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

THE APPLICATION OF FUNDAMENTAL VALUATION PRINCIPLES 327Based on a constant growth rate g for both after-tax operatingearnings and capital and the identities defined above in the DCFdiscussion, the formula for EVA value is restated as1XValue = SC 0 + OE 1 £ (1 + g) x¡1 £ (1 + h) ¡x¡x=11Xh £ C 0 £ (1 + g) x¡1 £ (1 + h) ¡x :x=1By factoring out the constants, this may be rewritten asValue = SC 0 + OE 1X1·(1 + g)¸x¡1(1 + h) (1 + h)¡ (h £ C 0 )(1 + h)1Xx=1x=1·(1 + g)(1 + h)¸x¡1:(EVA-3)(EVA-4)Again, we use identities defined in the DCF discussion tosimplify Equation EVA-4 to the following:Value = SC 0 + OE 1(h ¡ g) ¡ h £ C 0(h ¡ g) : (EVA-5)Formula EVA-5 can also be expressed asorororValue = SC 0 + OE 1(h ¡ g) ¡ (h ¡ g + g) £ C 0, (EVA-6)(h ¡ g)Value = SC 0 + OE 1(h ¡ g) ¡ (h ¡ g) £ C 0¡ g £ C 0(h ¡ g) (h ¡ g) , (EVA-7)Value = SC 0 + OE 1(h ¡ g) ¡ C 0 ¡ g £ C 0(h ¡ g) , (EVA-8)Value = FC 0 + C 0 + OE 1(h ¡ g) ¡ C 0 ¡ g £ C 0(h ¡ g) , (EVA-9)