In this article, let´s take a look at CenturyLink, Inc. (CLT, Financial), a $23.64 billion market cap, which is an integrated communications company, engaged primarily in providing an array of communications services to its residential, business, governmental and wholesale customers.
So in this article, let's take a look at a model which is applicable to stable, mature, dividend-paying firms and try to find the intrinsic value of the stock. Although the model has a number of characteristics that make it useful and appropriate for many applications, is by no means the be-all and end-all for valuation. The purpose is to force investors to evaluate different assumptions about growth and future prospects.
Valuation
In stock valuation models, dividend discount models (DDM) define cash flow as the dividends to be received by the shareholders. Extending the period indefinitely, the fundamental value of the stock is the present value of an infinite stream of dividends according to John Burr Williams.
Although this is theoretically correct, it requires forecasting dividends for many periods, so we can use some growth models like: Gordon (constant) growth model, the Two or Three stage growth model or the H-Model (which is a special case of a two-stage model).With the appropriate model, we can forecast dividends up to the end of the investment horizon where we no longer have confidence in the forecasts and then forecast a terminal value based on some other method, such as a multiple of book value or earnings.
To start with, the Gordon Growth Model (GGM) assumes that dividends increase at a constant rate indefinitely.
This formula condenses to: V0 = (D0 (1+g))/(r-g)=D1/(r-g)
where:
V0 = fundamental value
D0 = last year dividends per share of Exxon's common stock
r = required rate of return on the common stock
g = dividend growth rate
Let´s estimate the inputs for modeling:
Required Rate of Return (r)
The capital asset pricing model (CAPM) estimates the required return on equity using the following formula: required return on stockj = risk-free rate + beta of j x equity risk premium
Assumptions:
Risk-Free Rate: Rate of return on LT Government Debt: RF = 2.67%. This is a very low rate because of today´s context. Since 1900, yields have ranged from a little less than 2% to 15%; with an average rate of 4.9%. So I think it is more appropriate to use this rate.
Beta: β =0.57
GGM equity risk premium = (1-year forecasted dividend yield on market index) +(consensus long-term earnings growth rate) – (long-term government bond yield) = 2.13% + 11.97% - 2.67% = 11.43%[1]
rCTL = RF + βCTL [GGM ERP]
= 4.9% + 0.57 [11.43%]
= 11.42%
Dividend growth rate (g)
The sustainable growth rate is the rate at which earnings and dividends can grow indefinitely assuming that the firm´s debt-to-equity ratio is unchanged and it doesn´t issue new equity.
g = b x ROE
b = retention rate
ROE = (Net Income)/Equity= ((Net Income)/Sales).(Sales/(Total Assets)).((Total Assets)/Equity)
The “PRAT” Model:
g= ((Net Income-Dividends)/(Net Income)).((Net Income)/Sales).(Sales/(Total Assets)).((Total Assets)/Equity)
Let´s collect the information we need to get the dividend growth rate:
| Financial Data (USD $ in millions) | Dec. 2013 | Dec. 2012 | Dec. 2011 |
| Cash dividends declared | 1,301,000 | 1,811,000 | 1,556,000 |
| Net income applicable to common shares | (239,000) | 777,000 | 573,000 |
| Net sales | 18,095,000 | 18,376,000 | 15,351,000 |
| Total assets | 51,787,000 | 53,940,000 | 56,044,000 |
| Total Shareholders' equity | 17,191,000 | 19,289,000 | 20,827,000 |
| Ratios | Â | Â | Â |
| Retention rate | 6.44 | -1.33 | -1.72 |
| Profit margin | -0.01 | 0.04 | 0.04 |
| Asset turnover | 0.35 | 0.34 | 0.27 |
| Financial leverage | 2.84 | 2.69 | 3.68 |
| Â | Â | Â | Â |
| Retention rate = (Net Income – Cash dividends declared) ÷ Net Income = | 6.44 | ||
| Â | Â | Â | Â |
| Profit margin = Net Income ÷ Net sales = | -0.01 | Â | Â |
| Â | Â | Â | Â |
| Asset turnover = Net sales ÷ Total assets = | 0.35 | Â | Â |
| Â | Â | Â | Â |
| Financial leverage = Total assets ÷ Total Shareholders' equity = | 3.01 | Â | |
| Â | Â | Â | Â |
| Averages | Â | Â | Â |
| Retention rate | 1.13 | Â | Â |
| Profit margin | 0.02 | Â | Â |
| Asset turnover | 0.32 | Â | Â |
| Financial leverage | 3.07 | Â | Â |
| Â | Â | Â | Â |
| g = Retention rate × Profit margin × Asset turnover × Financial leverage | Â | ||
| Â | Â | Â | Â |
| Dividend growth rate | 2.47% | Â | Â |
| Â | Â | Â | Â |
Because for most companies, the GGM is unrealistic, let´s consider the H-Model which assumes a growth rate that starts high and then declines linearly over the high growth stage, until it reverts to the long-run rate. A smoother transition to the mature phase growth rate that is more realistic.
Dividend growth rate (g) implied by Gordon growth model (long-run rate)
With the GGM formula and simple math:
g = (P0.r - D0)/(P0+D0)
= ($41.47 × 11.42% – $2.16) ÷ ($41.47 + $2.16) = 5.9%.
The growth rates are:
| Year | Value | g(t) |
| 1 | g(1) | 2.47% |
| 2 | g(2) | 3.33% |
| 3 | g(3) | 4.19% |
| 4 | g(4) | 5.04% |
| 5 | g(5) | 5.90% |
G(2), g(3) and g(4) are calculated using linear interpolation between g(1) and g(5).
Calculation of Intrinsic Value
| Year | Value | Cash Flow | Present value |
| 0 | Div 0 | 2.16 | Â |
| 1 | Div 1 | 2.21 | 1.99 |
| 2 | Div 2 | 2.29 | 1.84 |
| 3 | Div 3 | 2.38 | 1.72 |
| 4 | Div 4 | 2.50 | 1.62 |
| 5 | Div 5 | 2.65 | 1.54 |
| 5 | Terminal Value | 50.89 | 29.64 |
| Intrinsic value | Â | Â | 38.36 |
| Current share price | Â | Â | 41.47 |
Final Comment
Using a margin of safety, one should buy a stock when it is worth more than its price on the market (plus a margin: I recommend 20%). In this case, we found that intrinsic value is about 8% lower than share price, but it is not enough to conclude that the stock is over/undervalued and it makes sense to conclude that the stock is fairly valued if you trust in the model and assumptions.
We have covered just one valuation method and investors should not be relied on alone in order to determine a fair (over/under) value for a potential investment.
While Jim Simons (Trades, Portfolio) added the stock, Mario Gabelli (Trades, Portfolio) and Ray Dalio (Trades, Portfolio) have sold it in the second quarter of 2014. Other gurus like Joel Greenblatt (Trades, Portfolio) and David Dreman (Trades, Portfolio) added the stock in that time frame.
Disclosure: Omar Venerio holds no position in any stocks mentioned.
[1] This values where obtained from Blommberg´s CRP function.
