Why 1% of $10 Billion Is Not $100 Million

I recently had the fortune to conduct a class about entrepreneurship and growing enterprises. Groups of undergraduates would select a company of their choice and apply the lessons learned to help the chosen company grow its revenue.  As the groups took their turns to present, one of them said something like:

“… our growth plan would expand into this related sector which is estimated to be an annual $10 Billion market. Based on a conservative estimate of capturing only 1% of the sector, our plan would promise to raise the company’s revenue by $100 Million …”

Wow, I thought, what a brilliant plan!  The related sector’s worth of $10 Billion was well supported by published figures.  The math was also easy to work out, that 1%, a really conservative and small figure, times $10 Billion would give $100 Million.  It justified the realism of achieving an increase in $100 Million revenue and thus a solid growth plan.  Great Work!

But wait…

Something wasn’t quite right, probably my right brain was murmuring to my left brain which did the math calculations.

Well-known and experienced people had already pointed out and warned that such top-down percentage-of-big-pie reasoning just wouldn’t work in making a convincing argument.  Something in this group’s presentation reminded me strongly of the famous book “Art of the Start” by Guy Kawasaki, in which Guy advised against using such percentage-of-big-pie reasoning.  Just don’t do it – it wouldn’t work.  But I needed a why; why wouldn’t such compelling math be convincing?

So back to the group’s presentation.  A big part of me understood that their argument was quite problematic, based on experience, vicarious wisdom and wide readings.  But I couldn’t quite reason out, and as you know, undergrads don’t take no reason for an answer.  So what should I do?  Do I give them benefit-of-doubt and award a high grade which might cost me half my conscience, or penalize them as it wouldn’t work but risk being chased by the group from campus to home with 24-hr email spamming for an explanation?

I decided to do what I preach – an entrepreneur tends to do first then say “sorry”.  I figured if chased, I could just say “sorry, I believe you could do better”.  Fully expecting it wouldn’t work for the relentless group of students, I could also “prove-by-intimidation” as taught (in jest) by my mathematics professor long ago in UC Berkeley.  I could always say, “Isn’t it obvious?  It’s clear that it wouldn’t work.  Go figure out yourself as part of the learning!”  Alright, that’s exploiting the instructor’s authority, something which I could not really do unless it’s in jest.

So why wouldn’t it really work?

Let’s turn the problem of justifying the capturing of a portion of a $10 Billion market from bottom up.  When the company offers a new product or service to the market, it has to go through at least 6 steps in order to trigger a customer purchase. These are: 

1.   marketing the product,

2.   customer has access to the marketing channel,

3.   customer reads about the product,

4.   customer likes the product,

5.   customer can afford or is willing to spend on the product,

6.   customer actually buys the product. 

Each transition from previous step to the next step involves a probability.  For example, if the company markets the product through television, we ask what is the probability of the targeted customer segment watching television?  Suppose it is 0.10 (or 10% probability).  Of course, we could also use social media, YouTube advertising and other channels for the calculation.  But let’s stick to television as it is easier to imagine.  Though watching television, the customer might not be so coincidentally watching the company’s commercial advertisement exactly when it was shown.  So what is the probability that while watching television at the right channel, the customer reads about the product?  Suppose it is 0.08 for the sake of differentiating from 0.10.

After reading about the commercial, what is the chance that the customer is impressed about the product, thinks about it more, and/or is more inclined to buy it? Let’s say it is 0.06.  As the customer wants to buy the product, s/he might find that the wallet is a bit tight and might postpone it till later.  What is the chance that the customer can afford the product or is willing to pay for it in the immediate future?  Let’s say that probability is 0.04.

Despite clearing all the hurdles above, the convinced customer might, at the point of touching the product, retract from the desire to purchase immediately due to various reasons like packaging, color, shop where it is sold, neighboring competitor’s product on the shelf looking more attractive, other alternatives popping up at the customer, etc.  So what is the probability that the customer actually buys the product?  Let’s say it is 0.02.

So now we ask, after marketing campaign is launched, what is the probability that an average customer in the targeted market will actually buy the product and hence contribute to the desired growth in revenue?  The answer is 0.10 x 0.08 x 0.06 x 0.04 x 0.02 = 0.000000384.  For an annual $10 Billion market, the expected revenue that can be captured would be 0.000000384 x $10 B = $3,840 per year!

What if we are way more optimistic and set all probabilities to 0.10 (ie 10% chance for all questions).  That would give us 0.10 x 0.10 x 0.10 x 0.10 x 0.10 = 0.00001, resulting in $100,000 per year.  While a lot more, it is still a far cry from the claim of $100 Million. This is also not forgetting that although we listed 5 stages of probabilities, there could be more stages of probabilities that would serve only to reduce, not increase, the resulting expected revenue.

No wonder great business plans showing millions of dollars of revenue blow up in smoke upon launching!

As for the team who gave that presentation?  Fortunately, they had not come chasing me for an explanation yet.  But if they did, I could always use “proof-by-LinkedIn-article” and ask them to refer to this page!

Chin Chee Kai