Reverse Engineering with the PB Ratio The following table provides summary data for Foot Locker Inc. (in millions). Analysts will often use the observed PB ratio to infer market expectations regarding a company’s future performance under various assumptions.

Market value of equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $9,201 Book value of equity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2,578 ROE (based on trailing 4 quarters) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6%

EPS growth (based on trailing 4 quarters) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2%

Required

a. Assume that the market’s expectations of future ROE and the discount rate are 20% and 8%, respectively. Solve for the implied growth rate.

b. Assume that the market’s expectations of future ROE and the growth rate are 20% and 4%, respectively.
Solve for the implied discount rate.

c. Assume that the market’s expectations of the discount rate and the growth rate are 8% and 4%, respectively. Solve for the implied future ROE.

d. Do the market expectations implied from the results of parts a through c seem reasonable? Explain.