This is the third part of my attempt to peek under Apple's financial reports to see if we can find any of the hidden tidbits we would like: the baked-in goodies for the future, the average price of assorted things, and whatever happened to that hobby of Steve Jobs, the Apple TV. Skim over

part 1 and

part 2 if you haven't.

On to the next report for 08Q1: CDR=816, NCDR=624, TDR=1440 (compare to previous 07Q4: CDR=346, NCDR=290, TDR=636). Once again the increase in CDR must be half of current non-GAAP sales. So 2*(816-346) = 940 is the combined ATV and iPhone sales value. TDR goes from 636 to 1440 from adding this 940 amount and backing out the baked in of 87 from previous periods and the fraction recognized from current sales. That gives us the formula:

636 + 940 - 87 - x = 1440

And we get x=49.5, which is the amount to get recognized from those $940m in sales value for the current quarter. The fraction of GAAP (current) over non-GAAP, 49.5/940 = 5.3% = 1/19 again not too far from the 1/16 (6.25%) if sales had been spread flat along the quarter. Calculating the day of the "center of mass" (91/2-49.5/940*728) we see it lies about a week after the middle of the quarter, making it slightly more back-loaded than the previous. This back-loaded quarter is of course a Christmas quarter, so this is not some great revelation here. It just confirms and reaffirms that the exact way to reconcile the deferred schedules is through daily subscription accounting, and that the 1/16 rule is a relatively good approximation only for a linear quarter, otherwise the non-linearity must be taken into account.

Now we need to figure out the breakdown between ATV and iPhone. Before, we used the fact that the iPhone had had a cut in pricing at a specific date, and the 1M milestone was achieved only 5 days later, which gave us important clues about the likely ASP range and units sold around those dates. This allowed us to check our calculated results against the expected pricing backdrop. But for this quarter we know the iPhone was launched in different markets with pricing varying wildly for different carrier partners and plans. I remember there was a €999 plan (back when the euro/dollar was up above 1.45), and I think another plan in which the iPhone was free? (this is out of memory so I could be wrong). Despite all these pricing plans, I would expect the ASP to come out a little higher than $399 which was the only price in the US where the bulk of sales still came from.

So let's organize what we know:

$940m combined sales value

$49.5m combined recognition from these sales

2315k iPhone units sold

Somewhat over $399 iPhone ASP

$241m total iPhone related revenue

$87m baked-in for recognition from previous periods (81+6 break between iPhone+ATV)

$325 ATV ASP

And we want to determine the separate sales value and recognition for ATV and iPhone. From these we would be able to calculate ATV units (sales/$325) and iPhone ASP (sales/2.3k). Using some variables and equations:

x + y = 940

p + q = 49.5

We might try using the fraction (which measures linearity) as follows:

f(iPhone) = p/x

f(ATV) = q/y

And we might even safely assume that both products had the same linearity because there were no major product introductions or changes in the models (this assumption would not work for the first quarter of iPhone sales for those 2-days of sales because the linearity is obviously very different than ATV). And of course this same linearity would be the one we calculated before, about 5.3%. So we have:

x + y = 940

f*x + f*y = 49.5 (we know f=.053)

Hmm... cool, two unknowns and two equations, right? Well, nice try but it won't work. Look:

f*x + f*y = 49.5

f*(x + y) = 49.5, and substituting x+y=940:

f*(940) = 49.5

f=49.5/940

Which was just what we had done before to get that combined linearity factor. The system is indeterminate when we assume both products have the same linearity. We could guess any value for one variable, and all the others would have a valid solution. Any value for x or y less than 940 determines the other, as well as p and q less than 49.5. In fact this is what we've been doing for the last couple of quarters that we "solved". We simply guessed at the variable we thought we could pin down as best we could by using some outside information. For the last quarter it was trying a range of ATV sales (y) and checking the resulting iPhone ASP against external pricing and an intermediate unit milestone that Apple luckily shared. In the previous quarter, the iPhone launch, we simply assumed ATV linearity was flat (1/16 rule of thumb), and used the very strong non-linearity from the late-in-the-quarter iPhone sales (3/(2*728) =0.002). This allowed us to solve our system for all the variables.

But what could we do now? We know that most of the sales value must come from iPhone. And we know the overall linearity. We could also assume there should be an uptick in ATV sales given this is a Holiday quarter. Taking a shot at a slight sequential increase in ATV sales might give us a pretty good idea of things, but I'm tired of this guessing game of "financial sudoku" (I'm sure you are even more tired of it). So, what then?

Well, here's a promising approach: take the overall sales value and divide by iPhone units. Because iPhone is the main contributor to these sales, this should give a rough estimate for its ASP, but with some ATV component added. Let's introduce u and v variables for iPhone and ATV units, and build that equation:

940/2.315 = 406 = (x+y)/u = x/u + y/u = ASP(iPhone) + ASP(ATV)*v/u

Because the ATV units (v) is very small compared to iPhone units (u) that ratio v/u is a small percentage (2% would represent 46k ATVs), and thus we know the ASP for iPhone should be only a few dollars less than $406. In fact using that 2% generous guess and our $325 ASP for ATV we get .02*325= $6.50 of "ATV froth" in that $406, or a lower limit for iPhone ASP of $399.50. Well, knowing that this was the US pricing and that European pricing was generally higher, I'm pretty sure this is the extreme case. Oh I hear you saying, "but you were tired of guessing!" Sure, but notice how simple and intuitive this aproach made the guessing game: you just divide two known numbers and you get the top limit for iPhone ASP. We could leave it at that if we want, in case we don't care about the measly ATV sales, or if we happen to know some external info about the expected real iPhone ASP or the expected ATV units sold we can easily integrate any of it into our rough number.

So, finishing up this quarter, I'll rather use about 31k ATV units: 31*325 = $10m sales value (y), 940-10 = 930m iPhone sales value (x). For the recognized fraction of these I'll assume the same overall linearity fraction (49.5/940=5.3%) for both products, so we get 10*.053 = 0.5m for ATV and 49.5-0.5 = 49 for iPhone to get recognized from these sales (p and q). Baked-in contribution to the following quarters increases by 10/8 = 1.25m for ATV and 930/8 = 116m for iPhone, and the total has now built up to $204m. Total recognized this quarter for iPhone is 81+49 = $130m, which subtracted from 241 total reported iPhone revenue leaves 111 from carriers and accessories. You could divide this amount into 2.3m units to get $48 other revenue per unit, although this is not the right way to measure carrier payments per user (you'd need to know the size of the installed base paying a contract) but it's still a somewhat insightful approach. The extra "ATV froth" built into that $406 ASP is 325*31/2315 = $4.35, so the real iPhone ASP is $401 and change. So much for all that currency-inflated premium pricing in Europe.

Here's our updated table:

(click on image for larger view) I know you must have a huge headache by now from all this. I'd just like to summarize the approach, a sort of "recipe" when navigating through this chaos, and make some general description of this "simple" method (don't look at me like that) which I'll use going forward. It's like a 5-step program, all based on the DR schedule for the current and previous periods, except for the final step where ASP's would need to get validated against the externally known pricing backdrop:

1. Get the combined sales value for the quarter (call it S) from the DR schedule and previous quarters' data. The formula is:

S/2 = CDR + [total recognized in the fourth-previous quarter] - [previous quarter CDR], or

S = 2*(CDRchg + R[-4]) (CDRchg is the net change in CDR, see R below).

2. Get the the total amount recognized for the quarter (call this R) using the S calculated before and the change in TDR:

R = S + [previous quarter's TDR] - TDR, or R = S - TDRchg (TDRchg is the net change in TDR).

3. Get the amount to get recognized from only the current quarter's sales (call it r) by backing out from R any baked-in revenue recognition from previous periods' sales. This baked-in amount is simply the average of all the S's from the previous 8 quarters, less the r from the very first of those 8. So the formula is:

r = R - (average(S[-8 to -1]) - r[-8]), or r = R - sum(S[-8 to -1])/8 + r[-8]4. Check the quarter's linearity r/S: near zero is a back-loaded quarter, 1/16 is a linear quarter, and near 1/8 is a front-loaded one. Also you could check the "center of mass" of the combined sales: days after mid-quarter = 91/2 - r/S*728. Positive is back-loaded and negative is front-loaded.

5. Calculate S/u to see if this maximum iPhone ASP makes sense. For the other extreme, consider some generous ATV unit sales and subtract this "froth" amount (v/u*(ATV ASP)) from S/u.

Finally (only if you're brave), try to incorporate any info or guesses you may have either about ATV units or the real ASP for iPhone, or anything else that might help. Guessing any one variable will lead you to all the others, even the "other iPhone related revenue," through the following equations:

x = (iPh ASP)*(iPh units)

y = (ATV ASP)*(ATV units)

p = (r/S)*x (unless a product launch suggests a different fraction, e.g. p = x*(days+1)/(2*728))

q = (r/S)*y (same observation, or alternatively consider linear ATV sales: q = y/16)

S = x + y

r = p + q

Where only x, y, p, and q are unknown, but all solvable once any single one of them gets assigned a value. Carriers+accessories can be derived (or even used as a guess to resolve the whole system) by backing out a couple of things from the reported total iPhone revenue: back out baked-in recognition from previous periods' iPhone sales, and back out p. So, calling this other iPhone sales 'o' (stands for "other"):

o = (total iPhone reported revenue) - sum(p[-7 to 0])That's it. For the next part I'm jumping right up to the latest two reports with 3G sales. Here's a final summary of the five calculation steps:

1. S = 2 * ( CDRchg + R[-4] )

2. R = S - TDRchg3. r = R - sum( S[-8 to -1] ) / 8 + r[-8]4. linearity factor = r / S5. max iPhone ASP = S / uIf you read all the way through here, I apologize for the length and please don't bill me for any pain killers you may have needed. Any drinks are on me though!

:D