The Salary Problem And Two Possible Solutions

A few days ago, I posted this problem:

You have two job offers, from two different companies (Company A and Company B) with the same starting salary, $50,000 per year. Company A gives you an offer which says “We will increase your salary by $500 at the end of every six months” and Company B counters that offer by saying “We will increase your salary by $2000 at the end of every year“. Considering all other factors equal, which company would you choose?

This seemingly dry and uninteresting problem generated some interest over the last couple of days. After a few comments on the post and after some interesting discussion with Yan of ProBargainHunter.com, I made a long comment on the situation…by far the longest comment ever (sucks that it had to be on my own post!). Just sharing the comment (with minor edits) which reflects my thoughts on the problem. Please feel free to point out flaws in the arguements.

In the following, Offer A = offer made by Company A, and Offer B = offer made by Company B.

OK, I won’t keep you guys hanging for long. The point is to show that it is not as straight forward to jump to a conclusion here….I think Yan’s confusion is valid.

Here is the original problem from the text from the puzzle book:

“First Option (Offer B in our case): Initial salary $40,000 to be increased after each 12 months by $2000.
Second Option (Offer A in our case): Initial salary $40,000 to be increased after each 6 months by $500.
Which option should you choose?”

The book says Offer A is better because of this (Yan’s 1st solution):

- It assumes that the $500 is distributed over the next 6 months. So if you break salaries over 6 months they would look like this:

Offer A: 25000 (0 to 6 months) + 25500 (6 to 12 months) + 26000 (12 to 18 months) + 26500 (18 to 24 months).

Gives TOTAL salary for first year as $50,500 and for second year as $52,500.

Offer B: 25000 (0 to 6 months) + 25000 (6 to 12 months) + 26000 (12 to 18 months) + 26000 (18 to 24 months).

Gives TOTAL salary for first year as $50,000 and for second year as $52,000.

Obviously, offer A is a better offer. That’s interesting, but I don’t agree with the book. While it is quite possible that some companies do that. But in that case, the appropriate/correct offer should have been stated this way:

- $25,000 per 6 months, increased at $500 per every 6 months. This would effectively mean that $500 is distributed over 6 months.

What usually happens is that companies talk in terms of “budgeted salary”. So when they give you a $500 raise, it is usually added to your “budgeted salary”. That means instead of $50,000 a year you will be getting at “the rate” of $50,500 a year. This is what makes Offer A look bad. Here is why:

- For the first six months you will be paid at the rate of $50,000 a year. For the next six months at the rate of $50,500 a year. The total salary in this case is NOT $50,500. It will be $50,250 (because $500 is distributed over a year, and not 6 months). You can figure that out either by calculating the monthly salary over the year, or you can calculate it in a complicated way like Yan did in his comment …or you can just take the average of the two rates (btw, this won’t require a calculator). At this point, Offer A beats Offer B by $250.

- After one year the salary will increase to $51,000 per year and after 18 months it will increase to $51,500 per year. But your average salary for the second year is just $51,250 in this case. Now, this is easily beaten by Offer B.

Anyways, I think the point is established. Things are not as obvious on the first glance, especially when it comes to numbers…you need to stop and think for a while.

Another lesson is that with the second case of “budgeted salary” the Offer A is better in the first year…but not good in the second year (like Yan and Ellen mention). Watch out for such offers…always play around with numbers and calculate a few years down the line before you make a salary decision.

….That’s the longest comment I have ever made. I hate myself.

Hopefully, some of you will revisit this all over again…and hopefully you will do it without a calculator