How many iPad minis did Apple sell? 12.5 million

Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everyone gets busy on the proof  — John Kenneth Galbraith

When Apple announced iPad mini I wrote in GigaOm,

At the high end, Apple could sell as many as 58 million (full year), but those chances are very very slim (1 percent). Considering all the possible scenarios, the expected value of volume is 40 million.

Apple released its Q1FY13 earnings today, let us estimate how many iPad minis Apple most likely sold. The iPad mini numbers are based on the Apple‘s report.

appleQ1_ipadThey sold a total of 22.8 million iPads (new iPad, iPad2 and iPad mini), compared to 14.03 million in the previous quarter (pre iPad mini). If you were to attribute all incremental volume to iPad mini it comes to 8.77 million. I could stop here and say my model is correct.

If you compare the Average Selling Price (ASP) between two periods, in Q4FY12 the iPad ASP (iPad and iPad2) was $508 but it dropped to $467 this quarter (Q1FY13).

ipad_mini_q1So let us plug in these numbers into the model I recently built to estimate the number of iPad minis Apple sold. We find that the 8.77 million is actually the lower limit. With the assumptions I have made, Apple likely sold 12.5 million iPad minis (all editions combined).

Apple put on some impressive iPad mini numbers. Did it cannibalize its full priced iPad? You bet it did. Last quarter Apple sold about 9.84 million full size iPad. (Again see the model.) That number dropped to 7.42 million units, thanks to iPad mini. So a cannibalization of 2.42 million units  — that is 2.42 million people who would’ve chosen full size iPad chose iPad mini.

How did I do with my previous prediction of iPad mini numbers in my GigaOm article?

I predicted an annual expected volume (considering all possible scenarios) of 40 million. But Apple could end up selling at least 50 (4 times 12.5) million iPad minis in FY13.

What did my model say were the chances of selling 50 million (full year) units or more?

Mere 12%.

As Galbraith said I could get busy arguing that is still within my scenarios and I am still correct. Galbraith’s writings have influenced my thought process in many ways, I will note his warning and not get busy with my proof.

It indeed appears I had started with some overly conservative numbers on iPad mini uptake based on the survey results I had used. Hence my model underestimated the iPad mini volumes considerably as iPad mini yearly volume could be 50-60 million units.

Model is only as good as the informed input we start with. After all we are paid to make better hypotheses and make informed assumptions.

 

 

 

 

Apple Playing High Risk Game with iPad mini – Monte Carlo Analysis

It appears iPad mini (or whatever branding Apple comes up with for their 7″ tablet) is real. Apple did announce an event for October 23rd which is highly likely the iPad mini event.

I have written about the profit impact of the iPad mini and so did many others. (See my longer piece at GigaOm.)
Many take the approach

  1. Apple will sell 10s of millions of iPad mini before Holidays
  2. iPad mini is a market share game
  3. There will be cannibalization but it is better to self-cannibalize
  4. There will be so much new volume from lower price point of iPad mini that Apple will capture marker share
  5. iPod Touch is a different product category and it will not be impacted by iPad Mini

My question has been centered around whether or not the new device will deliver incremental (net new). No one has done some real analysis to show what the impact is. Even my article stopped short of exact numbers. Articles by others (of course) are even worse, they expect us to believe on faith that Apple will do well with iPad mini.

Now there is some real answer, based on more rigorous analysis than just claims that self-cannibalization is better.

My analysis, using statistical modeling, shows Apple may end up selling 22-52 million iPad minis but is placing a high risk bet when it comes to profit. Let us start from the beginning.

As I did before for Pinterest revenue model I chose to do Monte Carlo analysis to find impact on Apple’s profits from iPad mini. This is a reliable tool to use when there are many variables and there is uncertainty in the result. It also helps to state the result as a probability distribution instead of absolute statements we see from some of the analysts.

The model starts with listing the different variables that feed into final result and their 90% confidence interval values. That is we list all the different variables and state the low and high values that we are 90% confident about (we are 90% confident the real value is between low and high and only 10% chance the real value is outside this range).

I am going to assume contribution margin from iPad is $225 (given its 40%-50% margin numbers stated by iSuppli and others). All volume numbers are for the full year. The trade-down numbers and the “steal” numbers come from a recent market research on iPad mini preference. Steal here means how many of current nook/Kindle/nexus customers will switch to iPad mini. New sales is the number of new customers entering the market because of iPad mini. Current iPad volume numbers are based on Apple’s past four earnings reports.

It is easy to see that

Total iPad mini sales = Trade-down volume + Steal +New sales

Profit from iPad mini = iPad Mini margin X Total iPad mini sales

Lost profit from Trade-down = iPad Margin X Trade-down volume

Net new profit = Profit from iPad mini  – Lost profit from Trade-down

Note that I ignored the effect on other products both iPod Touch and iPhone.

Running the model for 1600 iterations yields some stunning results.

First the total iPad mini volume numbers. These are huge. It is almost certain that Apple will sell at least 14 million units per year. There is 95% probability that they will sell somewhere between 22 million and 52 million iPad mini.  And considering all possible scenarios the expected volume is 35 million units. These kind of numbers blow out the ramp up curves we have seen with any of the electronics products.

Such numbers will bring smile to those who chase market share and will delight analysts who recommend chasing market shares. But what does that do to Apple’s profit?

Here is the big surprise. Despite huge volumes, profit estimates show Apple is playing a high risk game with iPad mini.

First there is a 47% chance Apple will lose money (not including fixed costs, just the marginal costs, so the real impact can be worse).

At its worst, there is 1% chance that Apple could see $2.2B drop in its gross profit. It does not get much better, there is 15% chance Apple could see $1 B drop in its profit.

At the other end there is only 1% chance they could make $2.3B additional profit and only 13% chance they could see $1B additional profit.

Considering all possible scenarios, the expected net new profit from iPad mini is just $97 million a year.

That is not a big enough considering other R&D and marketing expenses (fixed costs).

There you have it. Apple will likely sell 34 million units in the first year but runs the risk of seeing no impact or worse significant impact on its profit.

Analysts betting on Apple stocks, thinking iPad mini will a few dollars to their EPS, take note. iPad mini is a high risk game for Apple despite assured high volumes.

What are the chances mom will be home when we arrive and what does this have to do with Pinterest revenue?

Update: This article will help you understand my Gigaom guest post on Pinterest revenue: How much does Pinterest actually make?

One of the games my 7 year old and I play while driving home from her school is guessing whether mom will be home when we arrive.

I ask,”what are chances mom will be home when we arrive?”
She would almost always reply, “50-50”
Not bad for someone just learning enumerating the possibilities and finding the fraction. When we arrive home there is either mom or not. So 50-50 seem reasonable.

But are the chances really 50-50? If not how would we find it?

Well let us start with some safety and feel good assumptions, my drive time is constant, there is mom, she always leaves at fixed time and she will arrive.
Other than that we need to know

  1. What time is it now?
  2. What is her mean drive time?
  3. What is the standard deviation of drive time?

Assume that the drive times are normally distributed with the stated mean and standard deviation. It is then a question of finding, in what percentage of the scenarios the drive times show an earlier arrival time. That is the probability we were looking for and it is not 50-50 simply because there are only two outcomes.

Here we did a very simple model. But who knows what the mean is let alone standard deviation. We do not. So we do the next best thing, we estimate. We do not literally estimate the mean and standard deviation but we estimate  a high and the low value such that in 90% of the cases the drive time falls in that range. Stated another way, only 10% chance the drive time is outside this range.

This is the 90% confidence interval.We are 90% confident the value is in this interval. Once we have this then it is more simple math to find the mean and standard deviation.

Mean  is average of the low and high values. 
Standard deviation is the difference between high and low divided by number of standard deviations the 90% probability corresponds to  in a standard normal curve (3.29σ).

One you have the mean and standard deviation you can do the math to find the percentage of scenarios where drive time is below certain value.

This is still simple. We treated drive time as the measurable quantity and worked with it. But drive time is likely made up of many different components, each a random variable of its own. For instance time to get out of parking lot, time to get on the highway, etc.  There is also the possibility the start time is no more fixed and it varies.

(If you want to build more realistic model you should also model my drive time as random variable with its own 90% confidence interval estimate. But let us not do that today.)

In such a case  instead of estimating the whole we estimate our 90% confidence intervals of all these parts. In fact this is a better  and preferred approach since we are estimating smaller values for which we can make better and tighter estimates than estimating total drive time.

How do we go from 90% confidence interval estimates of these component variables to the estimate of drive time? We run a Monte Carlo simulation to build the normal distribution of the drive time variable based on its component variables.

This is like imagining driving home 10,000 times.  For each iteration randomly pick a value for each one of the component variable based on their normal distribution (mean and sigma) and add them up:

drive time (iteration n) = exit time (n) + getting to highway time (n) + …

Once you have these 10,000 drive times then find what percentage of the scenarios have drive time less than certain value. That is the probability we were looking for.

From this we could say, “there is 63% chance mom will be home when we arrive”.

We could also say, “there is only 5% chance mom will arrive 30 minutes after we arrive”.

When we know there is roadwork starting on a segment we can add another delay component (based on its 90% confidence interval) and rerun the simulation.

That is the power of statistical modeling to estimate any unknowns based on our initial estimates and state our level of confidence on the final answer.

Now what does this have to do with Pinterest revenue?

Read my article in Gigaom

Protected: Only one in three chance Pinterest makes more than $10 million a year

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