Sabrina Gupta, an investment adviser for a major brokerage firm, was looking at Wal-Mart Stores, Inc. (Wal-Mart) stock and its valuation. Gupta wondered if she would recommend the stock to any of her new clients or to existing clients who don't currently have Wal-Mart in their portfolios.

His key task was to use an intrinsic value approach to price the shares and then compare the resulting price to the price at which the shares were trading on the market. Gupta wanted to use alternative valuation methods and assumptions to produce intrinsic value estimates for Wal-Mart stock.

She was interested in seeing if the alternative methods would point to a consensus regarding the valuation of the shares and to see if the valuations suggested an investment opportunity given the current market price. The methods she contemplated using were:

Multi-stage growth model

price earnings multiple

Most of the valuation methods that Gupta considered required a common set of inputs:

Future Cash Flows for Wal-Mart Investors

Growth rate of future cash flows

Discount factor or rate of return required by Wal-Mart investors

Gupta gathered data to determine each of the above.

Gupta thought that dividends for Wal-Mart shareholders would adequately capture cash flows for Wal-Mart shareholders; he also thought that this approach would simplify his task and he would review more complex valuation models if he felt the need.

Gupta thought that CAPM would give him a relatively reliable estimate of the required rate of return. The CAPM-based required rate of return can be estimated using a risk-free rate, the firm's systematic risk, and the stock market risk premium. Gupta thought that in a valuation exercise involving long-term cash flows, the yield on 10-year government bonds would be an appropriate estimate of the risk-free rate of return. He checked the rate on the 10-year note and found that it was around 3.68%. Gupta looked up the Wal-Mart beta on Bloomberg. Bloomberg estimates betas by regressing S&P 500 returns on company returns over the past two years and arrives at a "raw" beta estimate. Bloomberg makes an adjustment to the raw beta based on some academic research. Gupta is confident Bloomberg's adjustment is justified and uses Wal-Mart's beta estimate of 0.66 in his analysis.

While Gupta is aware of the importance of EMRP's assumption, he believes Bloomberg's historical estimate of 5.05% is a safe assumption. She is cognizant of the fact that some studies suggest a higher risk premium of about six percent, while others suggest a much lower forward premium of less than four percent. She is aware of the arbitrary nature of her assumption and makes a note to revise this issue if her assessments produce unreasonable estimates.

Anticipated dividend growth (g) is often estimated in several ways.

First, the observed historical dividend growth can be assumed to continue in perpetuity.

Second, future dividend growth can be estimated based on recent analyst estimates.

Gupta noted that Wal-Mart's consensus annual dividend for fiscal 2011 was $1.21, and one respected analyst had estimated the expected steady dividend growth (in perpetuity) at about 3%.

As the chart suggests, earnings and dividend growth rates are declining, but appear to be higher than "respected analyst" estimates. Gupta decides to use several alternative perpetual growth assumptions to see the impact on price. Since Gupta decided to use variants of the dividend discount model (DDM), he checked anticipated earnings for 2011. Analyst estimates suggested earnings per share of $4.10. Gupta decided to use a 10% growth rate from 2011 to 2012 and assumed a steady decline to 3% over 13 years (until 2024), where the perpetual 3% growth rate resumes. He also assumed that Walmart will increase its dividend payout rate from 30% to 55% between the years 2012 and 2024. 

You are asked to reproduce Gupta's analysis of the multi-stage growth model and verify your valuation using an earnings multiple. You have all the data you need to perform multi-stage discounted growth model analysis, but you'll need to do some research on multiple valuation.