Wise Money Decisions

I had a high school math teacher whose husband was a math professor at Utah State University.  He was in the process of preparing an introductory-level college math textbook for publishing.  He needed to test the problems on a student and come up with the answers for the back of the book. 

I was a year or two away from that level of math, but my teacher thought I could handle it.  She recommended me for the job.

Her husband offered me the job.  I accepted. 

I spent my summer vacation doing math problems at $100/chapter.  I was The-Guy-Who-Puts-the-Answers-in-the-Back-of-the-Book.

It didn’t take long before I realized I was in over my head.  I didn’t have the foundation for this level of math.  The author’s writing style didn’t appeal to me. 

But I trudged on.

Most math books at this level have 30 or 40 straightforward problems at the end of each chapter, plus 2 or 3 difficult problems.  The straightforward problems can be answered quickly.  The difficult problems take some thought and effort.  They were used as extra credit by most teachers. 

This book, on the other hand, had 10 straightforward problems and 20 difficult problems for each chapter. 

Many of the difficult problems were proofs.  The book gave the first two steps of the proof, and the student was supposed to complete the proof. 

I learned to hate the proofs.  They took most of my time.  I couldn’t give up and look in the back of the book since it was my job to put the answer in the back of the book.

I learned a few life lessons that summer:

• You can’t be The-Guy-Who-Puts-the-Answers-in-the-Back-of-the-Book unless you know the math.  You need the right foundation to do the job. 
• If you’re asked to do math problems for $100/chapter, there are only two responses.  Negotiate a higher price, or flee.
• One thing I didn’t learn that summer but recently came to understand thanks to Abstruce Goose is why the author included so many proofs at the end of the chapter. 

It has been widely reported that David Sneath, who had worked in a Ford Motor Company warehouse for 34 years, won a $136 million Mega Millions jackpot on April Fool’s Day - his 60^th birthday. 

According to Wikipedia, Mega Millions pays out in either 26 annual payments or one lump sum.  If a winner chooses the lump sum, the payment is much less than the reported amount of the jackpot.

If Sneath had chosen 26 annual payments, the annual payment would be $5,230,769.  He did not choose the 26 annual payments.  He chose a lump sum payment of $84.3 million.

Is that a wise money decision?  Depends.  We can analyze the numbers to see if it’s an optimal decision financially, but there are also some individual factors (such as his tax situation) and intangible factors (such as his desire to give four of his co-workers a million bucks) that may drive the decision.  Since we can’t analyze the intangible factors, all we can do is look at the numbers.

The Numbers

To analyze whether the lump sum payment is the right choice, I calculated the rate of return he would need to recognize in order to turn $84.3 million into a stream of 26 equal annual payments of $5,230,769.  It’s a very simple calculation if you have a spreadsheet or a financial calculator. 

The answer is 3.924%.  In other words, if he can invest his money at a rate of return greater than 3.924%, then he made the right decision to take a lump sum payment.  His rate of return must take into account taxes of course.

Two Pieces of Unsolicited Advice for Sneath

First, be aware of the gift tax consequences of giving $1 million each to your co-workers.  You will likely owe gift tax upon making gifts of that magnitude. 

And finally, don’t be a dufus like Richard Hatch and neglect to pay your taxes.  It’s too late to blend in.  The IRS isn’t going to forget about you.

Ten years ago the proud new owner of a Honda Civic brought his car home from the dealer.  Days later he totaled it.  It was salvaged, went through a few owners, and is now my wife’s primary mode of transportation.

After several years with the Civic it is time for my wife to upgrade.  Over the last few weeks she has been shopping, test driving, pricing, and looking for financing.  I’ve been helping.

Today she test drove a Toyota Camry.  She likes the quietness. 

New Versus Used:  The Conventional Wisdom

This week we are facing the “new versus used” question.  The conventional wisdom says new cars lose a significant amount of their value when you drive off the lot. 

On the other hand, we regularly see used Camrys for sale at prices not much lower than their new price.  For example, I saw a used Camry with 8000 miles for sale at 10% below its new price.  We regularly see Camrys with around 30,000 miles for sale at 25% off their new price. 

The Camry just doesn’t seem to lose much of its value when driven off the lot.  I’m working under the assumption that the conventional wisdom doesn’t apply to the Camry.

Since I don’t have the conventional wisdom to guide my thinking, how do I know whether to buy new or used?  I use math.

The Two Candidates

We have identified two cars that seem like good candidates.  One is new and the other used.  They have similar features and upgrades. 

The new car costs $5000 more than the used car.  If we buy the used car we plan to get financing through a credit union at 6%.  If we buy the new car we can get financing through the dealer at 4.9% or less. 

The new car costs $5000 more but has three advantages:

• The car is new.
• It has the full original warranty.
• We obtain financing at a lower interest rate.

The full warranty has some value, but for simplicity I’m going to ignore it.

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