# Question

In Problem 10.16, we projected financial statements for Wal-Mart Stores, Inc. (Walmart) for Years +1 through +5. The data in Chapter 12’s Exhibits 12.16, 12.17, and 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, respectively, 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.

Required

Part I—Computing Walmart’s Share Value Using the Residual Income Valuation Approach

a. Use the CAPM to compute the required rate of return on common equity capital for Walmart.

b. Derive the projected residual income for Walmart for Years +1 through +5 based on the projected financial statements.

c. Project the continuing residual income in Year +6. 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 amount of residual income for Year +6.

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 income 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 income 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 the value of a share of Walmart common stock.

(1) Compute the total sum of the present value of all future residual income (from Parts d and e).

(2) Add the book value of equity as of the beginning of the valuation (that is, as of the end of 2008, or the start of Year +1).

(3) Adjust the total sum of the present value of residual income plus book value of common equity using the midyear discounting adjustment factor.

(4) Compute the per-share value estimate.

Part II—Sensitivity Analysis and Recommendation

g. Using the residual income valuation method, recompute the value of Walmart shares under two alternative scenarios. Scenario 1: Assume that Walmart’s long-run growth will be 2 percent, not 3 percent as above, and that Walmart’s required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Walmart’s long-run growth will be 4 percent, not 3 percent as above, and that Walmart’s required rate of return on equity is 1 percentage point lower than the rate you computed using the CAPM in Part a. To quantify the sensitivity of your share value estimate for Walmart to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

h. Using these data at the end of 2008, what reasonable range of share values would you have expected for Walmart common stock? At that time, what was the market price for Walmart shares relative to this range? What would you have recommended?

i. If you worked Problem 11.14 from Chapter 11 and computed Walmart’s share value using the dividends valuation approach, compare your value estimate from Part g of that problem with the value estimate you obtained here. Similarly, if you worked Problem 12.17 from Chapter 12 and computed Walmart’s share value using the free cash flows to common equity shareholders, compare your value estimate from Part f of that problem with the value estimate you obtained here. You should obtain the same value estimates for Walmart shares under all three approaches. If you have not worked both of those problems, you would benefit from doing so now.

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.

Required

Part I—Computing Walmart’s Share Value Using the Residual Income Valuation Approach

a. Use the CAPM to compute the required rate of return on common equity capital for Walmart.

b. Derive the projected residual income for Walmart for Years +1 through +5 based on the projected financial statements.

c. Project the continuing residual income in Year +6. 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 amount of residual income for Year +6.

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 income 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 income 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 the value of a share of Walmart common stock.

(1) Compute the total sum of the present value of all future residual income (from Parts d and e).

(2) Add the book value of equity as of the beginning of the valuation (that is, as of the end of 2008, or the start of Year +1).

(3) Adjust the total sum of the present value of residual income plus book value of common equity using the midyear discounting adjustment factor.

(4) Compute the per-share value estimate.

Part II—Sensitivity Analysis and Recommendation

g. Using the residual income valuation method, recompute the value of Walmart shares under two alternative scenarios. Scenario 1: Assume that Walmart’s long-run growth will be 2 percent, not 3 percent as above, and that Walmart’s required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Walmart’s long-run growth will be 4 percent, not 3 percent as above, and that Walmart’s required rate of return on equity is 1 percentage point lower than the rate you computed using the CAPM in Part a. To quantify the sensitivity of your share value estimate for Walmart to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

h. Using these data at the end of 2008, what reasonable range of share values would you have expected for Walmart common stock? At that time, what was the market price for Walmart shares relative to this range? What would you have recommended?

i. If you worked Problem 11.14 from Chapter 11 and computed Walmart’s share value using the dividends valuation approach, compare your value estimate from Part g of that problem with the value estimate you obtained here. Similarly, if you worked Problem 12.17 from Chapter 12 and computed Walmart’s share value using the free cash flows to common equity shareholders, compare your value estimate from Part f of that problem with the value estimate you obtained here. You should obtain the same value estimates for Walmart shares under all three approaches. If you have not worked both of those problems, you would benefit from doing so now.

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