In this article, let´s consider a giant that went public a decade ago, Apple Inc. (NASDAQ:AAPL). The $593 billion market cap has a trailing P/E ratio that indicates that the stock is relatively undervalued (PE 15.6x vs Industry Median 30.2x).
So in this article, let's take a look at a model which is applicable to stable, mature, dividendpaying 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, it is by no means the beall and endall 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.
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 AAPL 15Year Financial Data
 The intrinsic value of AAPL
 Peter Lynch Chart of AAPL
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 ThreeStage growth model or the HModel (which is a special case of a twostage 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))/(rg)=D1/(rg)
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 = riskfree rate + beta of j x equity risk premium
Assumptions:
RiskFree 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 =0.74
GGM equity risk premium = (1year forecasted dividend yield on market index) +(consensus longterm earnings growth rate) – (longterm government bond yield) = 2.13% + 11.97%  2.67% = 11.43%[1]
rAAPL = RF + βAAPL [GGM ERP]
= 4.9% + 0.74 [11.43%]
= 13.36%
Dividend growth rate (g)
The sustainable growth rate is the rate at which earnings and dividends can grow indefinitely assuming that the firm´s debttoequity 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 IncomeDividends)/(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) 
Sept. 2013 
Sept. 2012 
Sept. 2011 
Cash dividends declared 
10,564,000 
2,488,000 
 
Net income applicable to common shares 
37,037,000 
41,733,000 
25,922,000 
Net sales 
170,910,000 
156,508,000 
108,249,000 
Total assets 
207,000,000 
176,064,000 
116,371,000 
Total Shareholders' equity 
123,549,000 
118,210,000 
76,615,000 
Ratios 

Retention rate 
0.71 
0.94 
1.00 
Profit margin 
0.22 
0.27 
0.24 
Asset turnover 
0.83 
0.89 
0.93 
Financial leverage 
1.71 
1.81 
1.87 
Retention rate = (Net Income – Cash dividends declared) ÷ Net Income = 
0.71 

Profit margin = Net Income ÷ Net sales = 
0.22 

Asset turnover = Net sales ÷ Total assets = 
0.83 

Financial leverage = Total assets ÷ Total Shareholders' equity = 
1.68 

Averages 

Retention rate 
0.89 

Profit margin 
0.24 

Asset turnover 
0.88 

Financial leverage 
1.80 

g = Retention rate × Profit margin × Asset turnover × Financial leverage 

Dividend growth rate 
33.78% 

The retention ratio is the proportion of earnings kept back in the business as retained earnings. An alternative way to define the ratio, is that it is the opposite of the payout ratio, which measures the percentage of earnings paid out to shareholders as dividends. It is 100% for companies that do not pay dividends and 0% for companies that pay out their entire net income as dividends. So in this case that it is negative, it means that the company is paying more than what actually earns, taking the cash of its retained earnings.
Because for most companies, the GGM is unrealistic, let´s consider the HModel which assumes a growth rate that starts high and then declines linearly over the high growth stage, until it reverts to the longrun rate. A smoother transition to the mature phase growth rate that is more realistic.
Dividend growth rate (g) implied by Gordon growth model (longrun rate)
With the GGM formula and simple math:
g = (P0.r  D0)/(P0+D0)
= ($97.98 ×13.36% – $1.88) ÷ ($97.99 + $1.88) = 11.22%.
The growth rates are:
Year 
Value 
g(t) 
1 
g(1) 
33.78% 
2 
g(2) 
28.14% 
3 
g(3) 
22.50% 
4 
g(4) 
16.86% 
5 
g(5) 
11.22% 
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 
1.88 

1 
Div 1 
2.52 
2.22 
2 
Div 2 
3.22 
2.51 
3 
Div 3 
3.95 
2.71 
4 
Div 4 
4.61 
2.79 
5 
Div 5 
5.13 
2.74 
5 
Terminal Value 
267.45 
142.88 
Intrinsic value 
155.86 

Current share price 
97.98 
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%). We found that intrinsic value is almost 60% higher than share price, so we can conclude that the stock is undervalued and it makes sense to buy the stock if you trust in the model and assumptions.
We have covered just one valuation method and investors should not rely only on one to determine a fair (over/under) value for a potential investment. Hedge fund gurus have also been active in the company. Gurus like Leon Cooperman, John Burbank, Andreas Halvorsen and Paul Tudor Jones bought the stock in the second quarter of 2014.
Disclosure: Omar Venerio holds no position in any stocks mentioned.
[1] This values where obtained from Blommberg´s CRP function.