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

324 THE APPLICATION OF FUNDAMENTAL VALUATION PRINCIPLESAPPENDIX BDEMONSTRATION OF ALGEBRAIC EQUIVALENCE OF EVA ANDDCFThe general expression for value based on the discounted cashflow (DCF) approach is1XValue = FC 0 + [OE x ¡ ¢C x ] £ (1 + h) ¡x , (DCF-1)x=1whereFC 0 = Free cash available at time 0 to be released toshareholders;OE x = After-tax operating earnings generated in timeperiod x;¢C x = Change in required capital over time periodx = C x ¡ C x¡1 ,whereC x = required capital atthe end of time period x (this is equivalent tothe required capital at the beginning of timeperiod x +1); andh = Hurdle rate (required return on capital).Equation DCF-1 represents the sum of the free cash availableat time 0 and the present value of future free cash flows, wherefuture free cash flows (OE x ¡ ¢C x ) are defined as after-tax operatingearnings less the amount of required capital reinvestment.For ease of illustration, we have made the simplifying assumptionthat all cash flows occur at the end of the period.Distributing and separating Equation DCF-1 into two separatesums, we produce1X1XValue = FC 0 + OE x £ (1 + h) ¡x ¡ ¢C x £ (1 + h) ¡x :x=1x=1(DCF-2)