In early February Sujit asked a question at Chandoo.org, original post.
I require a formula stating criteria [0%-25% output will be 0, 26%-50% output will be 0.1, 51%-75% output will be 0.2, 76%-100% output will be 0.3 & 100% + output will be 0.4]
Kyle, responded with a neat Sumproduct formula
=SUMPRODUCT((B3>{0.25,0.5,0.75,1})*0.1)
I think it is so neat that it is worthy of sharing and detailing here at Formula Forensics:
So today we will pull Kyle’s answer apart to see what’s inside.
Kyle’s Formula
As usual we will work through this formula using a sample file for you to follow along. Download Here.
Kyle’s formula is a Sumproduct based formula
=SUMPRODUCT((B3>{0.25,0.5,0.75,1})*0.1)
Lets look at cell C3 as our example.
;
In C3 we see the formula: =SUMPRODUCT((B3>{0.25,0.5,0.75,1})*0.1)
Which consists of a Sumproduct function and a formula inside the sumproduct.
We know from Formula Forensics 007 that Sumproduct, Sums the Product of the Arrays, and that when there is only 1 array it simply sums the array elements.
In this case the Sumproduct only has a single array as an element
=SUMPRODUCT((B3>{0.25,0.5,0.75,1})*0.1)
and so the (B3>{0.25,0.5,0.75,1})*0.1 component must return an Array of elements for the Sumproduct to sum.
If we now look at the (B3>{0.25,0.5,0.75,1})*0.1 component.
We can see that it consists of a comparison B3>{0.25,0.5,0.75,1}
The result of the comparison is Multiplied by 0.1.
Sujit’s orginal question asked: 0%-25% output will be 0, 26%-50% output will be 0.1, 51%-75% output will be 0.2, 76%-100% output will be 0.3 & 100% + output will be 0.4
And Kyles formula is using B3>{0.25,0.5,0.75,1} to work out which category the value in B3 belongs to.
We can see this if in a blank cell say C5: we enter the following:
= B3>{0.25,0.5,0.75,1} press F9 not Enter.
Excel will respond with ={TRUE,TRUE,TRUE,FALSE}
This is showing us that the 1st, 2nd and 3rd elements in the formula: B3>{0.25,0.5,0.75,1}, are True
In our example the value in B3 is 80% which is 0.8 which is Greater than 0.25 and Greater than 0.5 and Greater than 0.75, but Not Greater than 1.0.
The next part of Kyle’s formula is (B3>{0.25,0.5,0.75,1})*0.1
In a blank cell say C7: enter the following:
= B3>{0.25,0.5,0.75,1}*0.1 press F9 not Enter.
Excel will respond with ={0.1,0.1,0.1,0}
This is showing us the result of
=(B3>{0.25,0.5,0.75,1})*0.1
={TRUE,TRUE,TRUE,FALSE} *0.1
={0.1,0.1,0.1,0}
Sumproduct now only has to add up the Array
=Sumproduct({0.1,0.1,0.1,0})
Which it does returning 0.3.
The Neat Part
The neat part of this is that Kyle has used the 0.1 Multiplier to Force the array to an array of Numbers for Sumproduct to sum.
Had Kyle used: =SUMPRODUCT((B3>{0.25,0.5,0.75,1}))*0.1
Excel would have returned an answer of 0
This is because as we saw in Formula Forensics 007, Sumproduct doesn’t know what to do with the array of True/False, they need to be converted to numerical equivalents for Sumproduct to operate on.
In a spare cell, say C9, enter: =SUMPRODUCT((B9>{0.25,0.5,0.75,1}))*0.1
Excel will respond with 0
Of course that can be fixed by using a double degative of a 1* inside the formula
In a spare cell, say C10, enter either:
=SUMPRODUCT(1*(B9>{0.25,0.5,0.75,1}))*0.1
or
=SUMPRODUCT(- -(B9>{0.25,0.5,0.75,1}))*0.1
Excel will respond with 0.3 as it should
Except that the formula is longer and now has to do 1 more multiplication.
Download
You can download a copy of the above file and follow along, Download Here.
Formula Forensics “The Series”
You can learn more about how to pull Excel Formulas apart in the following posts
We Need Your Help
I have received a few more ideas since last week and these will feature in coming weeks.
I do need more ideas though and so I need your help.
If you have a neat formula that you would like to share and explain, try putting pen to paper and draft up a Post like above or;
If you have a formula that you would like explained but don’t want to write a post also send it to Chandoo or Hui.
15 Responses to “Modeling Interest During Construction (IDC) – Excel Project Finance”
Thanks again for a very helpful post.
I had a similar problem when trying to model a balance sheet and profit and loss projection. The problem was that interest expense (in P&L) was dependent on a cash shortfall (in BS) which had to be funded. The cash shortfall depended on how much interest was paid, so the mutual dependency made a circular reference.
I addressed it with a macro that calculated interest outside of the P&L, then pasted the calculated amount into the P&L as a value. The model was out of balance, but by repeating the pasting and calculating loop the imbalance reduced to zero. It was a bit messy, and had to be repeated every time a line changed - but it worked.
If I have to do it again I'll read this article again first and see if it can be done more elegantly.
Hi,
The use of a circular reference can be avoided in this case. Just make use of the geometric sum to calculate the interest required. I’ll walk through the example from the spreadsheet.
First calculate the cash needed each year without the interest expense. So you year 1 you need 55 Mn, year 2 105 Mn, and 190 Mn for year 3. The total amount to borrow for year 1 is then (50 Mn)/(1-interest_rate) = (50)/(1-0.1). For years 2 and subsequent the amount borrowed is the cash needed in that year plus the interest_rate times the amount already borrowed. For year 2 (105 + interest_rate * sum(previous debt raised))/(1-interest_rate)=(105+0.1*61.1)/(1-0.1).
This process avoids the need for a circular reference, and makes the calculation more stable.
Thanks,
Tristan
The question is for the year 1 in your case, the amount works out to 45 mn. However in the year 2 you have applied the loan amount as 61.1 mn.
Am I missing something ! Please help !
very helpful information!!!
using circular references and to make model more stable we can use combination of "IF" and "ISERROR" functions. i.e
=if(iserror(formula1),"",(formula1))
this formula will return blank value if there is any error otherwise give the result required.
I usually use this in my models and it makes them very stable......
🙂 🙂 🙂
@Terry: Thats right. Exactly same problem is seen in Interest - Cash cycle in P&L and Cash Flow statement as well. In our trainings on financial modeling in excel, we demonstrate using both the circular loops as well as the macros to take care of this problem. Circular loops have their own pitfalls. If the model enters into a state of error, the error percolates!
@Tristan: Thanks for pointing out. I agree with you that if circular loops can be avoided, they should be avoided.
@Yogesh: This is one way of avoiding the problem. Although circular loops have another problem that they make your sheet slower. Each time, there is a change in the sheet, all the calculations are redone. So if they can be avoided, they should be avoided.
Please note that this was an example (a large one indeed) and I didn't have space to speak about the pitfalls of this approach! I just wanted to illustrate an approach and am glad that some of you found it useful!
I think while posting, there is an error in the images! The last image should be flipped with the one that is posted in step VII!
I think you can try the following simple solution given by Microsoft itself to make the circular works:
Windows: Excel Options -> Formulas -> Put a tick on "Enable iterative calculation"
Mac: Excel -> Preference -> Calculation ->Put a tick on "Limit iteration"
You can change the maximum number of calculation iterations as well as the maximum changes which iteration stops for goal seeking or for resolving circular references based on the number you type in the maximum change box.
Thank you.
Hey All
I heard that we can take care of the circularity with the help of macro for IDC. Can anybody help on the steps to construct the macro for the same.
Regards
Vinay
Hi Vinay,
If you look closely, you are essentially copying the values from the interest calculation to the IDC in project cost.
Basically you can record a macro, that takes the values from interest and pastes special the values in IDC row in project cost.
Then you can run that recorded code in a for loop.
Hope this helps.
Thanks Param for reply.
But before calculating interest, i need to provide for Upfront Equity and Equity, which are essentially part of total project cost. Hence, i need to put in Upfront Equity and Equity to calculate the IDC which is again hitting the total project cost.
Bit of confused on how to remove this circular reference.
Regards
Vinay
Wow, this was a brilliantly simple post. I was looking online for a while before I found this page. Never seen this been explained so beautifully yet so crisply before. Thanks for saving my ass at work! (i'm relatively new to finance + modeling)
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[…] Project Finance Modeling using Excel – Part 1 & Part 2 […]
I have been reading your blog since my college days. Today, I'm writing just to say thanks.
We have calculated Financial Rate of return of a hydropower projects, and the observer has raised an observation regarding Total Project cost with IDC Rs. 8616.01 million (PKR) and with-out IDC 8352.46 million (PKR). How does the Financial nalysis be calculated on the basis of with-out IDC Or With IDC?????
Please helpf. if possible to spare some time.