NPVGOAndTheConstantGrowthModel

# NPVGOAndTheConstantGrowthModel - NPVGO and the Constant...

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NPVGO and the Constant Growth Model 1 Notation: P 0 Price of the stock at time 0 D t Expected dividend at time t E t Expected earnings at time t I t Expected Investment at time t b plowback ratio ROE Return on equity r Discount rate Note: P 0 , D t , E t , I t are assumed to be a per-share basis. Assumptions: plowback ( b ) and return on equity (ROE) are constant over time. Because dividends are the cash ﬂows to equity: P 0 = D 1 1 + r + D 2 (1 + r ) 2 + D 3 (1 + r ) 3 + ··· (1) Note that growth in earnings is given by g = ROE b and is constant over time. Under the assumptions that b and ROE are constant, we have derived a formula for (1). Because D t = (1 - b ) E t = (1 - b )(1 + g ) t - 1 E 1 , the growing perpetuity formula can be applied to (1) to obtain P 0 = (1 - b ) E 1 r - ROE b . (2) Claim: P 0 = E 1 r + NPVGO (3) 1 Notes for Finance 100 (sections 301 and 302) prepared by Jessica A. Wachter.

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where NPVGO is the net present value of growth opportunities. Equation 3 is very general; it holds whether
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NPVGOAndTheConstantGrowthModel - NPVGO and the Constant...

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