Damian Illia

# Valuation of Wal-Mart 's Common Stock Using Dividend Discount Model (DDM)

Wal-Mart Stores Inc. (NYSE:WMT) is the largest retailer in North America. It operates retail stores in various formats worldwide, a chain of over 10,000 discount department stores, wholesale clubs, supermarkets and supercenters. The company operates in three segments: Walmart U.S. (59.0% of the company´s sales in fiscal 2013), Wal-Mart International (29%) and Sam's Club (12%).

Valuation

In stock valuation models, dividend discount models (DDM) define cash flow as the dividends to be received by the shareholders. The advantages are: 1) theoretically justified and 2) dividends are less volatile than earnings or free cash flow.

Where:

Vo = fundamental value

Di = dividends expected to be received at the end of each year i

Pn = Price of sale

r = required return on equity

n = holding period

Extending the period indefinitely, the fundamental value of the stock is the present value of an infinite stream of dividends, getting the John Burr Williams´s original DDM formula:

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.

The Gordon Growth Model (GGM) assumes that dividends increase at a constant rate indefinitely.

where:

V0 = fundamental value

D0 = last year dividends per share of Walmart's common stock

r = required rate of return on the common stock

g = dividend growth rate

1. Required Rate of Return (r)

The capital asset pricing model (CAPM) estimates the required return on equity using the following formula: required return on stock j = risk-free rate + beta of j x equity risk premium

Assumptions:

1. Risk-Free Rate: Investors commonly use the interest rate on a three-month U.S. Treasury bill as a proxy for the risk-free rate because short-term government-issued securities have virtually zero risk of default.

Rate of return on LT Government Debt: RF = 2.67%

2.Beta: measures the portfolio sensitivity of its returns on the “market portfolio” of risky assets. Systematic risk (β) of Walmart's common stock: βWMT =0.37

3. Equity risk premium: is the return in excess of the risk-free rate that investors require for holding equities securities. It is usually defined as the difference between the required return on a broad equity market index and the risk-free rate. There are two types of estimates of the equity risk premium: historical estimates and forward looking. The latter uses current information about economic variables. The constant growth model generates forward-looking estimates. The assumptions of the model are reasonable when applied to develop economies and markets. This method estimate the risk premium as the expected dividend yield plus the expected growth rate minus the current long-term government bond yield.

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]

rWMT = RF + βWMT [GGM ERP]

= 2.67% + 0.37 [11.43%]

= 6.9%

1. 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 can be estimated using Dupont formula:

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.

The growth rates are:

 Year Value g(t) 1 g(1) 15,15% 2 g(2) 12,42% 3 g(3) 9,68% 4 g(4) 6,95% 5 g(5) 4,21%

G(2), g(3) and g(4) are calculated using linear interpolation between g(1) and g(5).

1. Calculation of Intrinsic Value

Final Comment

The intrinsic value is more than the current share price, so the analysis is showing that the stock is worth more than its price and that it makes sense to buy the stock.

Hedge fund guru John Rogers (Trades, Portfolio) buy this stock. Others gurus like Richard Pzena (Trades, Portfolio), James Barrow (Trades, Portfolio), Jim Simons (Trades, Portfolio), Joel Greenblatt (Trades, Portfolio), John Hussman (Trades, Portfolio), Jim Simons (Trades, Portfolio) and Mario Gabelli (Trades, Portfolio), among others, added this stock to their portfolios, so I would advise fundamental investors to consider adding Wal-Mart to their portfolios as it seems to be an attractive option.

Disclosure: Damian Illia holds no position in any stocks mentioned.

[1] This values where obtain from Blommberg´s CRP function.

Damian Illia
A fundamental analyst at Lonetreeanalytics.com constantly looking for value and income investments.

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