Future: Graham-Buffett Analysis
Formerly Fundamental Analysis.
Input file variables
DE= Debt/Equity = LTD/TSECR= Current Ratio = TCA/TCLEPS= EPS (diluted)BVPS= TSE / n_dilutedDPS= Dividends / n_dilutedROA= NI / TA_avgROE= ROA * (TA/TSE)LA= (AP + ACC)/TAPB= Price/Book
All input data obtained from morningstar.com.
Rule #1: Vigilant management
Management is considered vigilant when they are managing their short-term and long term obligations.
Short-term obligations
Does the company have enough assets to cover short-term liabilities based on the historical current ratio?
\[ \text{current ratio} = \frac{\text{current assets}}{\text{current liabilities}} = CR > 1.5 \]
Apple’s latest current ratio (1.08) is below the 1.5 threshold but has declined since 2009. We should monitor the trend of this ratio going forward.
Long-term obligations
Has management done a good job managing long-term debt based on the historical debt-to-equity ratio?
\[ \frac{\text{Debt}}{\text{Equity}} = \frac{D}{E} < 0.5 \]
Apple’s debt to equity ratio (0.26) is below the 0.5 threshold. The increase from 0 to 0.26 in is due to tax avoidance. Apple has raised debt to pay dividends in order to avoid paying taxes on repatriated funds.
Rule #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.
Rule #3: Stable and understandable growth
To assess the stability and understandability of growth we look at the history of earnings per share (EPS), dividends per share (DPS), and book value per share (BVPS),
Earnings per share (EPS)
EPS took a dip in FY2013. The reason behind the EPS dip is probably worth further investigation.
Dividends per share (DPS)
Apple has just recently started paying dividends explaining the spike in DPS.
Book value per share (BVPS)
BVPS has grown steadily. 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
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:
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.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. \[ SGR = \frac{ROE\times RR}{\mu - \frac{L_0^*}{A}-ROE\times RR}\]
The historical growth rate of book value per share \(\left(BVPS\right)\)
Growth rate estimates
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 18.3243334%. As of 2014.09.19 the analysts forecasted 5 year growth is 12.77%.
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:
\[ DPS_\text{tot} = \frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) \]
Book value per share will grow at the specified growth rate for the next ten years.
\[ BV_{10} = BV_0 (1+g)^{10} \]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 \(PB_{min} \times BV_{10}\):
\[ V_0 =\frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) + \frac{PB_{min} \times BV_0 (1+g)^{10}}{(1+i)^{10}}\]
\(V_{max}\): 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.
\(V_{10}\): 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%. 
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
- We purchase the stock at \(P_0=\) 118.93 today.
- Annual dividends per share will remain constant at \(DPS_0=\) 1.81.
- 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 \(P_0=\) 118.93:
\[ P_0 =\frac{DPS_0}{E[R]}\left(1-\frac{1}{(1+E[R])^{10}}\right) + \frac{PB_{min} \times BV_0 (1+g)^{10}}{(1+E[R])^{10}} \]
## g ER
## IGR 0.1832433 0.1200107
## AVG 0.3260191 0.2508723
## BVPS 0.3883295 0.3085184
## SGR 0.4064843 0.3253523
\(E[R]\) appears to be a linear function of \(g\). It would be interesting to prove that via calculus and the \(P_0\) equation above.
Conclusion (final value estimate)
To assess the current value there are three critical inputs: growth rate, discount rate, and Price-to-Book at the time of sale 10 years from now. Assumptions:
The growth rate is halfway between the analyst five-year annual rate forecast of 12.77% and the internal growth rate of 18.32%. Therefore, g=15.55%.
The discount rate is the average annual return for the business equipment sector from 1927 to 2012 (see EfficientMinds™). Therefore, i=13.85%.
The Price-to-Book ratio 10 years from now will be the minimum of observed P/B ratios. Thus, P/B=3.3.
Current value
Given \(g=\) 15.55%, \(i=\) 13.85%, and \(P/B=\) 3.3, I estimate Apple’s current value (fundamental value) to be: 82.27.
In other words, pay 82.27, watch BVPS grow at \(g=\) 15.55% for 10 years, dividends remaine constant, sell in 10 years at \(P/B=\) 3.3 times book value, and you will earn the required return of \(i=\) 13.85%.
Current expected return given market price
Given \(g=\) 15.55% and current price \(P_0=\) 118.93, I estimate Apple’s expected return to be: 9.49%
In other words, if you pay \(P_0=\) 118.93 today, BVPS grows at \(g=\) 15.55%, dividends remain constant, and you sell in 10 years at \(P/B=\) 3.3 times book value you will earn 9.49%.