8.13 Siebel Incorporated, a nonpublicly traded company, has 2009 after-tax earnings of $20 million, which are expected to grow at 5% annually into the foreseeable future. The firm is debt free, capital spending equals the firm’s rate of depreciation, and the annual change in working capital is expected to be minimal. The firm’s beta is estimated to be 2.0, the 10-year Treasury bond is 5%, and the historical risk premium of stocks over the risk-free rate is 5.5%. Publicly traded Rand Technology, a direct competitor of Siebel’s, was sold recently at a purchase price of 11 times its 2009 after-tax earnings, which included a 20% premium over its current market price. Aware of the premium paid for the purchase of Rand, Siebel’s equity owners would like to determine what it might be worth if they were to attempt to sell the firm in the near future. They chose to value the firm using the discounted-cash-flow and comparable-recent-transactions methods. They believe that either method provides an equally valid estimate of the firm’s value.

a. What is the value of Siebel using the DCF method? Answer: $229.1 million

b. What is the value using the comparable-recent-transactions method? Answer: $220 million

c. What would be the value of the firm if we combine the results of both methods?

Answer: $224.5 million