Lecture 5 Valuation of the Stock.docx - Lecture 5 Valuation of the Stock The Present Value of Common Stock The value of any asset is the present value

# Lecture 5 Valuation of the Stock.docx - Lecture 5 Valuation...

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Lecture 5 Valuation of the Stock The Present Value of Common Stock The value of any asset is the present value of its expected future cash flows Stock ownership produces cash flows from: + Dividends & Capital Gain (when you sell the stock) The formula If we buy the stock at time 0 and sell it at time 1 for price of P 1 : P 0 = ¿ 1 + P 1 1 + R = ¿ 1 1 + R + P 1 1 + R If instead, we sell at time 2 (no more P 1 ), but can be calculated as: P 1 = ¿ 2 + P 2 1 + R = ¿ 2 1 + R + P 2 1 + R So now: P 0 = ¿ 1 1 + R + ¿ 2 + P 2 1 + R 1 + R ¿ 1 1 + R [ ¿ 1 + ( ¿ 2 + P 2 1 + R ) ] ¿ ¿ 1 1 + R + ¿ 2 ( 1 + R ) 2 + P 2 ( 1 + R ) 2 If holding the stock forever... ➝ perpetuity with dividend payment only P 0 = ¿ 1 1 + R + ¿ 2 ( 1 + R ) 2 + ¿ 3 ( 1 + R ) 3 + = t = 1 ¿ t ( 1 + R ) t Equity valuation: three scenarios This approach to valuing stock is based on the Dividend Growth Model – 3 variants depending on the growth of earnings (assumption) Dividend growth model 1. Zero growth : perpetuity
P 0 = ¿ 1 R 2. Constant growth : growing perpetuity P 0 = ¿ 1 R g 3. Differential growth : (2 subs) growing annuity + growing perpetuity P 0 t = 1 T ¿ ( 1 + g 1 ) t ( 1 + R ) t + ¿ T + 1 R g 2 ( 1 + R ) T Case 1: Zero growth Assume that dividends will remain at the same level forever ¿ 1 = ¿ 2 = ¿ 3 = Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: P 0 = ¿ 1 1 + R + ¿ 2 ( 1 + R ) 2 + ¿ 2 ( 1 + R ) 3 + P 0 = ¿ R Case 2: Constant Growth [Gordon Growth model (GGM)] Assume that dividends will grow at constant rate, g, forever, i.e. ¿ 1 = ¿ 0 ( 1 + g ) ¿ 2 = ¿ 1 ( 1 + g ) = ¿ 0 ( 1 + g ) 2 ¿ 3 = ¿ 2 ( 1 + g ) = ¿ 0 ( 1 + g ) 3 ¿ 0 ➝ the most recently paid (not the future one) Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: P 0 = ¿ 1 R g = ¿ 0 ( 1 + g ) R g Case 3: Differential Growth Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter To value a differential growth stock, we need to: Estimate future dividends in the foreseeable future

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• Fall '17
• Prof. Yvan Nezerwe

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