S Curve dilemma

tmontana

Board Regular
Joined
May 13, 2009
Messages
79
I have been provided monthly construction costs over an 11 month period that have been plotted using an S-curve weighting. Basically, the total construction cost number is $16,469,000 and is allocated as follows over 11 months:

<TABLE style="WIDTH: 58pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=77 border=0 x:str><COLGROUP><COL style="WIDTH: 58pt; mso-width-source: userset; mso-width-alt: 3285" width=77><TBODY><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 58pt; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right width=77 height=15 x:num="413863">$413,863 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="982200">$982,200 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="1433313">$1,433,313 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="1767204">$1,767,204 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="1983871">$1,983,871 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="2083316">$2,083,316 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="2065537">$2,065,537 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="1930535">$1,930,535 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="1678310">$1,678,310 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="1308861">$1,308,861 </TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="822190">$822,190 </TD></TR></TBODY></TABLE>

This really is a bell curve. How would I go about plotting it without hardcoding the numbers? There must be some formula based on the number of months.

Thanks
 

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Read your post thrice. Maybe it's just that it's Friday afternoon. But I haven't a clue in the world what you're asking with "...without hardcoding the numbers...". :confused: One can certainly plot cells whose values come from formulae. But I don't think that's what you're asking.
 
Upvote 0
Hmmm, do you mean that you just need to use a formula like:

=SUM(A$1:A1)

and copy it down so that you create a "S" shaped graph? (Assumes your data is in cells A1:A11.)
 
Upvote 0
I am currently working on complex financial property model.

I would like to know if anyone knows how to create an S curve distribution in excel for a specific period of time (e.g construction period).

In my cashflow I have periods (e.g. 1 to 100 - which represent the "months" of the project). In my assumptions page, construction period 1 means when the construction is set to start, and construction end1 is when it is set to finish. In other words, my construction costs in my cashflow will only appear if it fits the construction parameters specified in my assumptions page, otherwise 0.

What I would like to achieve is an S curve (or weighted) type of distribution which has a bell (hump) shape curve. If possible, I would like to have this distribution embedded in my formula so that I can control when construction starts and ends. In addition, I would not have to manually enter the distribution weight each time, which otherwise would defeat the purpose of having a flexible spreadsheet.

Another software package called Argus is able to generate this distribution based on the "S-curve". Since I do not subscribe to this package, I am trying to replicate the distribution using excel, which I'm fairly certain can be done.

As an example, if my total construction costs over an 11 month period (Oct-2010 to Aug-2011) are $16,469,200, how would I go about distrubuting this over the 11 months. The output/distribution I need to replicate should be as follows:

<TABLE style="WIDTH: 58pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=77 border=0 x:str><COLGROUP><COL style="WIDTH: 58pt; mso-width-source: userset; mso-width-alt: 3285" width=77><TBODY><TR style="HEIGHT: 11.25pt" height=15><TD class=xl25 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; WIDTH: 58pt; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right width=77 height=15 x:num="2.5129514487649673E-2">2.5130%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="5.9638598110412167E-2">5.964%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="8.7029910378160449E-2">8.703%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="0.10730357272970151">10.730%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="0.12045946372622836">12.046%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="0.12649770480654798">12.650%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="0.12541817453185339">12.542%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="0.1172209336215481">11.722%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="0.10190598207563209">10.191%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="7.9473259174701869E-2">7.947%</TD></TR><TR style="HEIGHT: 11.25pt" height=15><TD class=xl24 style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.25pt; BACKGROUND-COLOR: transparent" align=right height=15 x:num="4.9922886357564422E-2">4.992%</TD></TR></TBODY></TABLE>
 
Upvote 0
The formula needs to be based on the number of months, such that if I had a longer construction horizon, the curve would be flatter and vice versa for a shorter period.
 
Upvote 0
I'm not quite sure what you're after here. If you already know the monthly percentages, then you just want a formula like the one Greg provided, right? So, are you saying you want to find the S-shaped curve that best fits the figures you already have? If so, there are a number of ways of doing this, ranging from the simple to the much more complex. You might want to try a normal CDF or some tanh functions first.
 
Upvote 0
The issue is I have hundreds of different cost item (i.e. consruction costs, architectural costs, legal fees, broker fees, etc.) spread across various periods of time. What I do know is they all follow the same distribution pattern, which I believe is called the S curve. I need to create a formula that mimics this pattern so that i have the flexibility of changing my timing without having to manually change the weights each time.

I think the formula is based on some ploynomial function such as:

y = a +b(x)^2 +c(x)^3,

where y is the weight from 0% to 100% and x is the number of months. But I can't seem to get it to match.
 
Upvote 0
So, in each case, what's your starting point? That is, what do you know? Do you know the total cost, time period, and distribution, or some other set of parameters?
 
Upvote 0
Here are my inputs for each development cost:

(1) total cost (in $)
(2) Construction period (in months)
(3) Starting month
(4) Ending month

I even know the answer which is the distribution pattern described in my original email. I need to use the above inputs to be able to replicate that distibution.
 
Upvote 0
Basically the "S" chart is a cumulative sum of the costs as shown on the bell chart. If you want some type of a bell chart, you might play around with the NORMSDIST() function and a formula to create the standard deviation breakpoints you want...


<!-- Please do not remove this header --><!-- Table easily created from Excel with ASAP Utilities (http://www.asap-utilities.com) --><table border="1" bordercolor="#C0C0C0" bordercolordark="#FFFFFF" cellspacing="0"><tr><td width="74" height="25" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">Std Devs</font></td><td width="110" height="25" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">"S" Curve Data</font></td><td width="115" height="25" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">Bell Curve Data</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">-2.5</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0062</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0062</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">-2</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0228</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0165</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">-1.5</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0668</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0441</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">-1</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.1587</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0918</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">-0.5</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.3085</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.1499</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.5000</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.1915</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.5</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.6915</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.1915</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">1</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.8413</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.1499</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">1.5</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.9332</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0918</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">2</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.9772</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0441</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">2.5</font></td><td width="110" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.9938</font></td><td width="115" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">0.0165</font></td></tr></table>


<!-- Please do not remove this header --><!-- Table easily created from Excel with ASAP Utilities (http://www.asap-utilities.com) --><table border="1" bordercolor="#C0C0C0" bordercolordark="#FFFFFF" cellspacing="0"><tr><td width="74" height="25" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">Std Devs</font></td><td width="124" height="25" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">"S" Curve Data</font></td><td width="84" height="25" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">Bell Curve Data</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A2)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B2</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A3)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B3-B2</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A4)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B4-B3</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A5)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B5-B4</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A6)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B6-B5</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A7)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B7-B6</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A8)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B8-B7</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A9)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B9-B8</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A10)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B10-B9</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A11)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B11-B10</font></td></tr><tr><td width="74" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=ROW()/2-3.5</font></td><td width="124" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=NORMSDIST(A12)</font></td><td width="84" height="25" align="right" valign="bottom" style="white-space: nowrap"><font face="Tahoma" size="2" color="#000000">=B12-B11</font></td></tr></table>
 
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