PLEASE CHECK MATH FOR ACCURACY: Valuation Methods for Wal$-$Mart To evaluate Wal$-$Mart$$s stock, we employ four key valuation methods: Perpetual Growth in Dividends Forecasted Dividends with Future Sale Three$-$Stage Dividend Discount Model Price$/$Earnings Multiple Approach Each method provides unique insights into Wal$-$Mart$$s intrinsic stock value. $1.$ Perpetual Growth in Dividends The Dividend Discount Model $($DDM$)$ assumes that dividends will grow perpetually at a constant rate. Formula: P$=$ D$/($K$$ g$)$ Where: P$=$ Current stock price D$=$ Projected dividend for the next year $($$$1\mathrm{.}21$ for fiscal year $2011)$ K$=$ Cost of equity $($calculated via CAPM$)$ g $=$ Expected constant dividend growth rate $(5\%$ as estimated by analysts$)$ Using CAPM to compute the cost of equity: K$=$ Risk$-$free rate $+$ $($Market risk premium$)=3\mathrm{.}68\%+0\mathrm{.}665\mathrm{.}05\%=7\mathrm{.}99\%$ Now applying the DDM: P$=1\mathrm{.}21/(0\mathrm{.}07990\mathrm{.}05)$ P$=$ $$40\mathrm{.}47$ Insights: The perpetual dividend growth model estimates Wal$-$Mart$$s stock value at $$40\mathrm{.}47,$ lower than its current price of $$53\mathrm{.}48,$ suggesting it may be slightly overvalued using this model. $2.$ Forecasted Dividends and Future Sale This model values forecasts of near$-$term dividends and includes a terminal value for future dividends after a defined period. Formula: P$=[$D$/(1+$ K$)]+$ Pn $/(1+$ K$)$ Where: D$=$ Dividends for years $1$ through n Pn $=$ Terminal stock price at year n $($calculated using perpetuity formula$)$ Key assumptions: Dividend growth rate $($g$)=5\%$ annually. Terminal value assumed at year $5$ with growth in perpetuity. Calculations: Year $1$ Dividend $($D$)=$ $$1\mathrm{.}21$ Year $5$ Dividend $($D$)=$ $$1\mathrm{.}21(1+0\mathrm{.}05)^4=$ $$1\mathrm{.}47$ Terminal Pn $=$ D$(1+$ g$)/($K$$ g$)$ Pn $=$ $$1\mathrm{.}47(1+0\mathrm{.}05)/(0\mathrm{.}07990\mathrm{.}05)=$ $$51\mathrm{.}52$ Present value: P$=$ PV$($D$)+$ PV$($D$)+...+$ PV$($D$)+$ PV$($Pn$)$ P$=($$$1\mathrm{.}21/1\mathrm{.}0799)+($$$1\mathrm{.}27/1\mathrm{.}0799^2)+($$$1\mathrm{.}33/1\mathrm{.}0799^3)+($$$1\mathrm{.}40/1\mathrm{.}0799^4)+($$$1\mathrm{.}47/1\mathrm{.}0799^5)+($$$51\mathrm{.}52/1\mathrm{.}0799^5)$ P$$ $$49\mathrm{.}67$ Insights: The forecasted dividend approach results in a valuation of $$49\mathrm{.}67,$ slightly lower than the market price, suggesting a potential modest overvaluation. $3.$ Three$-$Stage Dividend Discount Model Wal$-$Mart is a mature company transitioning into long$-$term stable growth, making the three$-$stage model particularly relevant. Using Exhibit $4$ assumptions: High growth $(23\%)$ for $5$ years Transition growth $($decreasing annually$)$ for $12$ years Maturity $(6\mathrm{.}6\%$ growth and $45\%$ payout ratio$)$ The theoretical model $($in Exhibit $4)$ estimates Wal$-$Mart$$s value at $$120\mathrm{.}37$ per share, significantly higher than the current market price of $$53\mathrm{.}48.$ Insights: This model captures aggressive growth and aligns with market optimism, possibly overstating intrinsic value depending on transition and maturity assumptions. $4.$ Price$/$Earnings $($P$/$E$)$ Multiple Approach This approach estimates stock price using projected earnings and an appropriate P$/$E multiple. Formula: P$=$ EPS$$ Forward P$/$E Where: EPS$=$ Projected earnings per share $($$$3\mathrm{.}721\mathrm{.}104=$ $$4\mathrm{.}10)$ Forward P$/$E $=$ Industry average $(14\mathrm{.}23)$ P$=$ $$4\mathrm{.}1014\mathrm{.}23=$ $$58\mathrm{.}34$ Insights: Wal$-$Mart$$s valuation using the forward P$/$E multiple suggests an intrinsic value of $$58\mathrm{.}34,$ which is just above the current market price of $$53\mathrm{.}48,$ indicating the stock may be a reasonable investment. Recommendation Based on the analysis above: Perpetual Growth Model: Stock slightly overvalued. Forecasted Dividends $+$ Terminal Value: Similar conclusion, modest overvaluation at $$49\mathrm{.}67.$ Three$-$Stage Dividend Model: Suggests substantial undervaluation at $$120\mathrm{.}37,$ though based on aggressive assumptions. P$/$E Multiple Approach: Fair valuation at $$58\mathrm{.}34.$ Final Verdict: Given Wal$-$Mart$$s solid fundamentals, projected earnings growth, and alignment with industry averages, we recommend a "BUY" rating for the following reasons: The P$/$E approach suggests the stock is fairly valued, while the market price allows for moderate upside. Strong historical performance and consistent dividend growth. Competitive position as a global retail leader ensures sustainable growth. Key Risk Factors: Economic slowdowns affecting consumer spending. International expansion risks. Investors should remain mindful of downside risks, particularly if Wal$-$Mart fails to meet its aggressive growth targets.