Finance School of management The discounted dividend model a Chapter 8 shows how the Law of one Price can be used to deduce the value of known cash flows from the observed market prices of bonds. a In this chapter we consider the valuation of uncertain cash flows using a discounted cash flow(DCF approach. a The dcF approach to determining the value of a stock discounts the expected cash flows-either dividends paid to shareholders or net cash flows from trading. Assume: buy and hold for ever uesTc
6 Finance School of Management The Discounted Dividend Model ❑ Chapter 8 shows how the Law of One Price can be used to deduce the value of known cash flows from the observed market prices of bonds. ❑ In this chapter we consider the valuation of uncertain cash flows using a discounted cash flow (DCF) approach. ❑ The DCF approach to determining the value of a stock discounts the expected cash flows-either dividends paid to shareholders or net cash flows from trading. Assume: buy and hold for ever
Finance School of management The discounted dividend model a Discount-dividend model(DDM)is defined as any model that computes the value of a share of stock as the present value of its expected future cash dividends a The risk-adjusted discount rate or market capitalization rate is the expected rate of return that investors require to be willing to invest in the stock uesTc
7 Finance School of Management The Discounted Dividend Model ❑ Discount-dividend model (DDM) is defined as any model that computes the value of a share of stock as the present value of its expected future cash dividends. ❑ The risk-adjusted discount rate or market capitalization rate is the expected rate of return that investors require to be willing to invest in the stock
Finance School of management The discounted dividend model o The rate of return that investors expect, E(1), equals the market capitalization rate, k E(r1)= D1+B1 k 、D1+f D 1+k The price is the present value of the expected end-of-year dividend plus the expected ex-dividend price discounted at the required rate return jesT
8 Finance School of Management The Discounted Dividend Model ❑ The rate of return that investors expect, E(r1 ), equals the market capitalization rate, k. 1 1 0 1 0 ( ) D P P E r k P + − = = k D P P + + = 1 1 1 0 The price is the present value of the expected end-of-year dividend plus the expected ex-dividend price discounted at the required rate return
Finance School of management The discounted dividend model a Using the same logic employed to derive Pos the expected price of stock at the beginning of the second year is D+p 1+k u By substitution we can express p in terms of 152s and p D. +p 1+k(1+k)2 uesTc
9 Finance School of Management The Discounted Dividend Model ❑ Using the same logic employed to derive P0 , the expected price of stock at the beginning of the second year is: 2 2 1 1 D P P k + = + ❑ By substitution, we can express P0 in terms of D1 , D2 , and P2 : 1 2 2 0 2 1 (1 ) D D P P k k + = + + +
Finance School of management The discounted dividend model a By repeating this chain of substitutions, we get the general formula of the DDM D D D P (1+k)(1+k +…=∑ (1+k) The price of a share of stock is the present value of all expected future dividends per share. discounted at the market capitalIzation rate uesTc 10
10 Finance School of Management The Discounted Dividend Model ❑ By repeating this chain of substitutions, we get the general formula of the DDM: 1 2 0 2 1 (1 ) (1 ) (1 ) t t t D D D p k k k = = + + = + + + The price of a share of stock is the present value of all expected future dividends per share, discounted at the market capitalization rate