
·
Explain uses of mean, median, and mode, which
are measures of frequency or central tendency;
·
Explain uses of range, percentile, standard
deviation, and variance, which are measures of dispersion;
·
Describe and interpret the characteristics of a
normal distribution;
·
Describe and interpret correlation.
Quantitative concepts play a role in financial decisions,
such as saving and borrowing, and also form the foundation for valuing
investment opportunities and assessing their risks. The time value of money and
descriptive statistics are two important quantitative concepts. Part I of this series will be focusing on
time value of money.
The time value of money is useful in many walks of life: it
helps savers to know how long it will take them to afford a certain item and
how much they will have to put aside each week or month, it helps investors to
assess whether an investment should provide a satisfactory return, and it helps
companies to determine whether the profit from investing will exceed the cost.
Borrowing and lending are transactions with cash flow
consequences. Someone who needs money borrows it from someone who does not need
it in the present (a saver) and is willing to lend it. In the present, the
borrower has money and the lender has given up money. In the future, the
borrower will give up money to pay back the lender; the lender will receive
money as repayment from the borrower in the form of interest, as shown below.
The lender will also receive back the money lent to the borrower. The money originally
borrowed, which interest is calculated on, is called the principal. Interest
can be defined as payment for the use of borrowed money.
A simple interest rate is the cost to the borrower or the
rate of return to the lender, per period, on the original principal (the amount
borrowed). Interest compounds when it is
added to the original principal. Compound interest is often referred to as
“interest on interest”. As opposed to simple interest, interest is assumed to
be reinvested so future interest is earned on principal and reinvested
interest, not just on the original principal.
Two basic time value of money problems are finding the value
of a set of cash flows now (present value) and the value as of a point of time
in the future (future value). Before you
can calculate present or future values, you must know the appropriate interest
or discount rates to use. The rate will usually depend on the overall level of
interest rates in the economy, the opportunity cost, and the riskiness of the
investments under consideration. The following equations generalise the
calculation of future and present values:
The net present value (NPV) of an investment is the present
value of future cash flows or returns minus the present value of the cost of
the investment (which often, but not always, occurs only in the initial
period). Using NPV rather than present value to evaluate investments is
especially important when the investments have different initial costs.
Sample question:
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