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Which of those represent a correct relationship between the present value of the payments that the investor will receive and the price of the stock? 1. Pt = Di+1 D{+2 + (1+re) 2. R = = 4. Pt = Di+1 Pt+1-Pt + Pt Pt 3. Pt Pt+2 + (1+re)²¹ (1+re)² = (1+g) Dt(re-g) D₁ +2 D₁+1 (1+g) (1+g)² + + e Pt+2 (1+g)²

Which of those represent a correct relationship between the present value of the payments that the investor will receive and the price of the stock? 1. Pt = Di+1 D{+2 + (1+re) 2. R = = 4. Pt = Di+1 Pt+1-Pt + Pt Pt 3. Pt Pt+2 + (1+re)²¹ (1+re)² = (1+g) Dt(re-g) D₁ +2 D₁+1 (1+g) (1+g)² + + e Pt+2 (1+g)²

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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### Understanding the Relationship Between Present Value of Payments and Stock Price In finance, the price of a stock is often evaluated in terms of the present value of expected future payments. Here are four equations that attempt to model this relationship. Let’s examine each one: 1. \( \mathbf{P_t = \dfrac{D_{t+1}^e}{(1 + r_e)} + \dfrac{D_{t+2}^e}{(1 + r_e)^2} + \dfrac{P_{t+2}^e}{(1 + r_e)^2}} \) This equation states that the price of the stock today (\(P_t\)) is equal to the sum of the present value of expected dividends (\(D_{t+1}^e\), \(D_{t+2}^e\)) and the present value of the expected price of the stock in the future (\(P_{t+2}^e\)), all discounted back at the required rate of return (\(r_e\)). 2. \( \mathbf{R = \dfrac{D_{t+1}^e}{P_t} + \dfrac{P_{t+1}^e - P_t}{P_t}} \) This formula is representative of the expected return (\(R\)). It expresses the return as the sum of the dividend yield (\(\dfrac{D_{t+1}^e}{P_t}\)) and the capital gains yield (\(\dfrac{P_{t+1}^e - P_t}{P_t}\)). 3. \( \mathbf{P_t = \dfrac{(1 + g)}{D_t (r_e - g)}} \) This equation is incorrect in its current form. Typically, we have the Gordon Growth Model where \(P_t = \dfrac{D_{t+1}}{(r_e - g)}\), which represents the stock price given a constant growth rate (\(g\)) of dividends. 4. \( \mathbf{P_t = \dfrac{D_{t+1}^e}{(1 + g)} + \dfrac{D_{t+2}^e}{(1 + g)^2} + \dfrac{P_{t+2}^e}{(1 + g)^2}} \) This equation uses
Transcribed Image Text:### Understanding the Relationship Between Present Value of Payments and Stock Price In finance, the price of a stock is often evaluated in terms of the present value of expected future payments. Here are four equations that attempt to model this relationship. Let’s examine each one: 1. \( \mathbf{P_t = \dfrac{D_{t+1}^e}{(1 + r_e)} + \dfrac{D_{t+2}^e}{(1 + r_e)^2} + \dfrac{P_{t+2}^e}{(1 + r_e)^2}} \) This equation states that the price of the stock today (\(P_t\)) is equal to the sum of the present value of expected dividends (\(D_{t+1}^e\), \(D_{t+2}^e\)) and the present value of the expected price of the stock in the future (\(P_{t+2}^e\)), all discounted back at the required rate of return (\(r_e\)). 2. \( \mathbf{R = \dfrac{D_{t+1}^e}{P_t} + \dfrac{P_{t+1}^e - P_t}{P_t}} \) This formula is representative of the expected return (\(R\)). It expresses the return as the sum of the dividend yield (\(\dfrac{D_{t+1}^e}{P_t}\)) and the capital gains yield (\(\dfrac{P_{t+1}^e - P_t}{P_t}\)). 3. \( \mathbf{P_t = \dfrac{(1 + g)}{D_t (r_e - g)}} \) This equation is incorrect in its current form. Typically, we have the Gordon Growth Model where \(P_t = \dfrac{D_{t+1}}{(r_e - g)}\), which represents the stock price given a constant growth rate (\(g\)) of dividends. 4. \( \mathbf{P_t = \dfrac{D_{t+1}^e}{(1 + g)} + \dfrac{D_{t+2}^e}{(1 + g)^2} + \dfrac{P_{t+2}^e}{(1 + g)^2}} \) This equation uses
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