PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

326 THE APPLICATION OF FUNDAMENTAL VALUATION PRINCIPLESbecomesValue = FC 0 + OE 1(h ¡ g) ¡ C 0 £ g(h ¡ g) : (DCF-5)This is appropriately viewed as the sum of all free cash flows,or initial capital plus the present value of future earnings, minusthe present value of future required capital reinvestments.The general expression of EVA iswhere1XValue = SC 0 + [OE x ¡ (h £ C x¡1 )] £ (1 + h) ¡x ,x=1(EVA-1)SC 0 = Starting capital, which is equal to the sum offree capital and required capital at time 0(FC 0 and C 0 , respectively, as defined in theDCF discussion); andOE x , C x , and h have the same definitions as in the DCFdiscussion.Formula EVA-1 represents the required capital at the valuationdate (time = 0) plus the present value of future economic profits.Economic profits for time period x are defined as after-taxoperating earnings (OE x ) reduced by the cost of capital, whichis the product of the hurdle rate and the required capital at thebeginning of each period (h £ C x ).Distributing and separating Equation EVA-1 into two separatesums, we produce1X1XValue = SC 0 + OE x £ (1 + h) ¡x ¡ (h £ C x¡1 ) £ (1 + h) ¡x :x=1x=1(EVA-2)