Author: Austin Bogus Jarrod Fenstermacher Remi Omisore

For Review: Professor Gurdip S. Bakshi

“We, the aforementioned team, pledge on our honor that we have not given or received any unauthorized assistance on this assignment.” - University of Maryland Honor Pledge

September 24, 2012

Case Three 3.1 Question One

As of February 2010, what is your assessment of the worth of Walmarts stock? Utilize all of the methods discussed in the case to value the shares, including the following: • The perpetual growth in dividends • Forecasted dividends for the next several years plus sale of the stock in the future • The three-stage dividend model • The price/earnings approach

3.1.1

The perpetual growth in dividends

The standard method of ﬁnding stock price for perpetual dividends for a ﬁrm, given the ﬁrms dividend one year into the future and an expected growth rate for the dividend, is as follows: P0 = D1 (Ke − g)

where Ke is the investors’ required return, D1 is next year’s dividend and g is the expected growth rate of the dividend. However, since Walmart is being examined, and it is safe to consider Walmart in a steady state, it makes sense to use a slight variation to this formulation. P0 = E1 × p (Ke − g) g = (1 − p) × Ke

where E1 is the earnings 1 year into the future, and p is the payout ratio or the percentage of earnings paid in dividends. For this calculation an estimated earnings per share for the following year was found to be $4.11. This is the 2010 earnings per share of $3.72 increased by the quoted 10.4% (which is also roughly the growth rate over the last 6 years). If the 1

arithmetic average of the dividend payout ratio is taken over the life of Walmart, it comes to 14.4%, therefore this will be used in the calculation of P0 . P0 = E1 × p Ke × (1 − (1 − p)) $4.11 × 14.4% = 7.0% × 14.4% = $58.77

(3.1)

3.1.2

Forecasted dividends for the next several years plus sale of the stock in the future

Similarly, the dividends can be forecast n years into the future, after which time the stock is sold. This formulation is as follows: P0 = D1 D2 Dn Pn + + ··· + + 1 2 n (1 + Ke ) (1 + Ke ) (1 + Ke ) (1 + Ke )n

Using the method described above for perpetual dividends, the stock price was estimated for the following 4 years to provide a terminal sale price of the stock. Dividends were assumed to grow at the geometric average of the last 6 years, 20.28%. P0 = D2 Dn Pn D1 + + ··· + + 1 2 n (1 + Ke ) (1 + Ke ) (1 + Ke ) (1 + Ke )n $1.58 $2.28 $87.31 $1.31 + + ··· + + = 1 2 4 (1 + 7.0%) (1 + 7.0%) (1 + 7.0%) (1 + 7.0%)4 = $72.53

(3.2)

3.1.3

The three-stage dividend model

Some applications of dividend discount modeling can be more complex. One method divides the future growth in dividends into three periods, all of which have diﬀerent growth rates. This is useful when a company’s proﬁts are expected to grow rapidly and then gradually decline to an industry average. The complexities of this model are outside of the scope of this report, and the model can easily be run using tools found online. The assumptions of this calculation as follows. Walmart is no longer in a growth phase, so this calculation assumes that it is at the transitional phase.

Because of this, 2007 data is used to initialize the calculation (EPS, dividend, etc.,) and the ‘growth’ period was 3 years. Initial growth of EPS still assumed to be 10.4%. 14 transitional years, as required by the model (total of 17 years for growth and transition is required). All of these assumptions result in a 3 stage DDM value of $72.42. However, since it is assumed that this was initiated 3 years ago this value is actually a calculation of P−3 , moving this 3 years into the future with the required return rate gives a P0 value of $88.69. 2

3.1.4

The price/earnings multiple approach

P/E multiples are widely used in the investment industry because they are commonly available and easily used for comparative purposes. The formulation is simply P0 = EP S0 ×P/E0 . Using the values previously mentioned for 2011 and an P/E ratio for Walmart of 13.40, the P0 comes out to be: P0 = EP S0 × P/E0 = $4.11 × 13.40 = $55.03

(3.3)

Based on the analysis, as Sabrina Gupta, what recommendation would be made

Response Recommendation is to Buy. The Mean of the price for the 4 methods is $72.24. Removing the highest and lowest values and averaging the remaining ones gives $65.65. Due to the recent close price ($53.48) being much lower than these values, it makes sense at this time to buy.

Exhibit A Required Return CAP M

Figure A.1: Walmart Returns vs S&P500. From this plot, the adjusted beta can be captured for calculating required return.

From the graph, an adjusted beta value of 0.655 can be seen. This is required for the CAPM calculation of expected return for Walmart. This expected return will be used in this case as the investors’ required return. E(ri ) = rf + βi × {rm − rf } = 3.68% + 0.655 × {5.05%} = 7.0%

(A.1)