Friday 5 July 2019

CFA Institute Investment Foundations Program: Chapter 8 – Quantitative Concepts (Part I)

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.

Source: https://www.cfainstitute.org/en/programs/investment-foundations

Sample question:

The greater the risk associated with a borrower’s ability to repay a loan, the greater the:
 
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