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A company recently paid a $0.35 dividend. The dividend is expected to grow at a 10.5 percent rate. At a current stock price of $24.25, what return are shareholders expecting? ( LG 3-3 )
( LG 3-3 )
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 ( rs ) is the appropriate interest rate (discount rate) to apply to cash flows when evaluating the historical performance of an equity.
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