The normal distribution is essentially the familiar symmetrical bell curve that characterizes many phenomena.  Even when distributions of interest are asymmetrical, the normal distribution is central to sampling and confidence intervals that help guide efforts to make sense of massive data sets by working with representative data samples.  Working with the normal distribution highlights the importance of thinking about intervals measured by units of standard deviations away from the mean.

Hal Varian, Chief Economist at Google, was recently quoted in the New York Times from a McKinsey Quarterly interview as saying "that the sexy job in the next 10 years will be statisticians."  Perhaps more on point for MBAs, Tom Davenport and Jeanne Harris are releasing "Analytics at Work: Smarter Decisions, Better Results" this month as a follow up to their influential 2007 book Competing on Analytics.  Understanding normal distributions is a core skill in developing the statistical numeracy required to apply analytics to strategy.

Exercise:

Suppose the daily customer volume at a call center has a normal distribution with mean 4,600 and standard deviation 950. What is the probability that the call center will get fewer than 3,400 calls in a day?

Click here to view a standard normal (z-score) table, if you know how to use it.

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).

The market interaction of supply and demand is one of the classic business concepts that people encounter from school snack swaps to shopping at the mall, from start ups to too-big-too-fail banks, and from subprime real estate to U.S. Treasury bond auctions.

The concepts can be used qualitatively and quantitatively.   Like much in economics, supply and demand can be introduced equivalently in pictures or with equations. 

Here, we use equations for a situation involving a perishable agricultural commodity market.

Exercise:

Assume that the demand curve D(p) given below is the market demand for apples:

Q = D(p) = 270 - 15p, p > 0

Let the market supply of apples by given by:

Q = S(p) = 42 + 15p, p > 0

where p is the price (in dollars) and Q is the quantity. The functions D(p) and S(p) give the number of bushels (in thousands) demanded and supplied.

What is the consumer surplus at the equilibrium price and quantity?

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).

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.  The second accounting exercise introduced 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 journals and t-accounts as recording systems to handle the volume of transactions that companies generate.  Modern accounting recording systems are automated, of course, but putting pencil to paper with journals and t-accounts helps beginning students to internalize the logic of accounting.

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. 

Exercise:

Transfer the journal entries to T-accounts for the transactions below, compute closing amounts for the T-accounts, and construct a final balance sheet to answer the question.

Journal amounts in thousands

What is the final amount in Total Assets?

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).

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).

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.

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.