13.15 Computing Residual Income. Suppose the following hypothetical data represent total assets, book value, and market value of common shareholders equity (dollar amounts in millions) for three firms. Each of these firms, Southwest Airlines, Kroger, and Yum! Brands, operates in a different industry, but all of them operate in very competitive industries. Southwest Airlines is a U.S. domestic airline that provides low-cost point-to-point air transportation services. Kroger operates retail supermarkets across the United States. Yum! Brands operates and franchises quick-service restaurants, including KFC, Pizza Hut, Taco Bell, Long John Silvers, and A&W All American Food restaurants. These data also include hypothetical market betas for the three firms and analysts consensus forecasts of net income for Year 1. For each firm, analysts expect other comprehensive income items for Year 1 to be zero; so Year 1 net income and comprehensive income will be identical. Assume that the risk-free rate of return in the economy is 4.0% and the market risk

premium is 5.0%.

Southwest Airlines Kroger Yumi Brands

Total Assets 14308 23211 7242

Common equity

Book value 4953 5176 1139

Market value 7490 14870 15950

Market equity beta 1.10 .35 1.04

Analysts consensus forecasts

of net income for Year +1 252 1263 1010

a. Using the CAPM, compute the required rate of return on equity capital for each firm.

b. Project required income for Year 1 for each firm.

c. ProjectresidualincomeforYear1foreachfirm.

d. Rank the three firms using expected residual income for Year 1 relative to book value of common equity.

e. What do the different amounts of residual income imply about each firm? Do the projected residual income amounts help explain the differences in market value of equity across these three firms? Explain.