Question

ABC's common stock is currently selling for $40 per share. The dividend expected to be paid at the end of the coming year is $5. Its dividend payments have been growing at a constant rate for the last 5 years. 5 years ago, the dividend was $3.2. It is expected that to sell, a new common stock issue must be underpriced by $1 per share in floatation costs and a new common stock must be underderpriced $1 per share. show the calculation in detail and formula

Answer 1

Value of ABC's common stock will be calculated using the DDM (Dividend Discounting Method)
The variables required for this are:
- Coming Year's Dividend
- Dividend Growth Rate, and
- ABC's Cost of Capital
These are computed below.
Computation of Dividend Growth Rate
	It is given that divdend grows at a constant rate.
	Let rate of growth be "x"
	then, dividend for the years under consideraton are:
					(Current Year)	(Coming Year)
					(Current Year)	(Coming Year)
Year	1	2	3	4	5	6
Given Data	3.20					5.00
Dividend in "x"		=3.2*(1+x)	=3.2*(1+x)^2	=3.2*(1+x)^3	=3.2*(1+x)^4	=3.2*(1+x)^5
		5=3.2(1+x)^5
	or,	(1+x)^5=5/3.2
	or,	(1+x)^5=1.5625
	or,	(1+x)=1.5625^(1/5)
	or,	(x)=.0934	or, 9.34 %
The dividend figures or the years under consideration are as below:
					(Current Year)	(Coming Year)
Year	1	2	3	4	5	6
Given Data	3.20					5.00
Dividend in "x"		=3.2*(1+x)	=3.2*(1+x)^2	=3.2*(1+x)^3	=3.2*(1+x)^4	=3.2*(1+x)^5
Dividend	3.20	3.50	3.83	4.18	4.57	5.00
As the coming year dividend calculated matches the dividend as given in the question, we know that dividend growth rate is 9.34 %
Computing the Cost of Capital of ABC
Stock must be underpriced by $1 to sell
Therefore ABC's cost of capital would be				=5/(40-1)	or	0.128205128
					i.e.	12.82%
($5 is the expected dividend of coming year and share price must be reduced by $1 from current price of $40 to sell in the market as given in the question)
Computing the value of the share using the DDM method
As pr the dividend discounting method,
	Value of Share =		Coming Year's dividend / (ABC's Cost of Capital-ABC's Dividend Growth rate)
or,	Value of Share =		=5/(.1282-.0934)
or,	Value of Share =		$         143.68