This is based on a problem I tutored a college student on today, which baffled us both.
We have four variables, just call them A,B,C and D that when multiplied together give us our total costs.
Our original budget called for A=42,000, B=.07, C=.90 and D=$4,750, meaning a total cost (A*B*C*D) of $12,568,500. However, our actual results were A=42,000, B=.095, C=.85 and D=$4,900, for a total cost of $16,618,350.
Management has asked us to come up with the variance in the total dollar amount of cost (or cost savings) attributable to each change in the variables. That is, how much of the $4,049,850 cost overrun was attributable to the change in B, how much to the change in C, and how much to the change in D? (Since A did not change, obviously it did not cause any of the cost overrun).
My original thought was to figure out what the total costs would have been if B had stayed at its original level. Any difference between that total and the actual expenditures is attributable to the change in B. I came up with $4,373,250 attributable to B. Doing the same for the others, I found that the change attributable to C was -977,550 (that is, it saved us money) and the change attributable to D was 508,725. But when I added up all those changes it came out to $3,904,425, or $145,425 less than the total budget overrun.
So then I tried putting B only at the new level while leaving C and D at their budget estimates. Any difference between those total costs and the original budgeted cost must be due to the change in B. Following this through for C and D, I came up with the following attributions: B $4,488,750, C -698,250, and D 396,900. But when I added them up, they came out to total $4,187,400, or $137,550 more than the actual budget overrun.
Anybody know what I'm doing wrong here, and what the correct method is?
We have four variables, just call them A,B,C and D that when multiplied together give us our total costs.
Our original budget called for A=42,000, B=.07, C=.90 and D=$4,750, meaning a total cost (A*B*C*D) of $12,568,500. However, our actual results were A=42,000, B=.095, C=.85 and D=$4,900, for a total cost of $16,618,350.
Management has asked us to come up with the variance in the total dollar amount of cost (or cost savings) attributable to each change in the variables. That is, how much of the $4,049,850 cost overrun was attributable to the change in B, how much to the change in C, and how much to the change in D? (Since A did not change, obviously it did not cause any of the cost overrun).
My original thought was to figure out what the total costs would have been if B had stayed at its original level. Any difference between that total and the actual expenditures is attributable to the change in B. I came up with $4,373,250 attributable to B. Doing the same for the others, I found that the change attributable to C was -977,550 (that is, it saved us money) and the change attributable to D was 508,725. But when I added up all those changes it came out to $3,904,425, or $145,425 less than the total budget overrun.
So then I tried putting B only at the new level while leaving C and D at their budget estimates. Any difference between those total costs and the original budgeted cost must be due to the change in B. Following this through for C and D, I came up with the following attributions: B $4,488,750, C -698,250, and D 396,900. But when I added them up, they came out to total $4,187,400, or $137,550 more than the actual budget overrun.
Anybody know what I'm doing wrong here, and what the correct method is?
via International Skeptics Forum http://ift.tt/2hbCm1R
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