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Q: Finding a stock price with other financial information ( Answered ,   0 Comments )
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 Subject: Finding a stock price with other financial information Category: Business and Money > Finance Asked by: aufordboy-ga List Price: \$50.00 Posted: 19 Oct 2005 11:01 PDT Expires: 18 Nov 2005 10:01 PST Question ID: 582188
 ```Company A will not issue any dividends for the next three years. The company expects to pay a \$0.50 dividend on the 4th year, a \$0.75 dividend the 5th, and then increase dividends by 3 percent each year thereafter. If the required rate of return in the market for stocks of this risk is 18%, what is the current price of a share of Company A's stock? What is the stock price & how do you find it?```
 Subject: Re: Finding a stock price with other financial information Answered By: juggler-ga on 19 Oct 2005 12:07 PDT Rated:
 ```Hello. The theoretical current price, or present value, of the stock is the combined value of: (1) the present value of the dividends for the 4th and 5th years; and (2) the present value of the stream of dividends beginning in the sixth year. Let's start with part (1): The formula we use is Present Value = C4/(1+r)^4 + C5/(1+r)^5 where C4 is the dividend for the 4th year (i.e., \$0.50), C5 is the dividend for the 5th year (i.e., \$0.75) and "r" is the required rate of return (i.e., 18% or 0.18). Present Value = C4/(1+r)^4 + C5/(1+r)^5 PV = 0.50/(1+.18)^4 + 0.75/(1+.18)^5 PV = 0.25789 + 0.3278 PV = 0.5857 Now we move on to (2) the present value of the stream of dividends beginning in the sixth year. In the 6th year, the dividend will grow 3%, so it will be: \$0.75 * 1.03 = \$0.7725 From that point on, the dividend will continue to grow at 3%. Thus, we treat this as a growing perpetuity that begins in the 6th year. The formula for present value of this delayed growing perpetuity is PV = [C6 / r - g ] * [(1 / 1 + r)^(t - 1)] where C6 is the dividend in the sixth year (i.e., \$0.7725), r is the discount rate (0.18), g is the growth rate (i.e., 3% or .03), and t is the time period (year 6 here). PV = [C6 / r - g ] * [(1 / 1 + r)^(t - 1)] PV = [0.7725 / 0.18 - .03] * [(1 / 1 + .18)^(6 - 1)] PV = [0.7725 / 0.15] * [(1 /1.18)^5] PV = 5.15 * 0.4371 PV = 2.251 Finally, we must combine the present value of the dividends for the 4th and 5th years (i.e., 0.5857) with the present value of the stream of dividends beginning in the 6th year (i.e., 2.251). 0.5857 + 2.251 = 2.84 Thus, the theoretical current price, or present value, of the stock is \$2.84. See this powerpoint on Corporate Finance for more information: http://waltoncollege.uark.edu/lab/CWann/Powerpoint/Chap004.ppt ------ search strategy: "delayed growing perpetuity" Thanks.```

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