Question

Metal Corp. just paid $1 dividends and is assumed to grow at 7% per year. The required return of the company is 15%. The present value of the first 60 dividend payments is $13.198. What is the present value of all the dividend payments from year 61 to infinity assuming the required return and the growth rate stay constant? 

$.11 

$.177 

$3.375 

None of the answers is correct 

$13.375

Answer 1

Solution:
	Answer is 2nd option $.177
Working Notes:
	The stock is of constant growth stock, current stock price of any stock is the present of all dividend in its life, and if Present value of first 60 dividends is given the we can compute the present value of all the dividend payments form 61 to infinity, By simply deduction present value of first 60 dividends from current price of the stock , hence we have to compute current stock price.
Now	Current stock price is computed Using Gordon growth model
	P0 = D0(1+g) (Ke - g)
	Where
	ke = required rate of return = 15%
	P0=current share price = ??
	g= growth rate= 7%
	D0= Just paid Dividend=$1 per share
	P0 = D0(1+g)/(Ke -g)
	P0 = 1 x (1+7%)/(15% -7%)
	P0 = $13.375 per share
Hence	For present value of all the dividend payments form 61 to infinity =??
	Present value of first 60 dividends = $13.198
	current stock price of any stock is the present of all dividend in its life =$13.375 computed
	so
	current stock price = Present value of first 60 dividends + present value of all the dividend payments form 61 to infinity
	$13.375 = $13.198 + present value of all the dividend payments form 61 to infinity
	Present value of all the dividend payments form 61 to infinity =$13.375-$13.198
	Present value of all the dividend payments form 61 to infinity =$.177
	Answer is 2nd option $.177
Please feel free to ask if anything about above solution in comment section of the question.