PROBLEM 1–12 Ace Co. is to be taken over by Beta Ltd. at the end of year 2007. Beta agrees to pay the shareholders of Ace the book value per share at the time of the takeover. A reliable analyst makes the following projections for Ace (assume cost of capital is 10% per annum):

($ per share) 2002 2003 2004 2005 2006 2007 Dividends . . . . . . . . . . . . . . . . — $1.00 $1.00 $1.00 $1.00 $1.00 Operating cash flows . . . . . . . — 2.00 1.50 1.00 0.75 0.50 Capital expenditures . . . . . . . — — — 1.00 1.00 —

Debt increase (decrease) . . . . — (1.00) (0.50) 1.00 1.25 0.50 Net income . . . . . . . . . . . . . . . — 1.45 1.10 0.60 0.25 (0.10)

Book value . . . . . . . . . . . . . . . 9.00 9.45 9.55 9.15 8.40 7.30 Required:

a. Estimate Ace Co.’s value per share at the end of year 2002 using the dividend discount model.

b. Estimate Ace Co.’s value per share at the end of year 2002 using the residual income model.

c. Attempt to estimate the value of Ace Co. at the end of year 2002 using the free cash flow to equity model.