Please notice that this method is a derivation of the HareNiemeyer method. A practical implementation of this method you can see at this allocation of overhead costs.
Other, but similar methods are shown at D’Hondt Method and at sbExactRandHistogrm.
If you like to know more about the distribution of sums of rounded percentages, see Mosteller, Youtz and Zahn: "The Distributions of Sums of Rounded Percentages", Demography (1967), 4, p. 850  858, or Diaconis and Freedman: "On Rounding Percentages", Journal of the American Statistical Association, Vol. 74, No. 366. (Jun., 1979), pp. 359364.
You can download a 50 KB Excel 2013 © sample file here but please notice my disclaimer.
Name
sbRoundToSum  Calculate rounded summands which exactly add up to the rounded sum of unrounded summands
Synopsis
sbRoundToSum(vInput, [lDigits], [bAbsolute], [bDontAmend])
Description
sbRoundToSum calculates rounded summands which exactly add up to the rounded sum of the unrounded summands. It uses the largest remainder method which minimizes the absolute error to the original unrounded summands. This function needs to be entered as an array formula into the cells for the rounded summands.
Example
If you need to distribute 1 EUR to three people, all of them should get 1/3 EUR but you need to amend this to whole cents:
Options
vInput Range or array which contains unrounded summands
lDigits Optional  standard value is 2 if not provided Number of digits to round to. For example: 0 rounds to integers, 2 rounds to the cent, 3 will use thousands
bAbsolute Optional  standard value is True if not provided True  takes the summands as they are False  works on the summands' percentages to make all percentages add up to 100% exactly
bDontAmend Optional  standard value is False if not provided True  do not amend the rounded summands to match the rounded sum. This parameter is mainly for ease of use or presentation to see this function's impact False  perform amendments as described above
See Also
Think Cell’s TCRound © Allocation of Overheads D’Hondt Method sbExactRandHistogrm
Further Reading
Mosteller, Youtz and Zahn: "The Distributions of Sums of Rounded Percentages", Demography (1967), 4, p. 850  858 Diaconis and Freedman: "On Rounding Percentages", Journal of the American Statistical Association, Vol. 74, No. 366. (Jun., 1979), pp. 359364
