2010 #23 / TIA Practice Exam #10

[booyah81]

Did anyone do this by calculating average benefit rate (as with older problems that give you %workers and %wages) instead of total compensation as in the sample solution? My final direct effect comes out slightly different and I'm just wondering if it was because my method is wrong or there's rounding error or something inconsequential like that.

Old avg benefit rate = .48(64/291) + 1.2(29/291) + .8x(196.2+64.35+47.25)/429.35 = .8066
New avg benefit rate = .48(64/291) + 1.12(21+29)/291 + .8x(196.2+64.35)/429.35 = .7835

Direct effect = .7835/.8066 - 1 = -2.9%

Thanks in advance!

[Vorian Atreides]

I don't think your answer would get full credit. The first two terms are relative to the SAWW; the third isn't . . . you're trying to mix apples and carrots. A grader may grant some partial credit, but it'd be very small.

Calculating an avg benefit rate is accpetable, but you need to consider that your calculations need to show weights that add to one (which yours doesn't):

Here's how I'd calculate it (showing the current benefit rate relative to the SAWW):

0.48(24/291) + 1.28(29/291) + {0.8(196.2+64.35+47.25)/(144+33+21)}/1.5(198/291) = 0.7973.

Note that {0.8(196.2+64.35+47.25)/(144+33+21)} is the avg compensation for those between the min and max compensation; dividing this by 1.5 converts it to a ratio of the SAWW (so it's on the same level as the other two terms).

A similar calculation for the new compensation results in an avg benefit level of 0.7755; giving a direct benefit change of -2.73% (this is identical to the CAS sample solution subject to rounding errors in the intermediate steps).

[Vorian Atreides]

BTW, the CAS solution is more straight-forward and likely to take less time to develop/show your answer.