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Ten Years Earlier or Later, I Will Continue Recommending Apple

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, 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, it 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 =0.74

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]

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 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) 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 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)

= (\$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.

ovenerio
Omar Venerio is capital markets, derivatives, corporate finance and financial management professor. He is passionate about the stock market and providing independent fundamental research and hedge fund and insider trading-focused investigation.

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