The ABC Widget company paid its salaried employees each month 1/12 of their annual rate of pay. Then, on a month that began on a Sunday, they switched to paying them every other week 1/26 of their annual pay.

Alice said that works out worse for the employees, as in the first month, they'd get only 1/13 of their annual pay instead of 1/12.

Bob said "No, you're getting some of your money sooner by two weeks, more than making up for it, so that it's better for the employees."

Who is right?

Edited:  Oops, I misread the problem, the following applies to hourly employees making the same dollars per hour before and after the switch.  Larry
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Summary:
Old employees, with interest:  Alice right, Bob wrong
Future employees, with interest:  Alice wrong, Bob right
If no interest earned: Alice and Bob both wrong

Alice's reasoning is wrong because there will be some months that they get 3/52 of their annual pay.  But she is right that it is worse for the employees, slightly, because of the time value of money.

Bob's reasoning is wrong too.  They are getting their money later, not sooner.  On Sunday the 1st, they get 1/26th their annual salary instead of 1/12th.  Thereafter, it is as if every other paycheck has been delayed by 2 weeks.  On average, it is like their pay is coming a week later.  Over the next 365 days, they will get the same number of dollars in pay as they would have under the old method, but they will miss out on roughly one week of interest.

For an employee making $10/hour , getting 3% annual interest rate, the annual loss would be about $12.

The reverse is true if a new employee comes to work.  Since most employees get paid at the end of a pay period (how else would you know how many hours they worked), a new employee coming into the system would be better off since the first paycheck would come after working just 2 weeks instead of after a whole month.  So for future employees, Bob is correct.

If they put their money in a shoebox, or a non interest bearing account, then Alice and Bob are both wrong because the employees are no better, no worse with the new method.

Edited on January 2, 2005, 6:42 pm

Posted by Larry on 2005-01-02 18:34:34