# Cost of stock issue?

I just can't figure this out. Every formula I find assumes the dividend grows by a percent, not by a fixed amount. The problem: AYZ Company is planning on issuing common stock. Bankers have determined that the stock will be offered at 50 dollars per share and that a dividend of 2 dollars will be paid in one year. It is anticipated that there will a consistent growth in dividends of 4 dollars annually. Assuming no flotation cost, what will be the cost of this issue of stock? Thanks in advance!

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The question obviously asks for help with a homework assignment. –  vanguard2k 57 mins ago

In terms of stock valuation (please note I'm note certain if that is equivalent to the cost of stock issue), I believe you need to model the growth of the dividend separately as a growing perpetuity using the following equation:

P/i + Q/(i^2) where P is a constant payment and Q is the increasing part.

For your example, assume you start with 0 and then the dividend will increase by 4 per year (add 2 after). P=0 Q=4 i= rate of return assumed

If i=5%, then the present value as of t=1 is: 2+ 0/0.05 + 4/(0.05^2) 2+0+800= 802

Present value (t=0) = 802/1.05 = \$763.81

The valuation of the stock will then be the 50 dollars per share plus the present value of the dividends per share.

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