Van Gysel asked in a recent post at Chandoo.org for a way to calculate the costs of running a plantation. The twist is that the costs vary by year, and based on the age of the trees.
The following is a slightly simplified version of the solution I offered:
=SUM(IFERROR(LOOKUP(“Year”&MMULT(N($B$3:B$7>0),TRANSPOSE(COLUMN($B$3:B$7)^0)), $B$11:$I$11, $B12:$I12),0)*B$3:B$7) Ctrl+Shift+Enter
Today I am going to try and explain how the formula works.
As always at Formula Forensics, you can follow along with a sample file: Download Here
The Problem
In a plantation, the costs for planting and maintaining trees vary based on the age of the trees and by year. The table below shows the acres of trees planted per year and the yield and costs per year that vary based on the age of the trees.
Let us look at the calculations needed for each year.
Year 2013
- 300 acres of trees were planted in 2013. Calculations for 2013 are as follows. (Only Yield calculation is shown, but the process is similar for Nursery costs, Fertilizers, etc.)
- The trees do not yield any fruits in the first year. As such, Yield for year1=300*0=0
That was easy!
Year 2014
- 700 additional acres of trees will be planted in 2014. Calculations for 2014 are as follows. (Again, only Yield calculation is shown, but others are calculated similarly.)
- 300 acres of trees are 2 years old. 700 acres are 1 year old.
- The 300 acres from 2013 now yield fruit since it is year2. However, the new trees (700 acres) do not yield any fruits yet. So total yield for 2014=300*Year2Yield+700*Year1Yield=300*5+700*0
Year 2015
- 1000 additional acres are to be planted in 2015. Calculations for 2015 are as follows:
- 300 acres are from 2013 (3 years old); 700 acres are from 2014 (2 years old); 1000 acres are from 2015 (1 year old).
- Yield for 2015=300*Year3Yield + 700*Year2Yield + 1000*Year1Yield = 300*10 + 700*5 + 1000*0
Year 2016
- 1000 additional acres are to be planted in 2016. Calculations for 2016 are as follows:
- Yield for 2016=300*15+700*10+1000*5+1000*0
How do we simulate the above calculation in an Excel formula?
A Solution
Let us first look at how we performed the calculations above manually, using the 2016 Yield as an example.
- We took each acreage value in 2016, and determined its age by counting how many years it has been since that acreage was planted. You might have observed that the age can be counted by the number of times a value has been repeated up to that point. (In other words, if I planted 300 acres in 2013, I should see that same amount in 2014, 2015 and 2016.) As such, 300 acres is repeated 4 times. 700 acres is repeated 3 times. 1000 acres is repeated 2 times. And the latest planting of 1000 acres exists only once.
- Once we determine the age for a given acreage, we looked up the yield for that age in the second table
- We then multiplied the acreage with the corresponding yield value.
Calculation #1 can be expressed as follows:
- Age for acreage 1 (first planted in 2013)=count of B3:E3 where value is greater than zero. i.e. COUNTIF(B3:E3,”>0”)
- Age for acreage 2 (planted in 2014)=count of B4:E4 where value is greater than zero. i.e. COUNTIF(B4:E4,”>0”)
- Age for acreage 3 (planted in 2015)=count of B5:E5 where value is greater than zero. i.e. COUNTIF(B5:E5,”>0”)
- Age for acreage 4 (planted in 2016)=count of B6:E6 where value is greater than zero. i.e. COUNTIF(B6:E6,”>0”)
- Age for acreage 5 is zero since nothing has been planted for 2017 yet in 2016
The above approach would work if we were calculating the age one row at a time. However, that can become tedious really fast. We need to perform the calculation for the full range (B3:E7) together, but return the counts for each row individually.
Excel’s MMULT function comes to the rescue!
MMULT (which stands for Matrix Multiply) multiplies two matrices and returns a third matrix based on rules for matrix multiplication. I am planning to devote a whole article to explain the MMULT function. As such, for this article, we will summarize the utility of the function as “take a 2-dimensional array, add each column’s value for each row, and return a 1-column array”.
MMULT requires that its arguments be numeric.
So to obtain the counts for the year 2016, we can use the following:
MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0))
As you can see from the picture below, MMULT’s results are the addition of each column for each row.
In the above formula, you may have noticed that the range uses absolute and relative referencing (signified by the $ sign or lack thereof). This is to ensure that the range grows or shrinks as needed. The upper left address is held constant ($B$3). However, the lower right address for the range has columns that vary but row that is fixed on row #7. This ensures that the formula would work if we copy to the left, right, etc. in the final results.
Now that we have the age for each acreage value, we can look up the corresponding yield value using (what else?) LOOKUP function.
But before we can use LOOKUP, we will need to convert the numeric values returned from MMULT into the strings Year1, Year2, etc. found in the Costs table. Of course, you know how to do that… concatenate the string “Year” to the result from MMULT
“Year”&MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0))
For the 2016 example, we get {“Year4″;”Year3″;”Year2″;”Year1″;”Year0”}
We can now use LOOKUP as follows:
LOOKUP(“Year”&MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0)), $B$11:$I$11, $B12:$I12)
You may recall that LOOKUP looks up a value in the array indicated by the second argument, and returns the corresponding value from the third array argument. In this case, instead of looking up a single value, we look up an array of values (supplied in the first argument) to the function.
The above formula translates to the following:
LOOKUP({“Year4″;”Year3″;”Year2″;”Year1″;”Year0”}, {“Year1″,”Year2″,”Year3″,”Year4″,”Year5″,”Year6″,”Year7″,”Year8”}, {0,5,10,15,20,25,30,35})
The result from LOOKUP is {15;10;5;0;#N/A}
(The last value is #N/A because there is no acreage value for 2017 yet (as of 2016 column). The concatenation resulted in Year0 which does not exist in the “Age of The Trees” range (B11:I11) above.)
By using IFERROR(LOOKUP(…),0) we get {15;10;5;0;0}
We can now multiply the above result with the acreage values for 2016 to get {4500;7000;5000;0;0}
Finally, we SUM the values to get 16500
Putting it all together, we get the following formula (shown for Production for year 2016)
=SUM(IFERROR(LOOKUP(“Year”&MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0)), $B$11:$I$11, $B12:$I12),0)*E$3:E$7)
One of the benefits of the above formula is that you can copy the same formula to calculate values for additional years, as well as other plantation costs.
Download
You can download a copy of the above file and follow along: Download sample file.
Let me know (using the comments below) what you think of the above approach and solution, as well as any other approaches you have utilized to solve a similar problem. In the meantime, I wish you continued Excellence!
-Sajan.
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39 Responses to “Make a Quick Thermometer Chart to Compare Targets and Actuals”
You'll probably have some readers insist on bullet charts, which in my experience are no easier to read.
Note on the case where actuals may exceed targets, the target has to be the second series in the chart, not the first, so it appears in front of the actual.
@Jon.. good point. And yes, readers are already saying bullets are the way to go. Atleast @dmgerbino said it on twitter: http://twitter.com/dmgerbino/status/6761754333
But I feel the same as you did. Bullets need orientation to get started and not that easy to construct (here is a tutorial btw... http://chandoo.org/wp/2008/07/21/dashboard-bullet-graphs-excel/ )
When you just have to compare 2 sets of values, a chart like above is good and easy enough.
And yes, thank you for saying that data series order should be correct to show the target on top.
I think bullet charts are a good alternative. I'm not a huge fan of the formatting that you used above where the outline is so thick.
Another option would be to combine a line graph (plan/goal amounts) with the columns (actual) and select the option to remove the line. This leaves just the value (marker), which can be increased in size to leave only a line about the size of the bar. It's an easy and cleaner way to show actual to plan/goal. Does that make sense?
Tony -
I would use columns (or area) for goal, and lines and markers for actual.
What about if you go over the target? The chart doesn't work so well then.
The technique described today is a near bullet chart. As I stated early this morning on Twitter (link: http://bit.ly/4K3yPM ) , I am a fan of Stephen Few's Bullet Graph.
Hubert Urruttia and I started with Charlie Kyd's method, but as Jon Peltier and Chandoo said, they are not easy to contruct. We moved onto prototyping with Fabrice Rimlinger's SPARKLINES FOR EXCEL and now use XLCube's (BonaVista) Micro Chart tool. Both of these tools allow you to create bullet charts just as easy as any Excel chart type.
As far as reading and interpreting them, this chart type has been the easiest for us to present.
There are many chart types. Today's "Make a Quick Thermometer Chart to Compare Targets and Actuals" is fine for a start, but your ultimate goal should be to create Bullet Graphs. AS Stephen Few states in his overview, "The bullet graph was developed to replace the meters and gauges that are often used on dashboards. Its linear and no-frills design provides a rich display of data in a small space, which is essential on a dashboard. Like most meters and gauges, bullet graphs feature a single quantitative measure (for example, year-to-date revenue) along with complementary measures to enrich the meaning of the featured measure. Specifically, bullet graphs support the comparison of the featured measure to one or more related measures (for example, a target or the same measure at some point in the past, such as a year ago) and relate the featured measure to defined quantitative ranges that declare its qualitative state (for example, good, satisfactory, and poor). Its linear design not only gives it a small footprint, but also supports more efficient reading than radial meters."
@dmgerbino
Since @dmgerbino had to bring my name up I guess I should throw in my two cents.
@dmgerbino and I have both implemented Bullet Charts with great success. What is most interesting about this fact is that we have had a harder time implementing Sparklines than Bullet Charts. The reason for this revolves around the simple fact of familiarity. I will explain. People look at a Sparkline and they think it is a really small Line Chart and it is not. People are familiar with Line Charts since they have been around since 1786 when they were created by William Playfair. Bullet Charts on the other hand are different so they almost demand an explanation. Because of this there was a lot of face time that was needed to explain these charts but once people got them they understood the concept. This is similar to when I introduced Cycle Plots http://bit.ly/87ydVG (Thank you @nbrgraphs!) or Horizon Charts http://bit.ly/6PVavj.
Now about the Thermometer Charts… The first thing I want to address is Tony Rose’s statement. I totally agree that the outline on the chart is too think. It might come of as being a whole new series or a new variable. What I have done in instances like this is I have created a Bar Graph and Scatter Plot mixture. Then I have turned off the Data Series on the Scatter Plot and turned on the Horrizontal Error Bars on the Scatter Plot. The new horizontal line stands for the Plan and the Bar is the actual. The reason why I find this more useful is because this technique works if you have exceeded plan. Actually, I do not understand how Chandoo’s method would display the data if Plan is surpassed.
This reminds me of another blog post that @dmgerbino, @Jon_Peltier, and myself commented on over a year ago. http://bit.ly/PNdO Actually, I talk about similar things in regards to familiarity to charting techniques.
- @hubert_urruttia
[...] we have a post on using thermometer charts to quickly compare actual values with targets. Today we follow up the post with 10 charting ideas you can use to compare actual values with [...]
Hi Chandoo
How do I increase the width of the bar chart and also make the long axis labels come in the same line?
Thank you,
Rajiv
@Rajiv
Select the outer part of the chart "Chart Area" and note the cursor will change to arrows
drag the edges to what ever size you want
You can hold the Alt key as you drag and the chart will snap to the cell boundaries
Now click on the chart area inside the chart "Plot Area" and note that a box with small circles appears around it
drag the circles on the edge of that box to suit
You can hold the Alt key as you drag and the chart will snap to the cell boundaries
@ Hui
Thank you for your comments. But my question was not for the "Plot Area" instead I wanted to know about how should I increase the width of the individual bar charts because with my data all the individual bars are coming to be thin and I want to make them appear broader.
Thank You
@Rajiv
Right click on the Series you want to change and select Format Data Series
Under Series Options goto Gap Width and decrease it to suit
[...] Make a Quick Thermo-meter Chart using Excel [...]
Thank you for the great chart and explanation!
How do I show two amounts (Signed Revenue and Pipeline) as stacked within the Target amount?
@CL... you can use stacked column charts and follow the same technique to get this. See attached file for an example - http://img.chandoo.org/playground/thermo-meter-with-additional-details.xlsx
Chandoo - thanks for the quick response! What if I want the data label for the pipeline to be the actual pipeline value, not the signed rev + pipeline value? i.e. 15 instead of 55
Thanks!
How would i do this in excel 2003?
[...] Thermo-meter charts are very good to show how actual value compares with target (or budget). But how can we add another point for say Last Year value to the chart with out cluttering it. [...]
Hi Guys,
As Matt said,
"What if you if you go over the target?"
Is there a way to make it change color? or at least to show what the target was?
I am planning to use this with a "Forecasted vs Real" production chart but I do not know how to show overproduction.
Any clue?
Thanks
How do I do this if I have 2 bars I want side-by-side? ie 2012 Mean with 2012 benchmark overlapping and then 2013 mean with 2013 benchmark overlapping? I want the 2012 and 2012 mean bars sie by side to compare multiple categories.
Sorry, I meant to say the 2012 and 2013 mean bars side by side
I have a problem in that my PM wants a chart that shows a stacked column (Labor and Expense) and then have the overall buget shown as a thermo.
Everytime I try to do this, I either end up with all three being stacked or all of them being seperated.
Help?
Or if someone knows how to only outline the top and sides of a chart series....then I would have this solved. (Make a stacked column with labor, expenses, and remaining budget, then clear the fill and outline only the top and sides.) I just can't figure out how to do that/ not sure if excel will let me only outline part of a chart series.
[...] Thermometer chart to show budget vs. actual performance [...]
Your home is valueble for me. Thanks!...
I've created the thermometer chart as the Chandoo tutorial described. How do I move my columns closer together? I don't want wider columns; I want to move my narrow columns closer together. Thank you!
Dear Elite members,
could you please let me informed whether we could incorporate color formating in this thermometer approach i.e. if my actual performance is <Min then meter color sud go Red, in between min & target it sud change to Amber & target and above sud change to Green. pls advise. thanks,
I think the only way to do that would be with VBA programming.
@Abhinav
Yes, Simply use a stacked column chart, colored appropriately
Or
You may also want to read about Bullet Charts
@ Hui,
Could you pls demonstrate this with the help of an example.
let's have the below sample data
Actual=12
Min=10
Target=15
Max=20
if Actual>=Min then bar color sud be Red
in between Min & Target= Amber
between target(inclusive) & Max = Green
greater than or equal to Max= Blue
Thanks in advance
Abhi
Great blog post with awesome sample data. I've implemented two of the top "power tips" by changing the colour of the actual values, AND setting Actual to be 40% transparent. Looking good.
[…] easy with these charts. Use them sparingly. As a rule a thermo-meter chart would be better (easy to make, takes less space, scalable) for situations like […]
[…] easy with these charts. Use them sparingly. As a rule a thermo-meter chart would be better (easy to make, takes less space, scalable) for situations like […]
I recently purchased the template bundle and love the ease of use - thank you!
I would like to ask if it is possible to add an important 'block' to the dashboard to illustrate an important status for my executive team; 'billing status'? (ie budget / amount billed) something like that?
Thank you!
@Cheif449.. Thanks for your purchase and kind words.
You can add this easily to the dashboard. Follow below steps.
1. Unprotect the dashboard worksheet.
2. Add a text box (Insert > Drawing Shapes) to the dashboard
3. Put any text inside it as per your need.
4. Format it as needed.
5. Protect the dashboard again.
How do you do this in Excel 2010 - I am not seeing that option in Format data series.
how would we check target and actual sale for multiple years
Select any of the bar, right click and format data series