Graham-Buffett Analysis
By David J. Moore, Ph.D.
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.
Analysis for MSFT
1. Rule #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?
\[
\text{current ratio} = \frac{\text{current assets}}{\text{current liabilities}} = CR > 1.5
\] 
Latest current ratio is (2.5).
1.2 Long-term obligations
Has management done a good job managing long-term debt based on the historical debt-to-equity ratio?
\[
\frac{\text{Debt}}{\text{Equity}} = \frac{D}{E} < 0.5
\] 
Current debt to equity ratio is (0.23).
2. Rule #2: Long term prospects
What will this company be doing long term? Will it be around 20 years from now? Why?
Insert your narrative here.
3. Rule #3: Stable and understandable growth
Have earnings, book value, and dividends grown steadily? Do you believe the growth rate is sustainable?
To assess growth stability and understandability we look at the history of earnings per share (EPS), dividends per share (DPS), and book value per share (BVPS). 
Insert description here.
4. Rule #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:
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 \(\left(BVPS\right)\)
4.2 Growth rate estimates
AVG is the average of IGR, SGR, and BVPS growth rates.
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:
\[ DPS_\text{tot} = \frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) \]
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: The current value estimate presumes the stock will sell for 3.1 \(\times BV_{10}\) in year 10. A conservative estimate would be the Benjamin Graham Intelligent Investor 1.33. Anything above 1.33 is “too high”" according ot the Benjamin Graham Intelligent Investor approach. A less conservative assumption would be the minimum P/B over the last 10 years.
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 3.1 \(\times BV_{10}\):
\[ V_0 =\frac{DPS_0}{i}\left(1-\frac{1}{(1+i)^{10}}\right) + \frac{PB \times BV_0 (1+g)^{10}}{(1+i)^{10}}\]
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 3.1 \(\times BV\) 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 3.1 \(\times BV\) 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 this stock worth? Good question. That depends on what growth rate you believe will manifest 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 \(P_0=\) 48.42 today.
2. Annual dividends per share will remain constant at \(DPS_0=\) 1.07.
3. The stock will be sold for 3.1 times book value in year 10.
Again, estimates are highly sensitive to the growth rate \(g\) used. Here we set \(i=E[R]\) for numerous growth rates. Given \(P_0=\) 48.42:
\[ P_0 =\frac{DPS_0}{E[R]}\left(1-\frac{1}{(1+E[R])^{10}}\right) + \frac{PB \times BV_0 (1+g)^{10}}{(1+E[R])^{10}} \]
Expected returns vs. growth rate
## g ER
## IGR 0.09831 0.0769
## BVPS 0.13183 0.1074
## AVG 0.14357 0.1181
## SGR 0.20059 0.1708Estimated current value (fundamental value):
29.2
Assumptions:
The growth rate is the internal growth rate of 9.8305%.
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 3.1.