## Monday MBA Math: Annuities

The Monday MBA Math series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.

As described in the first and second Monday MBA Math finance exercises, quantitative finance builds incrementally. Those exercises deal with converting a single amount of money at one point in time into a different single amount at a different time. This exercise deals with converting multiple cash flows into a single cash flow. With this step, and the issues that it raises about rates and timeframes, finance supports the efforts of business people everywhere to capture the current value of future financial prospects as well as the efforts of individual and institutional investors to make current investments that will generate future cash flows.

Constant annuities, which are a set of equal periodic payments, are incredibly common, especially in the credit markets. If you've ever taken out a loan to buy a car or house or finance your education with student loans, you've sold an annuity. You get money upfront and the lender receives a stream of constant payments from you. The inability of the world's largest financial institutions to correctly value subprime mortgage annuities was the trigger to the ongoing financial meltdown.

**Exercise**:

What is the present value of an annuity in which $300 is paid each year for 4 years, assuming a discount rate of 8% and the first payment is received one year from now?

**Solution (with audio commentary): click here**

*Prof. Peter Regan created the self-paced, online MBA Math quantitative skills course and teaches live MBA courses at Dartmouth (Tuck), Duke (Fuqua), and Cornell (Johnson).*

## MBA Math Activity Ramping Up

As June closes, incoming student activity at MBA Math is ramping up. The coming four to seven weeks is the peak season for pre-term quant skills prep, as you can see from this chart of today's date marked on last year's activity levels. Incoming students, are you prepared?

## MBA Math Testimonial for Penn (Wharton)

Here is a testimonial from Andrew Troisi, a Class of 2010 student at The Wharton School of the University of Pennsylvania and member of the MBA Math Board of Advisors, about his pre-MBA use of the MBA Math online quantitative preparation course:

After deciding to attend Wharton, I wanted to prepare for what I knew would be a very analytical and rigorous program. Coming from a “non-traditional” background, I sought a fundamental knowledge of the accounting, statistics and finance topics that are a central part of the first year curriculum.

MBA Math offered that, and more. Working through the material on my own allowed me to put extra emphasis on unfamiliar material. The course topics were clearly outlined and the lectures and exercises gave a nice overview of the content I encountered in greater depth when the academic year began.

On more than one occasion during the school year, I logged back in to MBA Math for a quick refresher.

The first year (and particularly the first semester) MBA curriculum was very fast paced – I strongly believe taking the time to familiarize myself with the basics was a prudent decision.

I recently completed my first year at Wharton, where I am majoring in finance and strategic management. Prior to business school, I was a press secretary for the City of New York.

## Wash U (Olin) EMBA Chooses MBA Math

Olin Business School at Washington University in St. Louis purchased MBA Math subscriptions for selected executive MBA program students.

## Monday MBA Math: Probability

The Monday MBA Math series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.

Probability is a language for dealing with uncertainty. Like any language, it has structure and rules that take practice to internalize.

This exercise is at its core a simple logic challenge.

Uncertainty permeates business. While qualitative reasoning is essential to clarify appropriate strategy and tactics, high quality decision making often requires familiarity with probability to weight the consequences of possible futures associated with various choices.

**Exercise**:

Let X be a discrete random variable. If Pr(X<5) = 2/9, and Pr(X<=5) = 5/18, then** **what is Pr(X=5)?

**Solution (with audio commentary): click here**

*Prof. Peter Regan created the self-paced, online MBA Math quantitative skills course and teaches live MBA courses at Dartmouth (Tuck), Duke (Fuqua), and Cornell (Johnson).*

## Monday MBA Math: Marginal Analysis by Formula

The Monday MBA Math series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.

The first MBA Math economics exercise explained that marginal analysis discovers a firm's optimal production quantity and profit. Marginal analysis problems can be posed equivalently in terms of tables, formulas, or charts. The first exercise used data in tables. This exercise uses formulas but without invoking calculus.

Economics is tricky because it takes awhile to internalize the necessary chain of reasoning. Of course, it also has its own terminology (q^{th} unit?) that is confusing at first. The goal is generally clear, at least in intro economics exercises. In this exercise, we want to know what level of production yields the highest profit. The challenge is to build a chain of reasoning from the problem as stated to the goal.

Once you've got a clear solution path in your head, the rest is simple algebra. Starting with algebra before you know where you're headed is a common form of flailing for beginning (or returning) students.

Working with data in tables is more intuitive for many beginning students but, if you can accept that formulas represent the same information in shorthand, you can get more quickly to an answer with formulas. This one takes about 5 seconds when you know what you're doing.

The last step in a marginal analysis is to introduce fixed costs to determine whether the optimal strategy results in a true profit or loss. This has been the Twilight Zone world of U.S. car companies recently. However much they've (debatably) been closing the gap in quality and marginal production costs, the industry-wide drop in demand combined with their massive fixed cost burdens put them in the position of working like hell to lose the least amount possible.

**Exercise**:

Suppose that you can sell as much of a product as you like at $92 per unit. Your marginal cost (MC) for producing the q^{th} unit is given by:

MC=10q

If fixed costs are $350, what is the optimal output level?

**Solution (with audio commentary): click here**

*Prof. Peter Regan created the self-paced, online MBA Math quantitative skills course and teaches live MBA courses at Dartmouth (Tuck), Duke (Fuqua), and Cornell (Johnson).*

## Monday MBA Math: Balance Sheet Transactions

The first MBA Math accounting exercise explained that balance sheets provide a snapshot of a firm's financial condition at a moment in time, with "balance" referring to the equality between the left side's assets and the right side's combination of liabilities and equity. This exercise introduces transactions as the means by which the balance sheet changes over time. As long as the balance sheet equation (assets = liabilities + equity) is maintained for each transaction then the new balance sheet that results from a large sequence of transactions will remain in balance.

This exercise introduces the proper treatment of a few standard transactions at the level of the balance sheet equation. The full MBA Math course continues deeper into allocation of transactions to specific balance sheet accounts.

Internalizing the concepts and handling of standard transactions will help students to be ready for the more complex issues of proper revenue recognition and expense matching of accrual accounting that they will encounter in their MBA coursework.

Spending time in the accounting trenches working with transactions is critical to developing an informed understanding of the financial statements that MBAs will analyze in their classes and careers. In a business climate punctuated with outrage over accounting tricks and scandals, it pays to start early to understand accounting from the ground up.

**Exercise**:

Evaluate each of the following transactions in terms of their effect on assets, liabilities, and equity.

1. Buy $17,000 worth of manufacturing supplies on credit

2. Issue $90,000 in stock

3. Receive payment of $10,000 owed by a customer

4. Purchase equipment for $46,000 in cash

What is the net change in Total Assets?

**Solution (with audio commentary): click here**

## Arkansas (Walton) Recommends MBA Math

Walton College of Business at the University of Arkansas recommends MBA Math for incoming full-time and part-time students who need quantitative skills preparation.

## Monday MBA Math: Time Value of Money (Sub-Annual)

With this post, we begin our second pass through the main MBA Math topics of finance, accounting, economics, and statistics.

This exercise extends the first Monday MBA Math finance exercise by compounding interest more frequently than once per year as a single starting investment grows over time. Sub-annual compounding typically involves finite compounding such as semi-annually, quarterly, monthly, and daily. But it also includes continuous compounding, which is a logical limit to the process of ever-decreasing time slices.

Given four of the five parameters of starting value, total duration, rate, compounding period, and final value, the fifth can be solved using the time-value-of-money formulas.

Quantitative finance builds incrementally, starting with simpler concepts (like annual compounding) and adding successive levels (like sub-annual compounding). Starting your MBA coursework with a working knowledge of the time-value-of-money foundations helps you to keep up as the incremental layers are added in quick succession.

**Exercise**:

You deposit $500 in a bank account that pays 7% stated annual interest compounded semi-annually. What is the value of your investment at the end of 4 years?

**Solution (with audio commentary)**: click here

## Monday MBA Math: Variance

Variance is a basic summary statistic that reflects the degree of spread for a set of data from that data's average value. The wider the spread, the higher the variance.

Summary statistics are convenient because they allow us to talk meaningfully about phenomena with large underlying data sets (think retail sales at Amazon.com, Google search requests, and bank credit book stress tests) without being bogged down by the full details.

The variance calculations are very similar to those used for other common summary statistics so by understanding variance you build a foundation for other common statistical measures.

You'll also find that correlation among data sets (stock prices, mortgage defaults) involves a modest extension of variance calculations.

Sure, improper use of statistics is a partial cause of the ongoing financial crisis. But, to understand the mistakes made, and to know where the solid ground of fact transitions to the marshy swamp of judgment, you need to learn the fundamentals of statistics.

**Exercise**:

Unit sales for new product ABC have varied in the first seven months of this year as follows:

Month |
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |

Unit Sales |
428 |
391 |
459 |
161 |
410 |
367 |
466 |

What is the (population) variance of the data?

**Solution (with audio commentary)**: click here

## Forté MBA Women's Conference NYC June 26-27

My friends at Forté Foundation have also asked that I post about their MBA Women's Conference in New York on June 26-27, which overlaps with the Financial Services FAST Track Conference I posted about previously. I'll be presenting a two-hour MBA Math quantitative skills workshop on Friday morning, June 26 as part of the MBA Women's Conference.

You can learn more about the MBA Math workshop at www.mbamath.com/events/forte.htm

Below is the overview for the full conference:

**Reinvent. Reinvest. Realize.**

The Forté Foundation’s annual MBA Women’s Conference provides the inspiration you need to meet today’s challenges with a broad perspective and renewed vigor. Arm yourself with valuable contacts, fresh insights and new knowledge that will enable you to find hidden opportunities and embrace change. With an international membership that includes progressive companies, world-class business schools and exceptional women leaders, Forté is the only organization poised to support women as they reach for their career goals.

Who Can Attend: Forté Fellows and MBA women that are attending Forté sponsor schools (in the 2009, 2010, and 2011 classes).

Registration Fee: $50 before June 5. The fee will increase to $75 after June 5.

Location: NYU Kimmel Center, New York City

Learn more and register at: http://www.fortefoundation.org/mbaconf

## Forté Financial Services FAST Track Conference NYC June 25-26

My friends at Forté Foundation have asked that I post about their upcoming financial services FAST Track Conference in New York on June 25-26. Here's their event overview:

Interested in a career in financial services? Get on the fast track and gain valuable insight into this high-performance profession.

This exclusive event for incoming MBA women interested in finance will take an in-depth look at the cross-functional views of finance and put you in touch with senior-level professionals.

Who Can Attend: Forté Fellows and MBA women that are attending Forté sponsor schools (in the 2011 class).

Registration Fee: Complimentary. Please note: Participants will be given a stipend (maximum of $200) to help cover travel, lodging, and food expenses.

Location: NYU Kimmel Center, New York City

Learn more and register at: http://www.fortefoundation.org/fsft

## MBA Math Testimonial for Northwestern (Kellogg)

Here is a testimonial from R'Kes Starling, an executive MBA student at Kellogg School of Management at Northwestern and member of the MBA Math Board of Advisors, about his pre-MBA use of the MBA Math online quantitative preparation course:

After I graduated from pharmacy school from Purdue University, I became a registered pharmacist. Over the last nine years, I have been in various leadership roles in healthcare. As a result, I began to informally gain basic fundamentals of business accounting and finance. As my level of responsibilities increased, it became ever more important to formally sharpen my competencies in Excel, accounting, finance and statistics. Therefore, I decided to seek greater knowledge and understanding.

Unlike the other MBA Math Advisors, I am enrolled in an Executive MBA program at Kellogg (Miami Campus). As a part of the admission process, I was encouraged by the Admission Committee to take the MBA Math on-line course to demonstrate my quantitative latitude and to prepare for the rigorous quantitative courses. Again, due to the pharmacy curriculum, I had never taking accounting/finance courses and I was really concerned about keeping up in the accelerated program. After successful completion of the course, I was granted admission to the Kellogg program.

Due to having a non-business background, I have found the MBA math course to be extremely helpful. More specifically, in my Accounting and Statistic courses, I felt very knowledgeable about the basic fundamentals and was able to spend more time on the core business concepts. Also, I have used MBA Math as a resource to refresh my knowledge in methodologies leading up to particular courses. The “go at your own” pace option allowed me greater flexibility and convenience.

Overall, I am strongly satisfied with the math lessons that MBA Math provided and would highly recommend this course as comprehensive overview for any MBA program.

## LSU Chooses MBA Math

The Flores MBA at Louisiana State's Ourso College of Business purchased MBA Math subscriptions for the second year for all incoming students and recommends MBA Math for all incoming part-time students.