Graham-Buffett Analysis of TDS

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.

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?

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

The latest current ratio (1.75) 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

The debt to equity ratio (0.42) is below the 0.5 threshold.

2. Rule #2: Long term prospects

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

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 the growth stability and understandability 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

A bumpy ride indeed.

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:

  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. I would lean more towards the IGR of 1.0638%. As of 2014.09.27 the analysts forecasted 5 year growth is 14.00%. I have no idea where those analysts get that number.

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 10 years. The current value estimate presumes the stock will sell for \(PB_{min} \times BV_{10}\) in year 10. That is, \(P/B=\) 0.6 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 this company worth? Good question. That depends on what you believe the 10 year growth rate will be.

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 \(P_0=\) 24.49 today.
2. Annual dividends per share will remain constant at \(DPS_0=\) 0.51.
3. The stock will be sold for 0.6 times book value in year 10. Note: 0.6 is the minimum price-to-book ratio over the past 10 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 \(P_0=\) 24.49:

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

##            g      ER
## IGR  0.01064 0.02347
## SGR  0.02320 0.03488
## AVG  0.02774 0.03903
## BVPS 0.04938 0.05892

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 (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:

  1. Growth will occur at the internal growth rate of g=1.0638%.

  2. The discount rate is the average annual return for the Telecom sector (see EfficientMinds™). Therefore, i=11%.

  3. The Price-to-Book ratio 10 years from now will be the minimum of observed P/B ratios. Thus, P/B=0.6.

Given \(g=\) 1.0638%, \(i=\) 11%, and \(P/B=\) 0.6, I estimate the current value (fundamental value) to be: 11.88 This is well below the current market price of 24.49.