Calculating Overtime Bonus

[freshdye]

Hello all,

A bit of a different problem here, but I figure it may be considered Inter Algebra because of the wording and length.

Here is my situation: Say that I have a number that we will consider to be a yearly "bonus" for a worker. Say, the worker gets a $1,000 bonus that year. California law requires that you take that bonus and apportion it over the workweeks of the period during which it was earned. In other words, the bonus that is earned year-end will technically be a part of the yearly earnings of the worker. This causes a problem, though, because you need to go back and pay extra overtime (since we tend to pay overtime as it's earned already).

Assuming that the yearly bonus should be equally apportioned over all of the year's workweeks, I need to find a way to use this number to figure out any extra overtime that needs to be paid. For example, if a worker worked a total of 200 overtime hours during an entire year, I need to figure out some sort of formula that will allow me to easily figure out what I'm looking for.

I don't know if any of this is making sense, but I just need a mathematical formula that is easy enough to figure out what I'm looking for.

Example:

Worker earns $50,000 a year.
Worker receives a $5,000 bonus at the end of the year.
Worker worked 500 hours of overtime during said year.
Worker's bonus must be added to his yearly earnings, and his overtime he has already earned must be ADJUSTED according to the new bonus.

Seems like I'd figure out the new rate (adjusted by adding the bonus), and then multiply it by either 1.5 or .5 (I'm terribly confused here) to figure this out.


Aaaah! Sorry about the mess. I hope someone knows what I'm trying to say and can chime in!


Thank you, all.

 

[freshdye]

                        $     %
Year's total income : 58000  100
Regular (before o/t): 49300   85 [1]
================================
Year's overtime     :  8700   15 [2]

Bonus : 5000
[1]Applicable to regular:  5000 * .85 = 4250
[2]Applicable to overtime: 5000 * .15 =  750

That simple?

Thanks for the reply.

That would give me the % of time the worker earned in OT throughout the year, as well as the % of the bonus that applies to the overtime.

Problem is, that $5000 bonus will have to be added to the total earnings of the worker, so total earnings for the year would technically be $63,000. From that, we would have to calculate the actual, adjusted earnings (either per hour, day, week, etc... laws tend to refer to weeks) in order to adjust the OT rate the person received.

In other words, if the person normally earned $20/hour, and, as a result, was paid $30/hour overtime, their NEW adjusted rate after a hypothetical bonus would normally be $22/hour, and $33/hour for overtime. Hence, the employer would basically have to pay the worker an extra $3 for every hour the worker spent in overtime that year (in order to "adjust" earnings based on this bonus).

Does that make sense?



EDIT:

Here's a quick example.

Employee earns $12.50/hour.
" receives a $5,000 bonus.
If we divide the bonus by 52, he earned an extra $96.15 a week.
Since he earns $500/week normally, his adjusted earnings of $596.15/week equate to a new hourly rate of $14.90/hour.

Based on that (and the text I quoted below) the change in his hourly rate would be $2.40/hour.

And, based on THAT, and by multiplying the normal hourly rate by .5 to obtain OT hours, he would be owed an additional $1.20/hour of every OT hour worked.


Does that make any sense mathematically?

Here is the wording from the DOL website that basically explains what I'm trying to figure out:

For example, where it makes sense to assume an employee earned an equal portion of the bonus each workweek, the employer may divide the bonus amount by the number of workweeks in the period. Any additional overtime due the employee for a given workweek can then be calculated by dividing the weekly bonus amount by the total number of hours worked that workweek (to determine the regular rate increase attributable to the bonus) and then multiplying the result by one-half (representing half-time premium pay) times the number of overtime hours worked.

 

[stapel]

Here is the wording from the DOL website that basically explains what I'm trying to figure out....

It might help if you provided the exact text of the exercise, precisely as it appears in your homework assignment. Thank you!

 

[JeffM]

Thanks for the reply.

That would give me the % of time the worker earned in OT throughout the year, as well as the % of the bonus that applies to the overtime.

Problem is, that $5000 bonus will have to be added to the total earnings of the worker, so total earnings for the year would technically be $63,000. From that, we would have to calculate the actual, adjusted earnings (either per hour, day, week, etc... laws tend to refer to weeks) in order to adjust the OT rate the person received.

In other words, if the person normally earned $20/hour, and, as a result, was paid $30/hour overtime, their NEW adjusted rate after a hypothetical bonus would normally be $22/hour, and $33/hour for overtime. Hence, the employer would basically have to pay the worker an extra $3 for every hour the worker spent in overtime that year (in order to "adjust" earnings based on this bonus).

Does that make sense?



EDIT:

Here's a quick example.

Employee earns $12.50/hour.
" receives a $5,000 bonus.
If we divide the bonus by 52, he earned an extra $96.15 a week.
Since he earns $500/week normally, his adjusted earnings of $596.15/week equate to a new hourly rate of $14.90/hour.

Based on that (and the text I quoted below) the change in his hourly rate would be $2.40/hour.

And, based on THAT, and by multiplying the normal hourly rate by .5 to obtain OT hours, he would be owed an additional $1.20/hour of every OT hour worked.


Does that make any sense mathematically?

Here is the wording from the DOL website that basically explains what I'm trying to figure out:

Incredible: a penalty for paying a bonus. Amazing state California.

You probably need to consult an attorney licensed to practice in California, not math types. California may have its own multiplication table. In any case, here is what I think makes sense, but that of course has nothing to do with what is legal. My advice may land you in jail.

The first thing to do is to allocate the annual earnings by pay period, which is probably easy to do because you already have them in your accounting records.

Now let's say those annual earnings are a, and you want to pay a bonus for the year totaling b. You can't pay a bonus that high because of the overtime issue. You have to figure out how to divide what you want to pay into "bonus" and overtime. Here is how I would describe to my attorney what I was planning to do

Take a pay period's earnings and divide it by a and multiply it by b. That gives you the amount of desired extra payments attributable to that pay period. With me so far? Let's call the result of all this x (for extra).

\(\displaystyle Let\ r = regular\ hours\ for\ the\ pay\ period.\)

\(\displaystyle Let\ p = overtime\ hours\ for\ the\ pay\ period.\)

\(\displaystyle Let\ y = amount\ of\ "bonus"\ attributable\ to\ pay\ period.\)

\(\displaystyle Let\ z = amount\ of\ additional\ overtime\ attributable\ to\ pay\ period.\)

\(\displaystyle z = x - y\ and\ z = 1.5 * \dfrac{y}{r} * p = \dfrac{1.5py}{r} \implies rx - ry = 1.5py \implies y(1.5p + r) = rx \implies y = \dfrac{rx}{1.5p + r} \implies\)

\(\displaystyle z = x - \dfrac{rx}{1.5p + r} = \dfrac{1.5px + rx - rx}{1.5p + r} = \dfrac{1.5px}{1.5p + r}.\)

Let's see how that works in practice.

Suppose a person is making 11.50 an hour during a certain week and works 45 hours, 40 regular and 5 overtime. So the total pay for that week is 546.25. (Overtime rate is 11.50 + 5.75 = 17.25; overtime pay is 5 * 17.25 = 86.25. Regular pay is 40 * 11.50 = 460.)

Let's also suppose that you want to pay this person, who worked 50 weeks during the year, a TOTAL of $3,000 in extra money. And let's say that the person earned in total pay (before any extra amounts) $32,775.

Step 1: \(\displaystyle \dfrac{546.25}{32,775.00} * 3,000.00 = $50.00.\) This is the amount of extra payments attributable to this week.

\(\displaystyle y = \dfrac{40 * 50}{(1.5 * 5) + 40} = \dfrac{2000}{47.5} \approx 42.10.\)

That's the "bonus" for this week. These figures are not going to come out exactly even.

But California says that raises the regular hourly wage by 42.10 / 40 = 1.0525 to 12.5525 per hour. So overtime for this week is now 18.8275 per hour. That in turn means that you underpaid overtime for this week, which should have been about 94.14 rather than 86.25. So you owe about $7.89 in extra overtime. What do you know, 42.10 + 7.89 = 49.99. To avoid going to jail, make it 7.90 in extra overtime. So bonus of 42.10 + 7.90 in extra overtime = $50 on the nose.

Now you add up those bonuses for each week and you have your annual bonus, which will be less than what you are willing to pay. Add up the extra overtime for each week. The sum of those two totals should equal what you wanted to pay in the first place.

Now for goodness sake, check all this out with a lawyer (or at least your CPA). This method makes sense to me, but that does not make it legal, especially not in California. Or you could forget about paying bonuses to non-exempt employees in California: it sounds like it is more trouble than it is worth.

 

[freshdye]

Incredible: a penalty for paying a bonus. Amazing state California.

You probably need to consult an attorney licensed to practice in California, not math types. California may have its own multiplication table. In any case, here is what I think makes sense, but that of course has nothing to do with what is legal. My advice may land you in jail.

The first thing to do is to allocate the annual earnings by pay period, which is probably easy to do because you already have them in your accounting records.

Now let's say those annual earnings are a, and you want to pay a bonus for the year totaling b. You can't pay a bonus that high because of the overtime issue. You have to figure out how to divide what you want to pay into "bonus" and overtime. Here is how I would describe to my attorney what I was planning to do

Take a pay period's earnings and divide it by a and multiply it by b. That gives you the amount of desired extra payments attributable to that pay period. With me so far? Let's call the result of all this x (for extra).

\(\displaystyle Let\ r = regular\ hours\ for\ the\ pay\ period.\)

\(\displaystyle Let\ p = overtime\ hours\ for\ the\ pay\ period.\)

\(\displaystyle Let\ y = amount\ of\ "bonus"\ attributable\ to\ pay\ period.\)

\(\displaystyle Let\ z = amount\ of\ additional\ overtime\ attributable\ to\ pay\ period.\)

\(\displaystyle z = x - y\ and\ z = 1.5 * \dfrac{y}{r} * p = \dfrac{1.5py}{r} \implies rx - ry = 1.5py \implies y(1.5p + r) = rx \implies y = \dfrac{rx}{1.5p + r} \implies\)

\(\displaystyle z = x - \dfrac{rx}{1.5p + r} = \dfrac{1.5px + rx - rx}{1.5p + r} = \dfrac{1.5px}{1.5p + r}.\)

Let's see how that works in practice.

Suppose a person is making 11.50 an hour during a certain week and works 45 hours, 40 regular and 5 overtime. So the total pay for that week is 546.25. (Overtime rate is 11.50 + 5.75 = 17.25; overtime pay is 5 * 17.25 = 86.25. Regular pay is 40 * 11.50 = 460.)

Let's also suppose that you want to pay this person, who worked 50 weeks during the year, a TOTAL of $3,000 in extra money. And let's say that the person earned in total pay (before any extra amounts) $32,775.

Step 1: \(\displaystyle \dfrac{546.25}{32,775.00} * 3,000.00 = $50.00.\) This is the amount of extra payments attributable to this week.

\(\displaystyle y = \dfrac{40 * 50}{(1.5 * 5) + 40} = \dfrac{2000}{47.5} \approx 42.10.\)

That's the "bonus" for this week. These figures are not going to come out exactly even.

But California says that raises the regular hourly wage by 42.10 / 40 = 1.0525 to 12.5525 per hour. So overtime for this week is now 18.8275 per hour. That in turn means that you underpaid overtime for this week, which should have been about 94.14 rather than 86.25. So you owe about $7.89 in extra overtime. What do you know, 42.10 + 7.89 = 49.99. To avoid going to jail, make it 7.90 in extra overtime. So bonus of 42.10 + 7.90 in extra overtime = $50 on the nose.

Now you add up those bonuses for each week and you have your annual bonus, which will be less than what you are willing to pay. Add up the extra overtime for each week. The sum of those two totals should equal what you wanted to pay in the first place.

Now for goodness sake, check all this out with a lawyer (or at least your CPA). This method makes sense to me, but that does not make it legal, especially not in California. Or you could forget about paying bonuses to non-exempt employees in California: it sounds like it is more trouble than it is worth.

Quite the analysis, Jeff. Thank you very much. I'm going to review your equations and cross-check them against what I've come up with here on pen and paper; it does look like they're very similar, though.

...or ask Mary Jane, the payroll clerk from the company next door,

how she handles this

http://www.youtube.com/watch?v=dN3GbF9Bx6E

Hilarious. I'm sure she's given this as much thought as we have so far.


I appreciate it, guys.