Graham-Buffett Analysis of Apple, Inc.

By David J. Moore, Ph.D.

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Rule #1: Vigilant management

Management is considered vigilant when they are managing their long-term \( \left(\frac{\text{Debt}}{\text{Equity}} = \frac{D}{E} < 0.5 \right) \) and short-term \( \left( \text{current ratio} = \frac{\text{current assets}}{\text{current liabilities}} = CR > 1.5\right) \) obligations.

Apple's D/E ratio looks fine but the current ratio has been approaching the limit lately.

Rule #2: Long term prospects

At the moment we do not have quantifiable measures for long-term prospects. You could pontificate and say given consumers' continued willingness to stand in long lines for a phone with minimal changes means Apple will be around.

Rule #3: Stable and understandable growth

To assess the stability and understandability of Apple's growth we look at the history of book value per share (BVPS), earnings per share (EPS), and dividends per share (DPS).

BVPS has grown steadily. EPS took a dip in FY2013. The reason behind the EPS dip is probably worth further investigation. Apple has just recently started paying dividends explaining the spike in DPS. In sum, Apple does appear to have stable growth but concern about sustained earnings growth is warranted. It does not seem likely that stratospheric growth can be sustained.

Rule #4: Undervalued

The first step in determining whether or not a company is overvalued is to estimate the growth rate over the next 10 years. Here the growth rate is estimated three ways:
1. The historical growth rate of book value per share \( \left(BVPS\right) \)
2. The internal growth rate \( \left(IGR\right) \), i.e., the maximum the company can grow using internal and internally generated funds.
\[ IGR = \frac{ROA\times RR}{\mu - \frac{L_0^*}{A}-ROA\times RR} \] where \( \mu \) is the capacity utilization (currently set to 1 or 100%), \( L_0^*=AP+ACC \), \( A \) is total assets, and \( RR=1-DPR \) is the retention ratio.
3. The sustainable growth rate \( \left(SGR\right) \), i.e., the maximum the company can grow with borrowing but not exceeding the current debt-to-equity ratio. \[ SGR = \frac{ROE\times RR}{\mu - \frac{L_0^*}{A}-ROE\times RR} \]

Growth rate estimates

AVG_ISB is the average of IGR, SGR, and BVPS growth rates. Personally, I don't think Apple will average 20% annual growth over the next 10 years. This is where the real guesswork comes into play. What do you think Apple's growth rate will average over the next 10 years?

Growth rate vs. value

The following chart is based on the following Graham-Buffet model assumptions:
1. Dividends per share will remain constant.
The present value of 10 years of constant dividend payments can be calculated as the present value of an annuity:
\[ DPS_\text{tot} = \frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) \]
2. Book value per share will grow at the specified growth rate for the next ten years.
\[ BV_{10} = BV_0 (1+g)^{10} \]
3. The current value estimate presumes the stock is worth the book value in year 10. That is, \( P/B=1 \) at the time of the hypothetical sale in year 10. This is a conservative assumption given most stocks trade at \( P/B >1 \).

The G-B value estimate is sum of \( DPS_\text{tot} \) (which is the present value of the dividend “annuity'') and the present value of \( BV_{10} \):
\[ V_0 =\frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) + \frac{BV_0 (1+g)^{10}}{(1+i)^{10}} \]

The chart below reports two values, \( V_{max} \) and \( V_{10} \) for each growth rate estimate. \( V_{max} \) is the maximum value of the stock. At \( V_{max} \) you are better off purchasing a ten year Treasury Bond because it will produce the same return with no risk. \( V_{10} \) is the value at which you expect to earn 10% annual return on your investment if the three assumptions above hold true. Now for the graph.

So how much is Apple worth? Good question. That depends on what growth rate you believe Apple will realize over the next 10 years.

Expected return \( E[R] \) given the current price \( P_0 \)

Given an investor is a price-taker (you can't set prices for stocks) it is informative to estimate your expected return given the current market price. This is done by solving the GB value equation for \( i \).
Since we are using the actual market price \( P_0 \) in this equation \( i \) represents the expected return if
1. We purchase the stock at \( P_0 \) today, and
2. The three GB assumptions above hold true over the next ten years.
Again, estimates are highly sensitive to the growth rate \( g \) used. Here we compute \( E[R]=i \) for numerous growth rates. Given \( P_0= \) 556.18:

\[ P_0 =\frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) + \frac{BV_0 (1+g)^{10}}{(1+i)^{10}} \]

##           g       ER
## life 0.0667 -0.04655
## IGR  0.2013  0.05806
## AVG  0.3341  0.16759
## SGR  0.3902  0.21482
## BVPS 0.4107  0.23210

\( E[R] \) appears to be a linear function of \( g \). It would be interesting to prove that via calculus and the \( P_0 \) equation above.