# Question

In Problem 10.16, we projected financial statements for Walmart Stores for Years +1 through +5. The data in Chapter 12’s Exhibits 12.16–12.18 include the actual amounts for 2008 and the projected amounts for Year +1 to Year +5 for the income statements, balance sheets, and statements of cash flows for Walmart (in millions).

The market equity beta for Walmart at the end of 2008 was 0.80. Assume that the riskfree interest rate was 3.5 percent and the market risk premium was 5.0 percent. Walmart had 3,925 million shares outstanding at the end of 2008. At the end of 2008, Walmart’s share price was $46.06.

In this problem, we use these actual and projected financial statement data to apply the techniques in Chapter 14 to compute Walmart’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 Walmart’s market-to-book ratio at the end of 2008 to determine an investment recommendation. In addition, we compute the value-earnings and price-earnings ratios and the price differential and we reverse-engineer Walmart’s share price as of the end of 2008.

Required

Part I—Computing Walmart’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 Walmart.

b. Using the projected financial statements in Chapter 12’s Exhibits 12.16–12.18, derive the projected residual ROCE (return on common shareholders’ equity) for Walmart 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; then derive the projected residual ROCE for Year +6 for Walmart.

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 Walmart 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 Walmart as of the start of Year +6 based on Walmart’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 Walmart’s value-to-book ratio as of the end of 2008 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 (1), add 1 (representing the book value of equity as of the beginning of the valuation as of the end of 2008).

(3) Adjust the total sum from (2) using the midyear discounting adjustment factor.

g. Compute Walmart’s market-to-book ratio as of the end of 2008. 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 Walmart 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 Walmart.

i. If you computed Walmart’s common equity share value using the dividends valuation 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 problems, you would benefit from doing so now.

Part II—Analyzing Walmart’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 Walmart’s comprehensive income available for common shareholders in Year +1 by the number of common shares outstanding at the end of 2008. Using this Year +1 earnings-per-share forecast and the share value computed in Part h, compute Walmart’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 2008, compute Walmart’s price-earnings ratio. Compare Walmart’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 Walmart shares in the market: underpriced, overpriced, or fairly priced? Does this comparison lead to the same conclusions you reached when comparing value-tobook ratios with market-to-book ratios in Part g?

l. Compute Walmart’s price differential at the end of 2008. Compute Walmart’s price differential as a percentage of Walmart’s risk-neutral value. What dollar amount and what percentage amount has the market discounted Walmart shares for risk?

m. Reverse-engineer Walmart’s share price at the end of 2008 to solve for the implied expected rate of return. First, assume that value equals price and that the earnings and growth forecasts through Year +6 and beyond are reliable proxies for the market’s expectations for Walmart. Then solve for the implied expected rate of return (the discount rate) the market has impounded in Walmart’s share price. (Begin with the forecast and valuation spreadsheet you developed to value Walmart shares. Vary the discount rate until you solve for the discount rate that makes your value estimate exactly equal the end-of-2008 market price of $46.06 per share.)

n. Reverse-engineer Walmart’s share price at the end of 2008 to solve for the implied expected long-run growth. First, assume that value equals price and that the earnings forecasts through Year +5 are reliable proxies for the market’s expectations for Walmart. 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 Walmart’s share price. (Begin with the forecast and valuation spreadsheet you developed to value Walmart 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-2008 market price of $46.06 per share.)

The market equity beta for Walmart at the end of 2008 was 0.80. Assume that the riskfree interest rate was 3.5 percent and the market risk premium was 5.0 percent. Walmart had 3,925 million shares outstanding at the end of 2008. At the end of 2008, Walmart’s share price was $46.06.

In this problem, we use these actual and projected financial statement data to apply the techniques in Chapter 14 to compute Walmart’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 Walmart’s market-to-book ratio at the end of 2008 to determine an investment recommendation. In addition, we compute the value-earnings and price-earnings ratios and the price differential and we reverse-engineer Walmart’s share price as of the end of 2008.

Required

Part I—Computing Walmart’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 Walmart.

b. Using the projected financial statements in Chapter 12’s Exhibits 12.16–12.18, derive the projected residual ROCE (return on common shareholders’ equity) for Walmart 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; then derive the projected residual ROCE for Year +6 for Walmart.

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 Walmart 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 Walmart as of the start of Year +6 based on Walmart’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 Walmart’s value-to-book ratio as of the end of 2008 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 (1), add 1 (representing the book value of equity as of the beginning of the valuation as of the end of 2008).

(3) Adjust the total sum from (2) using the midyear discounting adjustment factor.

g. Compute Walmart’s market-to-book ratio as of the end of 2008. 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 Walmart 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 Walmart.

i. If you computed Walmart’s common equity share value using the dividends valuation 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 problems, you would benefit from doing so now.

Part II—Analyzing Walmart’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 Walmart’s comprehensive income available for common shareholders in Year +1 by the number of common shares outstanding at the end of 2008. Using this Year +1 earnings-per-share forecast and the share value computed in Part h, compute Walmart’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 2008, compute Walmart’s price-earnings ratio. Compare Walmart’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 Walmart shares in the market: underpriced, overpriced, or fairly priced? Does this comparison lead to the same conclusions you reached when comparing value-tobook ratios with market-to-book ratios in Part g?

l. Compute Walmart’s price differential at the end of 2008. Compute Walmart’s price differential as a percentage of Walmart’s risk-neutral value. What dollar amount and what percentage amount has the market discounted Walmart shares for risk?

m. Reverse-engineer Walmart’s share price at the end of 2008 to solve for the implied expected rate of return. First, assume that value equals price and that the earnings and growth forecasts through Year +6 and beyond are reliable proxies for the market’s expectations for Walmart. Then solve for the implied expected rate of return (the discount rate) the market has impounded in Walmart’s share price. (Begin with the forecast and valuation spreadsheet you developed to value Walmart shares. Vary the discount rate until you solve for the discount rate that makes your value estimate exactly equal the end-of-2008 market price of $46.06 per share.)

n. Reverse-engineer Walmart’s share price at the end of 2008 to solve for the implied expected long-run growth. First, assume that value equals price and that the earnings forecasts through Year +5 are reliable proxies for the market’s expectations for Walmart. 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 Walmart’s share price. (Begin with the forecast and valuation spreadsheet you developed to value Walmart 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-2008 market price of $46.06 per share.)

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