Question

Far Side Corporation is expected to pay the following dividends over the next four years: $9, $5, $2, and $1. Afterward, the company pledges to maintain a constant 3 percent growth rate in dividends forever.

  

Required:

If the required return on the stock is 10 percent, what is the current share price? (Do not round your intermediate calculations.)

Answer 1

Solution:
	Current share price is   $24.55
Working Notes:
Notes:	current stock price we compute using Dividend Discount Model (DDM)
	Using DDM
	P0= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + P4/(1+r)^4
	Where
	P0 = current stock price=??
	D1 = Dividend at end of first year = $9
	D2 = Dividend at end of 2nd year = $5
	D3 = Dividend at end of 3rd year = $2
	D4 = Dividend at end of 4th year = $1
	D5= Dividend at end of 5th year = D4 x (1+ g) =$1 x ( 1 + 3%) =1.03
	Required rate of return of the stock =r = 10%
Notes:	As after 4th year dividend will constantly growth , hence we will compute the stock price as terminal value using Gordon growth model at end of 4th year as below:
	Using Gordon growth model :
	P4 = D5 /( r - g)
	= $1.03/( 10% - 3%)
	= 14.7142857
At last	P0= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + P4/(1+r)^4
	P0= $9/(1+ 10%)^1 +$5/(1+ 10%)^2 + $2/(1+ 10%)^3 +$1/(1+10%)^4 + 14.7142857/(1+10%)^4
	P0= $24.54974776
	P0= $24.55
Hence	Current share price is   $24.55
Please feel free to ask if anything about above solution in comment section of the question.