EQUITY VALUATION
The valuation process for an equity instrument (such as preferred or common stock) involves finding the present value of an infinite series of cash flows on the equity discounted at an appropriate interest rate. Cash flows from holding equity come from dividends paid out by the firm over the life of the stock, which in expectation can be viewed as infinite since a firm (and thus the dividends it pays) has no defined maturity or life. Even if an equity holder decides not to hold the stock forever, he or she can sell it to someone else who in a fair and efficient market is willing to pay the present value of the remaining (expected) dividends to the seller at the time of sale.
Dividends on equity are that portion of a firm’s earnings paid out to the stockholders. Those earnings retained are normally reinvested to produce future income and future dividends for the firm and its stockholders. Thus, conceptually, the fair price paid for investing in stocks is the present value of its current and future dividends. Growth in dividends occurs primarily because of growth in the firm’s earnings, which is, in turn, a function of the profitability of the firm’s investments and the percentage of these profits paid out as dividends rather than being reinvested in the firm. Thus, earnings growth, dividend growth, and stock value (price) will generally be highly correlated. We begin by defining the variables we will use to value an equity:
D t Dividend paid out to stockholders at the end of the year t
P t Price of a firm’s common stock at the end of the year t
P 0 Current price of a firm’s common stock
r s Interest rate used to discount cash flows on an investment in a stock
As described above, time value of money equations can be used to evaluate a stock from several different perspectives. For example, the realized rate of return ( r s ) is the appropriate interest rate (discount rate) to apply to cash flows when evaluating the historical performance of an equity.
The valuation process for an equity instrument (such as preferred or common stock) involves finding the present value of an infinite series of cash flows on the equity discounted at an appropriate interest rate. Cash flows from holding equity come from dividends paid out by the firm over the life of the stock, which in expectation can be viewed as infinite since a firm (and thus the dividends it pays) has no defined maturity or life. Even if an equity holder decides not to hold the stock forever, he or she can sell it to someone else who in a fair and efficient market is willing to pay the present value of the remaining (expected) dividends to the seller at the time of sale.
Dividends on equity are that portion of a firm’s earnings paid out to the stockholders. Those earnings retained are normally reinvested to produce future income and future dividends for the firm and its stockholders. Thus, conceptually, the fair price paid for investing in stocks is the present value of its current and future dividends. Growth in dividends occurs primarily because of growth in the firm’s earnings, which is, in turn, a function of the profitability of the firm’s investments and the percentage of these profits paid out as dividends rather than being reinvested in the firm. Thus, earnings growth, dividend growth, and stock value (price) will generally be highly correlated. We begin by defining the variables we will use to value an equity:
D t Dividend paid out to stockholders at the end of the year t
P t Price of a firm’s common stock at the end of the year t
P 0 Current price of a firm’s common stock
r s Interest rate used to discount cash flows on an investment in a stock
As described above, time value of money equations can be used to evaluate a stock from several different perspectives. For example, the realized rate of return ( r s ) is the appropriate interest rate (discount rate) to apply to cash flows when evaluating the historical performance of an equity.
The expected rate of return, E(r s ) , is the appropriate interest rate when analyzing the expected future return on stocks, assuming the investor buys the stock at its current market price, receives all promised payments, and sells the stock at the end of his or her investment horizon
Finally, the required rate of return ( r s ) is the appropriate interest rate when analyzing the fair value of a stock investment over its whole lifetime. The fair value of a stock reflects the present value of all relevant (but uncertain) cash flows to be received by an investor discounted at the required rate of return ( r s ) the interest rate or return that should be earned on the investment given its risk. Present value methodology applies time value of money to evaluate a stock’s cash flows over its life as follows:
The price or value of a stock is equal to the present value of its future dividends (Dt) , whose values are uncertain. This requires an infinite number of future dividend values to be estimated, which makes the equation above difficult to use for stock valuation and r s calculationin practice. Accordingly, assumptions are normally made regarding the expected pattern of the uncertain flow of dividends over the life of the stock. Three assumptions that are commonly used are (1) zero growth in dividends over the (infinite) life of the stock; (2) a constant growth rate in dividends over the (infinite) life of the stock; and (3) nonconstant growth in dividends over the (infinite) life of the stock.
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