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# The Gory Details: Bumpiness Coefficient and Computational Cost

The computation for the bumpiness coefficient for a single company with 12 years of non-decreasing dividend history is:

=100/11*SQRT(SUM(
(div2010/div2009-1-DGR)^2;
(div2009/div2008-1-DGR)^2;
(div2008/div2007-1-DGR)^2;
(div2007/div2006-1-DGR)^2;
(div2006/div2005-1-DGR)^2;
(div2005/div2004-1-DGR)^2;
(div2004/div2003-1-DGR)^2;
(div2003/div2002-1-DGR)^2;
(div2002/div2001-1-DGR)^2;
(div2001/div2000-1-DGR)^2;
(div2000/div1999-1-DGR)^2
))

Where DGR is:

=(div2010/div1999)^(1/11)

On the other hand, the AADGR is:

=AVERAGE(
div2010/div2009-1;
div2009/div2008-1;
div2008/div2007-1;
div2007/div2006-1;
div2006/div2005-1;
div2005/div2004-1;
div2004/div2003-1;
div2003/div2002-1;
div2002/div2001-1;
div2001/div2000-1;
div2000/div1999-1)

Computing the BC requires fourteen divisions, twelve exponents, a multiplication and a square root.

Computing the AADGR requires twelve divisions.

When examining the computation cost of a procedure:

• Additions and subtractions are ignored because they are "computationally cheap".

• Multiplications and divisions are a bit more expensive but are ignored.

• Exponents and roots tend to be very expensive and they drive the "computational cost".

The number of exponents for computing the BC is equal to one plus the number of years of dividend increases.

The number of divisions for computing the AADGR is equal to one plus the number of years of dividend increases.

As the number of years of dividend payments increase the computational cost of the BC compared to the AADGR increases.

One further point, AADGR can be viewed as "a rule of thumb", an easily learned and easily computed procedure for approximating a score to predict the bumpiness of a company's non-decreasing dividend history.