142 PA R T I I APP LI CAT IO N Financial Markets Stock Valuation To see how Equation works, let s compare the price of the Royal Bank stock given the figures reported above You will need to know the required return on equity to find the present value of the cash flows Since a stock is more risky than a bond, you will require a higher return than that offered in the bond market Assume that after careful consideration you decide that you would be satisfied to earn 12% on the investment Solution Putting the numbers into Equation yields the following: P0 $1.25 0.12 $60 0.12 $1.12 $53.57 $54.69 Based on your analysis, you find that the stock is worth $54.69 Since the stock is currently available for $50 per share, you would choose to buy it Why is the stock selling for less than $54.69? It may be because other investors place a different risk on the cash flows or estimate the cash flows to be less than you The Generalized Dividend Valuation Model Using the same concept, the one-period dividend valuation model can be extended to any number of periods: The value of stock is the present value of all future cash flows The only cash flows that an investor will receive are dividends and a final sales price when the stock is ultimately sold in period n The generalized multiperiod formula for stock valuation can be written as: P0 D1 (1 ke )1 D2 (1 ke )2 Dn (1 ke )n Pn (1 ke )n (2) If you tried to use Equation to find the value of a share of stock, you would soon realize that you must first estimate the value the stock will have at some point in the future before you can estimate its value today In other words, you must find Pn in order to find P0 However, if Pn is far in the future, it will not affect P0 For example, the present value of a share of stock that sells for $50 seventy-five years from now using a 12% discount rate is just one cent [$50/(1.1275) $0.01] This reasoning implies that the current value of a share of stock can be calculated as simply the present value of the future dividend stream The generalized dividend model is rewritten in Equation without the final sales price: P0 * t Dn (1 ke )t (3) Consider the implications of Equation for a moment The generalized dividend model says that the price of stock is determined only by the present value of the dividends and that nothing else matters Many stocks not pay dividends, so how is it that these stocks have value? Buyers of the stock expect that the firm will pay dividends someday Most of the time a firm institutes dividends as soon as it has completed the rapid growth phase of its life cycle