Graham-Buffett Analysis of Apple, Inc.

By David J. Moore, Ph.D.

0. Input file variables

Var Description
DE Debt/Equity = LTD/TSE
CR Current Ratio = TCA/TCL
EPS EPS (diluted)
BVPS TSE / n_diluted
DPS Dividends / n_diluted
ROA NI / TA_avg
ROE ROA * (TA/TSE)
LA (AP + ACC)/TA
PB Price/Book

All input data obtained from morningstar.com.

1. Vigilant management

Management is considered vigilant when they are managing their short-term and long term obligations.

1.1 Short-term obligations

Does the company have enough assets to cover short-term liabilities based on the historical current ratio?

\[ \text{current ratio} = \frac{\text{current assets}}{\text{current liabilities}} = CR > 1.5 \] plot of chunk CR

Apple’s latest current ratio (1.47) is below the 1.5 threshold but has declined since 2009. We should monitor the trend of this ratio going forward.

1.2 Long-term obligations

Has management done a good job managing long-term debt based on the historical debt-to-equity ratio?

\[ \frac{\text{Debt}}{\text{Equity}} = \frac{D}{E} < 0.5 \] plot of chunk DE

Apple’s debt to equity ratio (0.24) is below the 0.5 threshold. The increase from 0 to 0.24 in is due to tax avoidance. Apple has raised debt to pay dividends in order to avoid paying taxes on repatriated funds.

2. Long term prospects

What will this company be doing long term? Will it be around 20 years from now? Why?

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. I do anticipate apple being around 20 years from now. With $130B plus on the books they should be okay.

3. Stable and understandable growth

Have earnings, book value, and dividends grown steadily? Do you believe the growth rate is sustainable?

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). plot of chunk EPS plot of chunk BVPS plot of chunk 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.

4. Undervalued

4.1 Growth rate estimation methods

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 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.

  2. 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. \[ SGR = \frac{ROE\times RR}{\mu - \frac{L_0^*}{A}-ROE\times RR}\]

  3. The historical growth rate of book value per share \(\left(BVPS\right)\)

4.2 Growth rate estimates

plot of chunk growthPlot AVG_ISB is the average of IGR, SGR, and BVPS growth rates. Personally, I don’t think Apple will average 30% 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? I would lean more towards the IGR of 17.4657%. Currently, analysts forecast 5 year growth at 12.90%.

4.3 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:
\[ DPS_\text{tot} = \frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) \]

  1. Book value per share will grow at the specified growth rate for the next ten years.
    \[ BV_{10} = BV_0 (1+g)^{10} \]

  2. 2014.08/25 update: Let \(PB_{min}\) represent the mininmum Price-to-Book ratio over the past 12 years. The current value estimate presumes the stock will sell for \(PB_{min} \times BV_{10}\) in year 10. That is, \(P/B=\) 3.3 at the time of the hypothetical sale in year 10. This is a conservative assumption given this history of the stock’s P/B ratio. However, anything above 1.33 is “too high”" according ot the Benejamin Graham Intelligent Investor approach.

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 \(PB_{min} \times BV_{10}\):
\[ V_0 =\frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) + \frac{PB_{min} \times BV_0 (1+g)^{10}}{(1+i)^{10}}\]

4.3.1 \(V_{max}\): Maximum value of the stock

If you purchase the stock for \(V_{max}\), dividends remain constant for the next 10 years, and you sell the stock for \(P_{min}\times BV\) in year 10 you will earn the same annual rate as a 10 year Treasury Bond \(Rf=\) 2.4%. At \(V_{max}\) you are better off purchasing a ten year Treasury Bond because it will produce the same 2.4% return with no risk. Paying more than \(V_{max}\) you can expect to earn less than the Treasury Bond’s 2.4% return.

4.3.2 \(V_{10}\): Maximum amount to pay in order to earn 10%

If you purchase the stock for \(V_{10}\), dividends remain constant for the next 10 years, and you sell the stock for \(P_{min}\times BV\) in year 10 you will earn 10% annual return on your investment. Paying more than \(V_{10}\) you can expect to earn less than 10%. plot of chunk valuePlot So how much is Apple worth? Good question. That depends on what growth rate you believe Apple will realize over the next 10 years.

4.4 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 \(P_0=\) 101.54 today.
2. Annual dividends per share will remain constant at \(DPS_0=\) 1.78.
3. The stock will be sold for 3.3 times book value in year 10. Note: 3.3 is the minimum price-to-book ratio over the past 12 years of data.

Again, estimates are highly sensitive to the growth rate \(g\) used. Here we set \(i=E[R]\) for numerous growth rates. Given \(P_0=\) 101.54:

\[ P_0 =\frac{DPS_0}{E[R]}\left(1-\frac{1}{(1+E[R])^{10}}\right) + \frac{PB_{min} \times BV_0 (1+g)^{10}}{(1+E[R])^{10}} \]

##           g     ER
## IGR  0.1747 0.1372
## AVG  0.3040 0.2582
## SGR  0.3459 0.2977
## BVPS 0.3915 0.3409

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

Conclusion

AAPL is overvalued at \(P_0 = \) $101.54

Since no one knows the future, the best we can do is estimate with the following assumptions:

  1. Book value per share will grow at \(g=\) 15.18% over the next 10 years. This growth rate is the average of IGR and the analysts’ five year forecast. Thus \(BV_{10} = \) $83.03.

  2. The stock will be sold at the end of ten years for $274. This represents the the book value in year 10 ($83.03) multiplied by the mininimum historical Price-to-Book ratio (3.3).

  3. Dividiends per share will remain constant at $1.78.

  4. The appropriate discount rate is \(i=\) 13.85%. This number represents the average annual return for the “Business Equipment” sector from 1927 to 2012. For more details see my EfficientMinds™ analysis of industry returns.

Given these assumptions Apple’s fundamental value is \(V_0 =\) $84.23. This is lower than the current market value of $101.54. Therefore Apple is currently overvalued. But wait! Does that mean it is a bad deal?

Expect a return of 11.61% at current price \(P_0 = \) $101.54

Again, no one knows the future. We estimate with the following assumptions:

  1. Book value per share will grow at \(g=\) 15.18% over the next 10 years. This growth rate is the average of IGR and the analysts’ five year forecast. Thus \(BV_{10} = \) $83.03.

  2. The stock will be sold at the end of ten years for $274. This represents the the book value in year 10 ($83.03) multiplied by the mininimum historical Price-to-Book ratio (3.3).

  3. Dividiends per share will remain constant at $1.78.

  4. You pay $101.54 for Apple today.

Given these assumptions you Apple’s expected return over the next 10 years is 11.61%.

So is AAPL a good deal now?

It depends.

Perspective 1: You are comfortable with (1) the assumptions, (2) the level of risk involved, and (3) the expected return of 11.61%. Yes, AAPL is a good deal now at \(P_0\) = $101.54.

Perspective 2: You are comfortable with the assumptions but think AAPL should return 13.85% given the level of risk. No, AAPL is not a good deal now. Wait for it to drop to $84.23, buy at that price, and expect 13.85% return.