# Khan Academy Videos & Other Resources for Pre-MBA Students

Pre-MBA preparation is very important for many students because many:

• Have not had exposure to quantitative topics during prior academic programs; or
• Have been out of school for many years and so feel the need to get a refresher on the basic quantitative skills prior to starting the MBA program; or
• Do not have any prior business background.

Our graduate tutors run a variety of pre-MBA boot camps to assist MBA students to be better prepared for their MBA programs. For those who prefer to study by themselves, Professor Alan Anderson has shortlisted Khan Academy videos to get you a good quantitative base for your MBA program. You can watch these videos at your own leisure.

• Professor Anderson’s Selected Khan Academy Videos

## Algebra for an MBA Student

Khanacademy.org offers a huge array of videos in quantitative subjects, such as statistics, algebra, geometry, calculus, differential equations, etc.  The following discussion details the videos that cover the most important concepts in algebra.  These videos are found under the heading “Algebra” under the category “Math by Subject.”

### 1) Foundations

This section covers the properties of the real numbers, including negative values, exponents, fractions and decimals.

### 2) Algebraic Expressions

This section introduces complex algebraic expressions, including variables, constants, exponents and operators.  Techniques for manipulating expressions into a more useful form are covered in detail.

### 3) Linear Equations and Systems of Equations

This section introduces the concept of linear functions and shows how to solve for variables with linear equations.  There is also a discussion on solving systems of linear equations.

This section introduces more complex expressions, known as polynomials.  A quadratic equation is one that contains at least one squared term.  Techniques for solving quadratic equations are covered, along with techniques for performing algebraic operations on quadratic equations.

## Pre-MBA Finance Preparation

The following discussion shows several of the most important topics that are required knowledge for all finance students, along with the most relevant videos from Khan Academy.  These can be found under the category “Finance and Capital Markets” under the Subject tab on the website’s home page.

1) Computing Interest

The following videos introduce students to techniques for computing interest rates and understanding the relationship between different definitions of interest rates.  These are found under the category “Interest and Debt.”

The first video explores the concept of interest rates, showing how it applies to many aspects of our daily lives.  The video provides a brief introduction to the concepts of present and future value.  The second video introduces the formulas used to compute present and future value.  The next video discusses the impact of different compounding conventions on interest rates.  The Rule of 72 video introduces a useful rule of thumb that can be used to quickly determine how long it takes to double a sum of money with a specified interest rate, or what rate of interest is required to double a sum of money within a specified time frame.  The last video discusses two alternative methods for expressing interest rates:  annual percentage rate (APR) and effective annual rate (EAR).  APR reflects simple interest only, while EAR reflects both simple and compound interest.

2) Time Value of Money

The time value of money is one of the most important concepts in finance.  For example, the value of all securities in the marketplace is determined by time value of money concepts.  The capital budgeting process, through which corporations choose investment projects, is also based on time value of money principles.  The following videos are found under the heading “Interest and Debt.”

The first video explains how time value of money concepts can be used to determine the value of cash flows received at different points in time.  The remaining videos show in detail how to use algebraic formulas to compute the present value for a variety of different situations.

3) Bond Pricing

Bonds are debt instruments that are issued by borrowers to raise funds.  Corporations and governments are major issuers of bonds.  The following videos explain the features of bonds, and show how bonds are priced using present value concepts.  They also explain how bond cash flows are discounted using a measure of interest rates known as “yield to maturity” or “yield”; yields are based on the prices of Treasury securities.  These videos are found in the section “Interest and Debt.”

4) Stock Pricing

A share of stock represents partial ownership, or equity in a corporation.  Stocks are issued in order to raise capital.  The following videos provide an introduction to the basic features of stocks and a comparison of their features with bonds.  These videos are found in the section “Stocks and Bonds.”

5) Options and Futures

Options, forwards and futures are three examples of derivative securities, which are extremely powerful hedging tools.  The pricing of these securities can be highly complex, especially for options.  These videos are found in the section “Options, Swaps, Futures, MBSs, CDOs,…”

The first two videos discuss the basic features of forward and futures contracts, which are very similar and can be used to lock in the price at which an asset may be bought or sold in the future.  The remaining videos introduce the key features of options.  A call option enables the owner to buy an asset in the future at a predetermined price, while a put option enables the owner to sell an asset in the future at a predetermined price.  American-style options can be “exercised” at any time up to the maturity date, while European-style options can only be exercised at maturity.  Payoff diagrams can be used to illustrate the relationship between the cash flows to an option and the price of the underlying asset.

One of the most important differences between forward/futures and options is that the buyer of an option must pay a price, or a premium.  Option pricing models are extremely sophisticated.  The first option pricing model was the Black-Scholes model, which is used to price European-style options; the developers of this model were awarded the Nobel Prize in Economics in 1997.  The prices of European-style puts can be derived from the corresponding calls through a relationship known as Put-Call Parity.

This should give you a strong  pre-MBA foundation on which to build your success in the MBA program. Good luck with your MBA program. If we can be of assistance, please do not hesitate to give us a shout.

## Pre-MBA Economics Preparation

The following discussion shows several of the most important topics that are required knowledge for all economics students, along with the most relevant videos from Khan Academy.  These can be found under the categories “Macroeconomics” and “Microeconomics” under the Subject tab on the website’s home page.

1) Introduction to Economics

This section provides an overview of the field of economics with an introduction to the classic work by Adam Smith, “The Wealth of Nations.”

2) GDP – Measuring National Income

This section introduces the concept of Gross Domestic Product and how it is computed.  The different components of GDP are analyzed, and the circular flow model of economic activity is explained.  The key distinction between real and nominal GDP is also covered.

3) Supply and Demand

This section introduces the most important concepts in economics:  supply and demand.  The law of supply and law of demand are analyzed in detail, showing the resulting supply and demand curves and how equilibrium is determined in the marketplace.  The factors that determine supply and demand are also explored.

4) Elasticity

This section covers a key concept in economics: elasticity.  This refers to the sensitivity of one variable to a change in another variable.  Elasticity is used to determine how sensitive consumers and producers are to changes in prices.  Elasticity can also be used to determine the optimal output of a business enterprise.  Other useful types of elasticity are also defined; these can be used to determine how consumer spending patterns change as incomes rise, or how the change in the price of a good can impact the quantity purchased of other goods.

5) Market Structures

This section covers several important types of market structures, including perfect competition, monopoly, oligopoly and monopolistic competition.  Many industries exhibit characteristics of one or more of these market structures; their pricing and output decisions will depend on the type of market structure in which they operate.

## Pre-MBA Statistics Preparation

The following discussion details the videos that cover the most important concepts in statistics.  These videos are found under the heading “Probability and Statistics” under the category “Math by Subject.”

1) Descriptive Statistics

This section provides an introduction to several measures that can be used to describe the key properties of populations and samples.  These include measures of central tendency and measures of spread or dispersion.

2) Probability

This section introduces the foundations of probability theory and defines the concept of the event.  The notion of independence is covered in detail; there is also a review of basic set theory.

3) Random Variables and Probability Distributions

This section introduces the concept of a random variable, which is a function that assigns values to the outcomes of a random experiment.  Using a random variable as a starting point, any number of probability distributions may be defined; these assign probabilities to the values of a random variable.  Many probability distributions are especially useful in finance, including the binomial and normal distributions.  This section also explains the concept of moments, which are summary measures of the properties of a random variable.

4) Sampling Distributions and Confidence Intervals

This section introduces the concepts of sampling distributions and confidence intervals.  A sampling distribution is a probability distribution that describes the properties of a sample statistic, such as the sample mean.  A confidence interval is a type of interval estimate; it provides an estimated range of values for a population value such as the mean.

5) Hypothesis Testing

This section covers the key concept of hypothesis testing.  A hypothesis test is a series of steps designed to test whether or not there is sufficient evidence to reject a specified proposition.  Hypothesis testing is used in a wide variety of applications throughout statistics, and is especially important for financial applications.

6) Regression Analysis

Regression analysis is one of the most important tools of statistics; it can be used to test the strength and direction of the relationship between different variables.  Regression analysis is heavily used in economics and finance.

## Pre-MBA Accounting Preparation

1) Financial Statements

The following videos are found under the category “Accounting and Financial Statements.”  There are several sections dedicated to accounting; of particular interest to finance students is the discussion of financial statements analysis.  The financial condition of a corporation can be found in its financial statements, especially the balance sheet and income statement.

The first video introduces the balance sheet and income statement, showing what items are listed on them.  The next two videos provide students with an opportunity to get some practice with financial statements; there is an embedded calculator that enables students to attempt to answer a series of questions about a fictional balance sheet and financial statement.  The last video explores the items that appear on a cash flow statement, taken from the information found on the balance sheet and the income statement. Another view of these financial statements can be had here at:

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