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Who is not interested in buying a new house? Owning a (at least the first one) house is like a dream come true for most! If you have ever bought (or thought of buying) a house in a building that is yet to be constructed, you would realize that there are clearly two parts of the business for the developer – the construction period (which is when the building is being built for the first 2-3 years) and the operations/ sales period (after the construction, they would sell or lease the building).
As we discussed last time, one of the key aspects of any Infrastructure/ Real Estate Project is the long gestation period of the project. Typically in the construction period the project would utilize all the cash and when the operations/ sales period starts, the costs are almost zero as compared to the revenue being generated from the project.
So what’s the big deal about the cash flow structure?
One of biggest concern in the construction period (Lets say it runs for 3 years) is that it consumes all your cash. If my total cost of building the project is going to be USD 30 Million (Spread equally over the three construction years), my Profit and Loss Statement would look something like:
P&L (all figures in USD Mi)
But my building is not yet built (hence I cannot sell it), so I can take this as a Work In Progress (WIP) to my balance sheet (more about this can be learnt from accounting books and we would also be delving into this concept in detail in our training). But one thing is for sure, I would have a cash deficit of USD 10 Mn in the first year and a similar situation would continue for the first three years (till the point construction is complete and you start selling/ operations).
Typically, these projects also have a large amount of debt. For example, if I am expecting to construct the building for USD 30 Mn, I would try to take a bank loan of at least USD 20 Mn.
If you were a bank, the decision making of whether to lend money is taken on the interest and principal repaying capacity. If as a bank I analyze your P&L, I find that you have no cash to pay me my interest and principal! Traditional bankers lend you money ONLY if you can EASILY pay me back my money (typically look at a ratio of (interest + repayment) amount to the cash generated – called coverage ratio). If you can’t do that – I will not lend!
So how do Banks view this?
As a banker, I understand that you are going to construct for 3 years and that is when you need my money (And would not be able to pay me interest). So I agree to not take interest and principal repayment as cash each year. But I cannot let go of this money!
Think of it as – I let you take additional loan to fund this payment! For example, let us assume:
Interest Rate prevailing: 10% per year
Loan amount in first year: USD 10 Mn
- So Interest on this loan: USD 1 Mn
- Now you can’t pay me back, so take additional loan (In first year itself) of USD 1 Mn
- That means total loan: USD 11 Mn (10 that you originally took and 1 that you took to pay the interest)
- That means interest is actually USD 1.1 Mn (Instead of the original 1 Mn)
- That means that effective loan: USSD 11.1 Mn (11 that we had calculated earlier and 0.1 to fund this gap)
- So interest: USD 1.11 Mn
- So effective Loan amount: USD 11.11
… and so on
There is a clear circular logic in this concept – My loan changes interest and interest changes loan
Interpreting the circular logic
Summarizing our thoughts:
- When an asset is developed, and there is a considerable period between the start of a project and its completion, the interest costs related to the construction are generally included in the cost of the asset, that is, the interest cost is capitalized
- The capitalization period ends when the asset is ready for use
- While modeling in excel, Interest During Construction (IDC) introduces a circular loop into the sheet due to the circular references explained below (1-2-3-4)
o Equity and Grant commitments can be either a specific amount, or a certain percentage of the total project funds required (that is, a fixed percentage in the capital structure)
[Tip: Learn more about Excel Circular References.]
The Case – Modeling Interest During Construction in a typical Real Estate Project
Let us consider the construction period of a project at place X, where government wants to build a hospital.
The costs of the project are stated below:
The government is ready to provide a grant of USD 50 Mn in the project and the project builder has to infuse equity of USD 100 Mn in the project
The shortfall in the funds can be funded through debt.
A complete model for financing has to be prepared for the construction period.
The Concept
The basic concept behind the model is pretty simple
Total cash outflow in a year = Total Cash Inflow in the year
- So the first step is to calculate the cash outflow in all the years. This cash outflow also includes the cost of paying the interest (which we would not know in the first pass).
- As a next step, we find the amount available to us through the equity and grants.
- We know that cash inflow has to be equal to cash outflow for all years.
- Whatever is the shortfall, we raise debt to fund it.
- Calculate the cumulative debt
- We calculate the interest on this debt.
- Whatever is the interest on the debt, we plug it back in the project cost (and hence introduce the circular logic in the model)
Step I: Getting the Cash Outflow (Project Costs)
Based on the case, calculate the cash required in each year.
We know the costs of each of the items and what should be the contribution in each year. Multiply the values to get the amounts in each year!
In the same step, we add all the costs (Including the Interest During Construction, though we don’t know it right now)
Step II: Getting the Cash Available (through Equity and Grants)
Based on the equity and grant infusion schedule, we calculate the cash inflows
Step III: Cash Inflow = Cash Outflow
Since the cash outflow has to be matched with cash inflow, we make the total project cost in all years equal to funding in the year
Step IV: Fund the shortfall through debt
Since the only source to fund the shortfall is debt, lets raise the debt as the total fund needs less whatever is available through equity and grants
Step V: Calculate the total debt outstanding
Since there is no way that we can pay the debt in the construction time, we make the outstanding debt as the cumulative debt raised (See me use a trick to accumulate!)
Step VI: Calculate the interest on the debt
Since we have taken money from the bank, we need to pay an interest on it. The interest rate is given to us, let us link the amount to the interest to calculate the interest.
Step VII: The Circular Logic (Plugging back the interest in the project cost)
Since the interest is also a cost of the project (and we are not paying it back to the bank each year), we take it to the project cost.
Out here, if you notice, excel starts a circular calculation and updates all the values! This can be verified by looking at the bottom left of excel and noticing this sign of “calculate”
Beware! Circular References can be dangerous!
What we have achieved in this tutorial is one of the most intricate concepts in project finance -Interest During Construction (IDC). We have also used a fairly advanced function in excel – Circular loops. But please note that circular loops in excel is a dangerous tool. If by chance your excel sheet gets an erroneous value, the error would propagate through the model and there is no way for the model to recover back from the error, unless you know where the circular loop is and you delete and go back from there. For example, if I change 10% interest to “ten”,
I figure that my model is corrupt (It was expecting a numeric input and I gave a string!). But I can go back to 10%, my model does not go back!!
I leave it as a homework for you to figure out, how to go back to a stable state!! 🙂
I will give you a trivial solution (close the sheet and open it again) :). You figure out, where the circular loop is and delete those lines and break it to come back!!
In the meanwhile, happy modeling!!
Project Finance Modeling – Templates to download
I have created a template for you, where the assumption numbers are given and you have to link the complete model!
You can download the same from here. You can go through the case and fill in the yellow boxes. I also recommend that you try to create this structure on your own (so that you get a hang of what information is to be recorded).
Also you can download this filled template and check, if the information you recorded, matches mine or not! 🙂
I am just doing that for the single sheet model and recommend that you do the same for multi-sheet model as a homework problem. If you face any issue, post your excel with the exact problem and we can discuss the way to move forward.
Next Steps
This series gives you a flavor of how project finance modeling is done and an idea about specific nuances in modeling for long gestation projects. I do hope to see you in the financial modeling school.
Join our Financial Modeling & Project Finance Classes
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For any queries regarding the cash impact or financial modeling, feel free to put the comments in the blog or write an email to paramdeep@edupristine.com
20 Responses to “Simulating Dice throws – the correct way to do it in excel”
You have an interesting point, but the bell curve theory is nonsense. Certainly it is not what you would want, even if it were true.
Alpha Bravo - Although not a distribution curve in the strict sense, is does reflect the actual results of throwing two physical dice.
And reflects the following . .
There is 1 way of throwing a total of 2
There are 2 ways of throwing a total of 3
There are 3 ways of throwing a total of 4
There are 4 ways of throwing a total of 5
There are 5 ways of throwing a total of 6
There are 6 ways of throwing a total of 7
There are 5 ways of throwing a total of 8
There are 4 ways of throwing a total of 9
There are 3 ways of throwing a total of 10
There are 2 ways of throwing a total of 11
There is 1 way of throwing a total of 12
@alpha bravo ... welcome... 🙂
either your comment or your dice is loaded 😉
I am afraid the distribution shown in the right graph is what you get when you throw a pair of dice in real world. As Karl already explained, it is not random behavior you see when you try to combine 2 random events (individual dice throws), but more of order due to how things work.
@Karl, thanks 🙂
When simulating a coin toss, the ROUND function you used is appropriate. However, your die simulation formula should use INT instead of ROUND:
=INT(RAND()*6)+1
Otherwise, the rounding causes half of each number's predictions to be applied to the next higher number. Also, you'd get a count for 7, which isn't possible in a die.
To illustrate, I set up 1200 trials of each formula in a worksheet and counted the results. The image here shows the table and a histogram of results:
http://peltiertech.com/WordPress/wp-content/img200808/RandonDieTrials.png
@Jon: thanks for pointing this out. You are absolutely right. INT() is what I should I have used instead of ROUND() as it reduces the possibility of having either 1 or 6 by almost half that of having other numbers.
this is such a good thing to learn, helps me a lot in my future simulations.
Btw, the actual graphs I have shown were plotted based on randbetween() and not from rand()*6, so they still hold good.
Updating the post to include your comments as it helps everyone to know this.
By the way, the distribution is not a Gaussian distribution, as Karl points out. However, when you add the simulations of many dice together (i.e., ten throws), the overall results will approximate a Gaussian distribution. If my feeble memory serves me, this is the Central Limit Theorem.
@Jon, that is right, you have to nearly throw infinite number of dice and add their face counts to get a perfect bell curve or Gaussian distribution, but as the central limit theorem suggests, our curve should roughly look like a bell curve... 🙂
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I'm afraid to say that this is a badly stated and ambiguous post, which is likely to cause errors and misunderstanding.
Aside from the initial use of round() instead of int(),.. (you've since corrected), you made several crucial mistakes by not accurately and unambiguously stating the details.
Firstly, you said:
"this little function generates a random fraction between 0 and 1"
Correctly stated this should be:
"this little function generates a random fraction F where 0 <= F < 1".
Secondly, I guess because you were a little fuzzy about the exact range of values returned by rand(), you have then been just as ambiguous in stating:
"I usually write int(rand()*12)+1 if I need a random number between 0 to 12".
(that implies 13 integers, not 12)
Your formula, does not return 13 integers between 0 to 12.
It returns 12 integers between 1 and 12 (inclusive).
-- As rand() returns a random fraction F where 0 <= F < 1, you can obviously can only get integers between 1 and 12 (inclusive) from your formula as stated above, but clearly not zero.
If you had said either:
"I usually write int(rand()*12) if I need a random number between 0 to 11 (inclusive)",
or:
"I usually write int(rand()*12)+1 if I need a random number between 1 to 12 (inclusive)"
then you would have been correct.
Unfortunately, you FAIL! -- repeat 5th grade please!
Your Fifth Grade Maths Teacher
Idk if I'm on the right forum for this or how soon one can reply, but I'm working on a test using Excel and I have a table set up to get all my answers from BUT I need to generate 10,000 answers from this one table. Every time, I try to do this I get 10,000 duplicate answers. I know there has to be some simple command I have left out or not used at all, any help would be extremely helpful! (And I already have the dice figured out lol)
Roll 4Dice with 20Sides (4D20) if the total < 20 add the sum of a rerolled 2D20. What is the average total over 10,000 turns? (Short and sweet)
Like I said when I try to simulate 10,000turns I just get "67" 10,000times -_- help please! 😀
@Justin
This is a good example to use for basic simulation
have a look at the file I have posted at:
https://rapidshare.com/files/1257689536/4_Dice.xlsx
It uses a variable size dice which you set
Has 4 Dice
Throws them 10,000 times
If Total per roll < 20 uses the sum of 2 extra dice Adds up the scores Averages the results You can read more about how it was constructed by reading this post: http://chandoo.org/wp/2010/05/06/data-tables-monte-carlo-simulations-in-excel-a-comprehensive-guide/
Oh derp, i fell for this trap too, thinking i was makeing a good dice roll simulation.. instead of just got an average of everything 😛
Noteably This dice trow simulate page is kinda important, as most roleplay dice games were hard.. i mean, a crit failure or crit hit (rolling double 1's or double 6's) in a a game for example dungeons and dragons, if you dont do the roll each induvidual dice, then theres a higher chance of scoreing a crit hit or a crit failure on attacking..
I've been working on this for awhile. So here's a few issues I've come across and solved.
#1. round() does work, but you add 0.5 as the constant, not 1.
trunc() and int() give you the same distributions as round() when you use the constant 1, so among the three functions they are all equally fair as long as you remember what you're doing when you use one rather than the other. I've proven it with a rough mathematical proof -- I say rough only because I'm not a proper mathematician.
In short, depending on the function (s is the number of sides, and R stands in for RAND() ):
round(f), where f = sR + 0.5
trunc(f), where f = sR + 1
int(f), where f = sR + 1
will all give you the same distribution, meaning that between the three functions they are fair and none favors something more than the others. However...
#2. None of the above gets you around the uneven distribution of possible outcomes of primes not found in the factorization of the base being used (base-10, since we're using decimal; and the prime factorization of 10 is 2 and 5).
With a 10-sided die, where your equation would be
=ROUND(6*RAND()+0.5)
Your distribution of possible values is even across all ten possibilities.
However, if you use the most basic die, a 6-sided die, the distributions favor some rolls over others. Let's assume your random number can only generate down to the thousandths (0.000 ? R ? 0.999). The distribution of possible outcomes of your function are:
1: 167
2: 167
3: 166
4: 167
5: 167
6: 166
So 4 and 6 are always under-represented in the distribution by 1 less than their compatriots. This is true no matter how many decimals you allow, though the distribution gets closer and closer to equal the further towards infinite decimal places you go.
This carries over to all die whose numbers of sides do not factor down to a prime factorization of some exponential values of 2 and 5.
So, then, how can we fix this one, tiny issue in a practical manner that doesn't make our heads hurt or put unnecessary strain on the computer?
Real quick addendum to the above:
Obviously when I put the equation after the example of the 10-sided die, I meant to put a 10*RAND() instead of a 6*RAND(). Oops!
Also, where I have 0.000 ? R ? 0.999, the ?'s are supposed to be less-than-or-equal-to signs but the comments didn't like that. Oh well.
How do you keep adding up the total? I would like to have a cell which keeps adding up the total sum of the two dices, even after a new number is generated in the cells when you refresh or generate new numbers.
So, how do you simulate rolling 12 dice? Do you write int(rand()*6) 12 times?
Is there a simpler way of simulating n dice in Excel?
I've run this code in VBA
Sub generate()
Application.ScreenUpdating = False
Application.Calculation = False
Dim app, i As Long
Set app = Application.WorksheetFunction
For i = 3 To 10002
Cells(i, 3).Value = i - 2
Cells(i, 4).Value = app.RandBetween(2, 12)
Cells(i, 5).Value = app.RandBetween(1, 6) + app.RandBetween(1, 6)
Next
Application.ScreenUpdating = True
Application.Calculation = True
End Sub
But I get the same distribution for both columns 4 and 5
Why ?
@Mohammed
I would expect to get the same distribution as you have effectively used the same function