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!
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.