Problem 13.18 and Exhibit 13.7 in Chapter 13 present selected data from projected financial statements for Steak ’n Shake for Year +1 to Year +11. The amounts for Year +11 reflect a long-term growth assumption of 3 percent. The cost of equity capital is 9.34 percent. The market value of common shareholders’ equity in Steak ’n Shake on January 1, Year +1, is $309.98 million.

Required
a. Compute the value-to-book ratio as of January 1, Year +1, using the residual ROCE valuation method.
b. Using the analyses developed in Part a, prepare an exhibit summarizing the following ratios for Steak ’n Shake as of January 1, Year +1:
1. Value-to-book ratio (using the amounts from Part a)
2. Market-to-book ratio
3. Value-earnings ratio, using reported earnings for Year 0 of $21.8 million
4. Price-earnings ratio, using reported earnings for Year 0 of $21.8 million
5. Value-earnings ratio, using projected earnings for Year +1 of $24.5 million
6. Price-earnings ratio, using projected earnings for Year +1 of $24.5 million
c. Compute the risk-neutral value of Steak ’n Shake as of January 1, Year +1, using a risk-free rate of 4.2 percent. Use the projected earnings for Year +1 to Year +10 and the projected earnings for Year +11 given in Exhibit 13.7. Maintain the continuing value growth assumption of 3 percent. Compute the price differential for Steak ’n Shake as of January 1, Year +1. Compute the ratio of market value to risk-neutral value for Steak ’n Shake as of January 1, Year +1.
d. Use reverse engineering to solve for the long-run growth rate in continuing residual income in Year +11 and beyond that is implicitly impounded in the market value of Steak ’n Shake on January 1, Year +1. Use the 9.34 percent cost of equity capital and the projected earnings amounts for Year +1 to Year +10 in Exhibit 13.7 before solving for the long-run growth rate in continuing residual income.
e. Using the analyses in Parts a–d, evaluate the extent of the market’s mispricing (if any) of Steak ’n Shake.