Monday MBA Math: Bonds

The Monday MBA Math series returns after a break since mid-July for classroom teaching.  The 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 three Monday MBA Math finance exercises, quantitative finance builds incrementally.  The first and second finance exercises deal with converting a single amount of money at one point in time into a different single amount at a different time.  The third exercise, covering constant annuities, deals with converting multiple future cash flows into a single current cash flow.   

Bonds, which we cover in this lesson, combine a steady stream of small, periodic coupon payments with a single large payment in the last period.  The coupon payments, typically paid every six months, are a constant annuity and the single large payment is a future value. 

Companies and governments (local, state, and national) raise money by issuing bonds, typically for long-term projects.  The key to valuing bonds is determining the appropriate discount rate to reflect the chance that the borrower will default and fail to pay the borrowed money.

The bond market can turn quickly on companies or governments that appear vulnerable financially.  President Bill Clinton's advisor James Carville famously captured the immense power of the bond market when he quipped that if he could be reincarnated he wanted to come back as the bond market.  Understanding bonds begins with the mechanics underlying this exercise.

Exercise:

What is the current value of a $1,000 bond with a 10% annual coupon rate (paid semi-annually) that matures in 5 years if the appropriate stated annual discount rate is 12%?

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).

Posted on Monday, January 11, 2010 at 12:00AM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

MBA Math Completes Successful 4th Year

More Schools: During 2009, MBA Math helped approximately 4,000 students to build a solid pre-MBA quantitative foundation. Fifteen schools purchased subscriptions for their incoming full-time (10), part-time (4), and/or executive (9) MBA program students, up from 12 in 2008. Notably, six schools purchased MBA Math subscriptions for the first time in 2009 for their Executive MBA students, building greater awareness away from the full-time program format where the course originated. Numerous other schools recommend or require that their students purchase MBA Math subscriptions.

More Problem Solving: Reflecting MBA Math's active problem solving focus, students submitted solutions to 590K exercises in 2009, bringing the cumulative total over four years to 1.4M.

Greater Student Proficiency: Demonstrating proficiency gains that position students for success when first-year classes start, across 60K quizzes submitted in 2009, the average pre-quiz score of 57% rises to an average post-quiz score of 91%.

Admitted Students Joined by Applicants and Enrolled Students: Among individual subscription purchases, applicants represent 28%, admitted students 57%, and enrolled students 15%. Applicants often submit MBA Math transcripts to bolster their admissions package, sometimes at the request of admissions officers seeking demonstrated proficiency with MBA quant skill basics.

Live Teaching Shapes Material: Live multi-day courses, at Dartmouth (Tuck) and Cornell (Johnson), coupled with a Forté Foundation workshop, continue to shape the course material.

Thanks to students, faculty, and administrators who support MBA Math and provide suggestions. Special thanks to current and former students who serve on the MBA Math Board of Advisors.

Posted on Thursday, January 7, 2010 at 11:56AM by Registered CommenterPeter Regan in | CommentsPost a Comment

Better Designed Tuck Math Camp

In a major re-design prompted by Tuck's revised core curriculum and my experience with prerequisite mbamath.com lessons for the Cornell 3-day course, all incoming Tuck students completed eight online mbamath.com lessons.  Learning this material before coming to campus freed up considerable space for new, more advanced material in this year's 5-day quant skills course at Dartmouth's Tuck School in late August.

About 65 incoming first years participated.  Beyond the core lessons from previous years, I wove the ongoing financial crisis into several lessons, expanded the statistics coverage to support a redesigned stats core course, pushed into accrual accounting issues, and examined real financial statements after learning the debits and credits of basic transactions.

And we still found time mid-week to paddle canoes and kayaks on the Connecticut River.

Five second-year TAs, all of whom were math campers the previous year, eased the new students into Tuck.

Posted on Thursday, December 3, 2009 at 02:23PM by Registered CommenterPeter Regan in , , | Comments1 Comment

Quant Skills Sharpened at Cornell

I was in Ithaca, New York in early August for the third year to teach a 3-day Quantitative Skills Course for about 75 incoming first years of Cornell's Johnson School.  We covered topics in finance, economics, marketing, and accounting.  Students completed six introductory lessons of online pre-work at mbamath.com, thereby allowing us to proceed deeper into the subjects in the classroom.  Topics from the ongoing financial crisis connected the quantitative basics to the business news headlines.

With the rest of the first year class arriving the following weekend, the Quant Skills students get back into the student groove, start friendships, and explore the restaurants and watering holes of Collegetown and downtown Ithaca.

Two second-year TAs and a recent graduate instilled a healthy mix of anticipation and fear about the challenges of the first year core.

Posted on Thursday, December 3, 2009 at 02:06PM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

Classroom Teaching Completed

Having recently completed several months of classroom teaching at Cornell's Johnson School and Dartmouth's Tuck School after supporting the intense summer online MBA Math rush of incoming students, I can now gather my thoughts.  I am taking a break this year from teaching Professional Decision Modeling at Duke's Fuqua School during winter term. 

Instead, I'll be refining and extending the MBA Math online course using ideas that have emerged from classroom teaching.

Posted on Thursday, December 3, 2009 at 01:50PM by Registered CommenterPeter Regan in , , , , | Comments3 Comments

Notre Dame (Mendoza) EMBA Chooses MBA Math

Mendoza College of Business at the University of Notre Dame purchased MBA Math subscriptions for all incoming Chicago Executive MBA program students, extending its existing use of MBA Math for the one year and two year program students.

Posted on Thursday, November 12, 2009 at 09:14AM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

Boston University EMBA Chooses MBA Math

Boston University purchased MBA Math subscriptions for incoming executive MBA program students.

Posted on Wednesday, September 30, 2009 at 09:12AM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

Upcoming Forté Forums for MBA Women

Friends at the Forté Foundation asked that I post the following about their upcoming Forte Forums.  From my experience at their past two Women's Conferences in New York, they run a first-class event.

Thinking about an MBA?  Register today for a Forté Forum, the largest MBA event designed for women interested in pursuing an MBA.  This fall's Forum series will be held in various locations throughout the United States.

Attend a Forté Forum in the city nearest you to:

  • Learn about the career opportunities enabled by an MBA degree
  • Connect with representatives from top business schools to help you get started on the admissions process
  • Network with women like yourself who are also interested in pursuing an MBA
  • Hear first-hand from a panel of women who’ve already received their MBA

Sept. 14: Washington, DC
Sept. 15: Atlanta
Sept. 21: San Francisco
Sept. 22: Los Angeles
Sept. 23: Chicago
Sept. 29: New York City I
Sept. 30: New York City II
Oct. 1: Boston

Posted on Thursday, September 3, 2009 at 01:54PM by Registered CommenterPeter Regan in | CommentsPost a Comment

Virginia Tech (Pamplin) EMBA Chooses MBA Math

Pamplin College of Business at Virginia Tech purchases purchased MBA Math subscriptions for incoming executive MBA program students.

Posted on Monday, August 31, 2009 at 09:10AM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

UNC Chapel Hill (Kenan-Flagler) EMBA Chooses MBA Math

Kenan-Flagler Business School at University of North Carolina purchased MBA Math subscriptions for all incoming Weekend Executive MBA program students.

Posted on Friday, July 31, 2009 at 09:06AM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

Villanova Chooses MBA Math

Villanova School of Business at Villanova University purchased MBA Math subscriptions for all incoming Fast Track and Flex Track MBA program students.

Posted on Friday, July 31, 2009 at 09:04AM by Registered CommenterPeter Regan in , | CommentsPost a Comment

Monday MBA Math: Linear Regression

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.

Linear regression helps to identify the best line characterizing two sets of data. Regression generally is used where one factor managers control, such as advertising, is believed to influence another factor of interest, such as sales. The notion of causality can be wrong, however, so like much of statistics it is important to understand the tool and use it wisely. Linear regression also quantifies the degree of linearity in a relationship, which you can see in a scatterplot by the extent to which the data create a line versus a scattered set of dots.

Various nonlinear regression options are available at the click of a button in Excel, all with risks of incorrect assumptions and unwise overprecision.

One need only look at the monumental financial consequences of failure to anticipate the end of rising house prices to understand that extrapolating the past blindly into the future can be disastrous. Understanding linear regression is an important step in absorbing the value and limits of statistics.

Exercise:

Consider the following sample data for the relationship between advertising budget and sales for Product A:

Observation 1 2 3 4 5 6 7 8 9 10
Advertising ($K) 60 70 70 80 80 90 100 100 100 110
Sales ($K) 362 416 417 499 485 536 602 623 616 663


What is the slope of the "least-squares" best-fit regression line?

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).

Posted on Sunday, July 19, 2009 at 07:00PM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

Monday MBA Math: Marginal Analysis by Calculus

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 two economics exercises examined marginal analysis. which 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.  The second exercise used formulas but without invoking calculus.  This exercise uses formula and calculus.

The calculus bit is the only aspect of this exercise that is different from the second one.  The key idea, which is explained in the full MBA Math course, is that the derivative of the total cost function is the marginal cost function.  The derivative examines the incremental change in a function (e.g., y = f(x)) given a small change in the underlying value (e.g., x).  That's just what we want when we are considering the marginal cost, which shows how much total cost (e.g., TC = f(q)) has changed for a small change in quantity (e.g., q). 

Similarly, the derivative of the total profit function is the marginal profit function and the derivative of the total revenue function is the marginal revenue.  At least it's consistent.

Scary as calculus may be to many incoming b-school students, the main idea is quite straightforward if you can keep your brain from locking up in fear.  And the mechanics of taking the derivative of a polynomial, which is a fancy name for the functions determining cost, are refreshingly simple, taking no more than 15 minutes to recover from the memory vault of lost ideas from high school.

Exercise:

Suppose a competitive firm has as its total cost function:

TC = 24 + 2q2

Suppose the firm's output can be sold at $66 per unit.

Using calculus and formulas (but no tables) to find a solution, how many units should the firm produce to maximize profit?

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).

Posted on Monday, July 13, 2009 at 10:33AM by Registered CommenterPeter Regan in , , | CommentsPost a Comment

Monday MBA Math: Income Statement

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 two MBA Math accounting exercises examined the balance sheet, which represents the sources and uses of a firm's funds at a snapshot in time.  The first exercise focused on balance sheet structure and logic.  The second exercise focused on how transactions during a period in time must be appropriately processed to create a new balance sheet at the end of the period.

This exercise introduces the income statement, which is a financial statement that shows a firm's revenues and expenses during a period of time, typically a quarter or a year.  The proverbial "bottom line" in business is the profit or loss at the bottom of the income statement.

Before you can interpret an income statement, you need to understand how its structure flows from revenue at the top to profit or loss at the bottom, with various categories of cost in between.

Exercise:

Suppose Lightspeed Industries has the following revenue and expenses (listed in alphabetical order) for 2008:

Revenues of $8,800,000
Cost of Goods Sold of $2,640,000
Depreciation Expenses of $1,200,000
Income Taxes of $1,452,000
Interest Expenses of $50,000
Other Expenses of $400,000
Sales, General, & Administrative Expenses of $880,000

Create an income statement with amounts in thousands

What is the value of Pre-Tax Income?

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).

Posted on Monday, July 6, 2009 at 12:00AM by Registered CommenterPeter Regan in , , | Comments1 Comment

UT Austin (McCombs) EMBA Chooses MBA Math

McCombs School of Business at The University of Texas at Austin purchased MBA Math subscriptions for all incoming Executive MBA program students, extending its existing use of MBA Math for its Full-Time, Houston, Dallas, and Evening MBA programs.

Posted on Sunday, July 5, 2009 at 06:02PM by Registered CommenterPeter Regan in , , | CommentsPost a Comment