how to calculate overtime pay 2: something weird

This is all very strange. I've been crunching numbers for a good part of the evening, and something's not right.

TIME SPENT ON EACH CLASS:

(SUBJECT, scheduled time, elapsed time x #times/week = hrs per week)

TOPICS, 7:40-8:50 = 1:10 x 4 = 4:40
CORE 2, 10:50-12:00 = 1:10 x 4 = 4:40
INTENSIVE 2, 1:10-2:35 = 1:25 x 4 = 5:40
INTENSIVE 5, 2:45-4:10 = 1:25 x 4 = 5:40
DRAMA, 4:20-5:50 = 1:30 x 1 = 1:30

ONE-WEEK TOTAL = 22:10 (22hrs, 10mn)

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According to my contract, overtime is calculated as W20,000 per hour over 18 hrs/week worked. This is where the office got its 72 hrs/month figure.

For July, I worked:
Week 1 = 22:10 (i.e., 4:10 hrs overtime)
Week 2 = 22:10 (i.e., 4:10 hrs overtime)
Week 3 = 22:10 (i.e., 4:10 hrs overtime)
Week 4 = 22:10 (i.e., 4:10 hrs overtime)

Total July hours = 88:40 - 72 = 16:40
JULY OVERTIME PAY = 16:40 x 20,000 = W333,333
TOTAL NET PAY FOR JULY = 2,200,000 + 333,333 = W2,533,333

By this reckoning, I received too much overtime pay.

And now-- August:

Week 5 = 11:50 (missed 2 days for break; 0 overtime hours)
Week 6 = 22:10 (i.e., 4:10 hrs overtime)
Week 7 = 18:00 (1 day missed for break, 1 class made up; 0 hrs overtime)
Week 8 = 22:10 (i.e., 4:10 hrs overtime)

Total August hours = 74:10
AUGUST OVERTIME (a) = 74:10 - 72 = 2:10 (if calculated by month)
AUGUST OVERTIME (b) = 8:20 (if calculated week by week)

Notice a discrepancy? Makes a big difference whether you calculate by week or by month.

August overtime is EITHER
(a) 2.16667 x 20,000 = W43,333... or
(b) 8.33333 x 20,000 = W166,667


Note these proportions:

74.17 / 88.67 = 83.6%
(i.e., My Aug. hrs were 83.6% of my July hrs)


166,667 / 333,333 = 50%
(i.e., My Aug. overtime pay is 50% of my July overtime pay)


2,366,667 / 2,533,333 = 93.4%
(i.e., My pay for Aug is 93.4% of my pay for July)

I guess it all depends on how you play with the numbers. One could draw the conclusion that the office miscalculated in my favor, which is fine. But something still feels funny.

13.5 out 16 days in August is 84%... August overtime should, ideally, also be 84%, should it not? The only thing I can conclude is that, by substracting a fixed number of hours each month instead of working the matter proportionately, the overtime calculation gets skewed. By that warped formula, the office did give me too much, but it's still a formula that shortchanges me. Note, though, that the only way to arrive at a number close to the W220,000 figure given in my previous post is to calculate week by week, not substract 72 hours from the total number of hours worked in a month.

Any accountants out there have any input? Am I engaging in fuzzy math?

(By the way, the above calculations are all gross, not net.)


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