Problem 10.16 projects financial statements for Wal-Mart Stores for Years +1 through +5. The data in Exhibits 12.16, 12.17, and 12.18 in Chapter 12 include the actual amounts for Year 4 and the projected amounts for Year + 1 to Year +5 for the income statements, balance sheets, and statements of cash flows for Wal-Mart (amounts in millions).
The market equity beta for Wal-Mart at the end of Year 4 is .80. Assume that the risk-free interest rate is 4.0 percent and the market risk premium is 5.0 percent. Wal-Mart has 4,234 million shares outstanding at the end of Year 4. At the end of Year 4, Wal-Mart's share price was $52.40.
In this problem, we use these actual and projected financial statement data to apply the techniques in Chapter 14 to compute Wal-Mart's required rate of return on equity and share value based on the value-to-book valuation model. We also compare our value-to-book ratio estimate to Wal-Mart's market-to-book ratio at the end of Year 4 to determine an investment recommendation. In addition, we compute the value-earnings and price-earnings ratios, compute the price differential, and reverse engineer Wal-Mart's share price as of the end of Year 4.
Required
Part I - Computing Wal-Mart's Value-to-Book Ratio Using the Value-to-Book Valuation Approach
a. Use the CAPM to compute the required rate of return on common equity capital for Wal-Mart.
b. Using the projected financial statements in Chapter 12, Exhibits 12.16 to 12.18, derive the projected residual ROCE (return on common shareholders' equity) for Wal-Mart for Years +1 through +5.
c. Assume that the steady-state long-run growth rate will be 3 percent in Year +6 and beyond. Project that the Year +5 income statement and balance sheet amounts will grow by 3 percent in Year +6, and then derive the projected residual ROCE for Year +6 for Wal-Mart.
d. Using the required rate of return on common equity from part a as a discount rate, compute the sum of the present value of residual ROCE for Wal-Mart for Years + 1 through +5.
e. Using the required rate of return on common equity from part a as a discount rate, and the long-run growth rate from part c, compute the continuing value of Wal-Mart as of the start of Year +6 based on Wal-Mart's continuing residual ROCE in Year +6 and beyond. After computing continuing value as of the start of Year +6, discount it to present value at the start of Year +1.
f. Compute Wal-Mart's value-to-book ratio as of the end of Year 4 with the following three steps. (1) Compute the total sum of the present value of all future residual ROCE (from parts d and e). (2) To the total from item (1), add one (representing the book value of equity as of the beginning of the valuation as of the end of Year 4). (3) Adjust the total sum from item (2) using the midyear discounting adjustment factor.
g. Compute Wal-Mart's market-to-book ratio as of the end of Year 4. Compare the value-to-book ratio to the market-to-book ratio. What investment decision does the comparison suggest? What does the comparison suggest regarding the pricing of Wal-Mart shares in the market: underpriced, overpriced, or fairly priced?
h. Use the value-to-book ratio to project the value of a share of common equity in Wal-Mart.
i. If you computed Wal-Mart's common equity share value using the dividends valua- tion approach in Problem 11.14 in Chapter 11, and/or the free cash flows to common equity valuation approach in Problem 12.17 in Chapter 12, and/or the residual income valuation approach in Problem 13.20 in Chapter 13, compare the value estimate you obtained in those problems with the estimate you obtained in this case. You should obtain the same value estimates under all four approaches. If you have not yet worked those prior problems, it would be valuable to do so now.
Part II - Analyzing Wal-Mart's Share Price Using the Value-Earnings Ratio, the Price-Earnings Ratio, Price Differentials, and Reverse Engineering
j. Use the forecast data for Year +1 to project Year +1 earnings per share. To do so, divide the projection of Wal-Mart's comprehensive income available for common shareholders in Year +1 by the number of common shares outstanding at the end of Year 4. Using this Year +1 earnings per share forecast, and using the share value computed in part h, compute Wal-Mart's value-earnings ratio.
k. Using the Year +1 earnings per share forecast from part j, and using the share price at the end of Year 4, compute Wal-Mart's price-earnings ratio. Compare Wal-Mart's value-earnings ratio with its price-earnings ratio. What investment decision does the comparison suggest? What does the comparison suggest regarding the pricing of Wal-Mart shares in the market: underpriced, overpriced, or fairly priced? Does this comparison lead to the same conclusions that you reached by comparing value-to-book ratios with market-to-book ratios in part g?
1. Compute Wal-Mart's price differential at the end of Year 4. Compute Wal-Mart's price differential as a percentage of Wal-Mart's risk-neutral value. What dollar amount and what percentage amount has the market discounted Wal-Mart shares for risk?
m. Reverse engineer Wal-Mart's share price at the end of Year 4 to solve for the implied expected rate of return. First, assume that value equals price, and assume that the earnings and growth forecasts through Year +6 and beyond are reliable proxies for the market's expectations for Wal-Mart. Then solve for the implied expected rate of return (the discount rate) the market has impounded in Wal-Mart's share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Wal-Mart shares. Vary the discount rate until you solve for the discount rate that makes your value estimate exactly equal the end of Year 4 market price of $52.40 per share.)
n. Reverse engineer Wal-Mart's share price at the end of Year 4 to solve for the implied expected long-run growth. First, assume that value equals price, and assume that the earnings forecasts through Year +5 are reliable proxies for the market's expectations for Wal-Mart. Also assume that the discount rate implied by the CAPM (computed in part a) is a reliable proxy for the market's expected rate of return. Then solve for the implied expected long-run growth rate the market has impounded in Wal-Mart's share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Wal-Mart shares, and use the CAPM discount rate. Set the long-run growth parameter initially to zero. Increase the long-run growth rate until you solve for the growth rate that makes your value estimate exactly equal the end of Year 4 market price of $52.40 per share.)