Question

The Duo Growth Company just paid a dividend of $1.00 per share. The dividend is expected to grow at a rate of 21% per year for the next three years and then to level off to 5% per year forever. You think the appropriate market capitalization rate is 16% per year.

a. What is your estimate of the intrinsic value of a share of the stock?

b. b. If the market price of a share is equal to this intrinsic value, what is the expected dividend yield?

Answer 1

a.	$    14.10
Working:
As per dividend discount model, current price of stock is the present value of future dividends.
Step-1:Present value of dividends of next 3 years
Year	Dividend	Discount factor	Present value
a	b	c=1.16^-a	d=b*c
1	$       1.21	0.862069	$       1.04
2	$       1.46	0.743163	$       1.09
3	$       1.77	0.640658	$       1.13
Total			$       3.27
Working:
Dividend of Year:
1	=	$       1.00	*	1.21	=	$       1.21
2	=	$       1.21	*	1.21	=	$       1.46
3	=	$       1.46	*	1.21	=	$       1.77
Step-2:Present value of dividend after year 3
Present value	=	D3*(1+g)/(K-g)*DF3		Where,
	=	$    10.83		D3	$       1.77
				g	5%
				K	16.00%
				DF3	0.640658
Step-3:Sum of present value of future dividends
Sum of present value of future dividends	=	$       3.27	+	$    10.83
	=	$    14.10
So, price of stock is		$    14.10
b.	Dividend yield	=	Annual dividend	/	Current market price
		=	$       1.21	/	$    14.10
		=	8.58%