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There are probably a number of reasons that Apple's (AAPL) stock has fallen from $455 on Monday to $429 on Wednesday including hitting resistance levels, rotation into Google (GOOG) and hedge funds reporting that they sold shares in the March quarter (which is actually a good situation since at some point in time they could become buyers).

One other reason that has cropped up is an analysis by David Trainer at New Constructs, which values Apple's shares at $240. From what I have read, Trainer uses a combination of Net Operating Profit After Tax (NOPAT), Return on Invested Capital (ROIC) and its relation to other companies' ROIC to determine a stock price. The table below shows two ways to calculate NOPAT.

Trainer lays out in detail the results of various calculations from 1998 to 2012 and what he labels as Current (which I assume is fiscal 2013) and his calculations for NOPAT, ROIC and various other metrics.

Trainer calculates that Apple's ROIC is 271% and assumes that it can't be maintained since it is so much higher than other companies. While in many ways I agree that numbers that are extreme tend to revert, I don't agree with the net income and cash flow numbers that are the result of his assumption.

Source: New Constructs

Net income Vs. NOPAT analysis

The following table is Apple's Net Income vs. the Trainer's NOPAT calculation from fiscal 2005 to fiscal 2013. From 2005 to 2011, there is less than an 11% or at most a $672 million delta between Apple's reported net income and New Construct's NOPAT calculation.

This doesn't raise any red flags in my view since I expect there to be some differences between Apple's reported net income and Trainer's NOPAT calculation since the NOPAT adjusts for some numbers that are not in GAAP net income calculations.

($ mil)200520062007200820092010201120122013E
Apple Net Income$1,230$2,026$3,496$4,834$7,585$14,013$25,922$41,733$37,011
Source: Company reports and Chuck Jones estimates
New Constructs200520062007200820092010201120122013
NOPAT$1,097$1,809$3,169$4,465$8,184$13,358$25,250$10,827$8,004
$ Delta$133$217$327$369($599)$655$672$30,906$29,007
% of NI89%89%91%92%108%95%97%26%22%
Source: New Constructs

However, what Trainer does is assume that ROIC drops to 70.4% in 2012 and 52% in Current (which I assume is fiscal 2013) to determine a $240 price target.

What this drives in his analysis is that Apple's 2012 NOPAT should be $10.8 billion. However, Apple reported net income of $41.7 billion in fiscal 2012 so since this has already occurred I don't understand why he is using lower results.

Also, Apple reported net income of $13.1 billion in the December 2012 quarter, $9.5 billion in the March 2013 quarter and I am projecting $37 billion for the year. However, in Trainer's analysis he has NOPAT (which is close to net income) of only $8 billion for the year. Unless he is expecting Apple to lose money for the rest of this year, I don't think the analysis makes sense.

Cash Flow Analysis

I thought it would also be worthwhile to compare cash flows since a free cash flow analysis is included in Trainer's analysis. One potential challenge is that cash flows are inherently more volatile than income statements.

In 2005 (13%) and 2006 (39%) there is a fairly wide difference between Apple's reported numbers and Trainer's calculation. However, with smaller numbers this isn't a big concern. Especially since from 2007 to 2011 the numbers are actually pretty close. The deltas range from 1% to 9% with $683 million being the biggest difference.

However similar to net income vs. NOPAT in 2012, the reported cash flows have a large delta vs. Trainer's calculation. I calculate that Apple's free cash flow (net income minus capital expenditure and dividends and stock buybacks) in 2012 was $31.6 billion. Trainer's calculation is a negative $773 million. Again, since this has already occurred, I don't understand why he is using this calculation unless it is to make a point.

For 2013, the delta isn't as wide but is still substantial since I am estimating free cash flow to be over $4.6 billion while Trainer is projecting a negative $(3.6) billion.

($ mil)200520062007200820092010201120122013E
Operating CF$1,328$1,989$3,496$4,834$7,585$14,013$25,922$42,364$37,840
Cap Exp($260)($657)($735)($1,091)($1,500)($2,005)($4,260)($8,295)($10,000)
Dividends$0$0$0$0$0$0$0($2,488)($10,688)
Buybacks$0($355)($3)$0$0$0$0$0($12,500)
Free Cash Flow$1,068$977$2,758$3,743$6,085$12,008$21,662$31,581$4,652
Source: Company reports and Chuck Jones estimates
New Constructs200520062007200820092010201120122013
Free Cash Flow$925$599$2,986$4,088$6,172$12,691$21,004($773)($3,596)
$ Delta$144$378($228)($345)($87)($683)$658$32,355$8,249
% of FCF87%61%108%109%101%106%97%(2)%(77)%
Source: New Constructs

Conclusion

It appears to me that there is a flaw in using an assumption for ROIC to determine a stock price when it results in net income and free cash flows that look to be very different vs. not just what is expected to occur but what has already happened.

Unless one believes that net income and cash flows are going to mirror his calculations (huge downsides), I would take this analysis with a big grain of salt.

Source: David Trainer's $240 Apple Price Target Analysis Just Doesn't Add Up