*Title: Semi-monthly dilution example where hourly cost is lower in a shorter period*

*Brief description:*

This topic illustrates the impact of cost dilution based on semi-monthly periods with more or fewer business days (96 vs 88, for example.). The diluted (effective) cost rate will vary based on hours worked and an even 86.667 hours per month (2080 annual business hours/24 periods). As a result, a shorter period can have a lower cost rate than a longer period since **the calculation is based upon hours worked** and not hours in period.

*What’s covered in this document:*

## Calculation on Shorter and Longer Periods depends on hours worked, not length of period

The dilution calculation will be to come up with a dilution factor, which is 86.6667/hours worked that are able to be diluted (based on pay code setup). Then that dilution factor will be applied to the person's profile cost rate ($96.15385 in the examples below).

If a person works 102 hours in the 88-hour period of January 1-15, the calculation will be 86.6667/102 hours (the hours worked). This is 0.8496735294117647, which is then multiplied by the $96.15385, which results in an effective cost rate of $81.69938 (second screenshot below).

If a person works 96 hours in the 96-hour period of January 16-31, the calculation will be 86.6667/96 hours (the hours worked, not the hours in the period although in this case they are the same). This is 0.902778125, which is then multiplied by the $96.15385, which results in an effective cost rate of $86.80559 (third screenshot below).

A few points on this:

- If a person always works 8 hours/day, then longer periods (e.g., 96 hours) will have lower cost than shorter periods (e.g., 88 hours.). This scenario is fairly rare for salaried employees as they typically work more than 8 hours per day.
- If a person works the same number of hours in a longer period as in a shorter period (works 102 hours in an 88-hour period and 102 hours in a 96-hour period), then the cost rate will be the same in both periods. This would also be fairly rare. This is because the hours in the period is always a consistent 86.667.
- If a person works varying hours per period, then the cost rate will vary by period. For example, if a person works more hours in a shorter period than in a longer period (102 hours in a 88-hour period versus 96 hours in an 96-hour period as in the two examples illustrated here), then the cost rate in the shorter period will actually be lower than the cost rate in the longer period. See example below where the shorter period has 11 business days and the longer period has 12 business days. The shorter period has a lower cost rate because more hours were worked ($81 vs $86).

In summary, the cost rate is going to vary based on hours worked, and will not always be lower in longer periods. This can be especially relevant for cost plus type contracts where the cost drives the revenue.