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**These days if you want to gain access to investment funds you better be able to create a good business case. The marvels of the business case are many. Opportunities are quantified while all (relevant) aspects are captured in a structured manner. This means we can easily compare and prioritize, etc. etc. **

How did we survive before the invention of the business case? Or are there possible down-sides to this powerful tool?

First of all let me stress that I think the business case is a very potent and powerful tool. The whole concept of project and program portfolio management would be very hard to implement without a tool to ensure you can compare like-for-like. Furthermore the use of business cases ensures that people with “a brilliant idea” sit back and reflect for a moment and are forced to look at their idea from different perspectives (financial, economical, risk, strategic, etc.) before they start wasting other peoples time pushing clearly flawed ideas.

But as with most tools in live that which can bring good can also be used for evil. The value of quantification has its limits. To proof a point the following example. If statistics is not your strongest point please bare with me, you will probably be amazed at the conclusions achieved. If you do not believe me when I say that everything in the example is statistically and mathematically sound ask an expert to verify. Of course there is a catch which I promise to explain at the end of the article. Here goes:

In a Casino one of the games is roulette. As part of roulette you can make a bet whether the next number will be red or green. Since there are just as many red numbers as green numbers on the roulette wheel changes are exactly 50 percent that either red or green comes up. The exclusion is the number zero which is black. However in some casinos, if zero comes up bets on green and red “ride” this means no loss and no gains and the bet stays on the table for the next round of the roulette wheel. As a result, for the purpose of this Business Case there is no influence from having the number zero.

I know of a system to play roulettes which will give you an incredible Return on Investment (we are talking double digit percentages) at a given (known) investment with a negligible risk of loss. Interested? You start playing by betting your base amount (let’s say 5 Euro) on either red or green. If the bet wins you won 5 euro and the cycle ends. You start a new cycle. The change of winning is 50 percent. If you lose you double your bet in the next round so now you bet 10 euro.

If you win in the second round you have won 10 euro but since you lost 5 euro on the first round your net winning is (again) 5 euro. Winning concludes the cycle. You start again with a new cycle by betting 5 euro. The change you lose two times in a row, however, is 0,5 (50 percent) x 0,5 (50 percent) = 0,25 (25 percent). This is a basic mathematical law of change.

Still there is a good chance you lose two times in a row, if so again you double your bet for the next round (so this time to 20 euro’s). If you win in the third turn your net gain is 5 euro (20 - 10 - 5 = 5). The changes of losing three times in a row 0,125 (12,5 percent) = 0,5x0,5x0,5.

I hope you get the picture: You keep doubling your bet when you lose until you win at which point you always have a net return of 5 euro. The system only has one risk and that is that you run out of money and cannot double your bet anymore. In that case you will not be able to recover your previous losses and basically you will be bankrupted. But we saw that we can calculate the changes of a series of consecutive losses and that the change is getting smaller and smaller (1 round 50 percent, 2 consecutive losses 25 percent, 3x 12,5 percent etc.).

So by ensuring we have enough capital available we can mitigate the risk to an acceptable level. The change (for instance) that you lose 17 times in a row (the residual risk factor) is 0,001 percent which I will hold is negligible small (especially if you compare it to the risks on the stock market). So if you ensure you have enough investment capital to keep doubling your bet 17 times you can accept the residual risk. We can calculate that your investment capital needs to be euro 655.355. With this capital you will make a return of 5 euro per cycle (ROI: 0,0008% per cycle). Is that all? That is not very impressive.

Not yet! If we assume that it takes 2 minutes to play a round on the roulette table (place the bet, roll the ball, collect the losses and pay the winner) we can calculate the average time it takes to play a cycle. Rules of change tell you that on average a winning cycle (the number of times it takes before you win the 5 euro’s and start over) contains 2 rounds.

So you will be able to play an average of 15 cycles per hour winning 5 euro each cycle that means you win 75 euro per hour. If we than assume you play 8 hours per day, 200 days per year you will have won 120.005 euro per year. This translates to a yearly return on investment of 18%. So if you have 655.355 euro’s in the bank and find a 0,001 percent change of loss acceptable start playing, a yearly income of 120.000 euro’s will be yours. How is that for a business case?

If you accept that all figures used are correct the conclusion seems warranted. I wonder if you have spotted the “catch”. In short the moral of this example is something my statistics professor used to say: With the right data set I can proof anything! This is the first risk of using business cases, it may offer false security. By using a lot of numbers the business case looks really sound, only a subject matter expert (in this case I would expect a risk expert of mathematician) will be able to identify the logic flaw.

A second issue is the use of assumptions. My business case contained the assumption that it takes 2 minutes to play a round on the roulette table. If I recalculate based on an adjusted business case of 5 minutes per round one can only play 6 rounds per hour and thus win “only” 48.000 euro’s per year (a yearly ROI of 7 percent). Though still not bad there is a substantial difference.

So some assumptions can have major influence on the final conclusions. Very seldom do I see business cases that clearly identify the assumptions. It is even more rare that an explanation is given of why the assumption is quantified on the value as presented. Finally it is extremely rare that the consequences are calculated should the assumption be wrong. If information is present it should be available in the risk section of the business case since wrong assumptions are basically a risk.

I have read business cases that reached quantified conclusions that were quoted in 3 decimals (look at my residual risk factor). Thus suggesting a very high accuracy of calculation. However in one particular case it also contained a completely unfounded assumption that was hard to pick up on. When I adjusted the assumption “downward” by only one percent the business case conclusion changed from a profit at a healthy return on investment into an unrecoverable loss.

I cannot but wonder if the writer did not knowingly manipulate his figures to reach the desired conclusion trying to hide the “weak” assumptions. It happens and to me that kind of behavior boarders on fraud: Willingly leading people to make bad decisions by supplying untrustworthy information and presenting the information as “sound” for personal gain. That type of use of business cases is evil.

Which brings me to the third flaw of business cases. Not all benefits and or (business) value is easily quantifiable. I have been known to say that I can quantify anything should you want me to and I will. I will just make ever bigger assumptions. In business the example often used is the value of advertising. What is my return on investment on advertising spending? This is one of the hardest things to quantify but it can be done.

I will give you an example of how one could quantify (with imaginary figures): A full page add in a daily newspaper costs 10.000 Euros (imaginary fact) the paper has 10.000 subscribers (imaginary fact) and is read by, on average, 2 people per delivery address (assumption) this would give an exposure to 20.000 people. 5% actively notices/ reads the add (assumption) that would mean 1000 readers. If 1 percent would be interested in my product (assumption) I would have reached 10 potential clients.

I sell, for instance, cars at a 1000 euro profit margin (imaginary fact). That would mean I break even if every potential customer actually bought the product (assumption). As most people would agree the added value of such a quantification is basically zero since it is just a bunch of assumptions stacked on top of one another.

For some things quantification is just not worth the effort. For instance I tell you that you should buy suntan lotion because the sun is hot and you run the risk of sunburn. Would you ask me for a business case to justify the investment against the possible pain and agony of having to walk around with a burned skin? If so my response would be that any quantification is just a stack of assumptions and thus offers phony security. Would you than conclude that you will not consider the suggestion because if it cannot be quantified it cannot be real?

When it comes to investing in things like (IT) Governance, Risk, Compliance, Security and Control I encounter that line of thinking almost on a daily basis! It even went as far that these days we are trying to accommodate this drive for quantification by models like Return on Security Investment (ROSI). Using the business case tool to create barriers against valuable investment proposals just because it is hard to quantify the (business) value is using a perfectly good tool for evil!

PS. I promised to tell the catch of my business case. As every risk expert (should) know, to assess risk you should not just look at the probability but also to the impact. In this case: The changes of losing all the investment money because there is no more money to double goes down with larger “pockets” but if the risk does occur the amount of money lost increases just as fast. In the example: If the investment money is only 5 euro the change is 50 percent of going broke the risk value, change x impact (5 x 50%) = 2,5. With investment money available for 17 rounds this value calculates to 5.

When you build a spreadsheet (as I have) showing investment requirements and residual risks for different cycle lengths you will find this value starts at 2,5 and increases towards 5 which it approaches ever closer. I learned from experimenting that the value approaches your starting stake so if you start the cycle with 10 euro it closes towards 10, etc. I could probably explain that if I sat down for it but since it is of no particular importance for this story I will leave that for the mathematicians amongst my readers.

To try and explain in a different way: I have a risk of losing euro 655.355 while winning 5 euro per cycle. I would have to play 655.355 / 5 = 131071 cycles to recover the lost investment should the unthinkable happen (18 consecutive losses) since the average number of rounds per cycle is 2 this would mean the roulette table has turned 131071 x 2 = 262142 to win that much money. If you have played that long the change of the unthinkable happening is that much greater. If you wait long enough every risk bigger than zero (no matter how small) will occasionally happen. Unless, off course, you avoid the risk all together (do not play the roulette). I hope this makes sense otherwise just trust me, the system doesn’t work!

**By Arno Kapteyn**