Question

DB company just paid a dividend of $ D0 per share. It is estimated that the company's dividend will grow at a rate of 10 percent per year for the next 2 years, then the dividend is expected to grow at constant rate of 6 percent thereafter. You are also given that DB stock’s has beta of 1.2, and the expected market rate of return is 11% and the risk-free rate is 6%. Based on this, the current price of the DB stock is $28.48. What is the value of D0?

Answer 1

Value of D0 is $ 1.50

As per dividend discount model, current price of stock is the present value of future dividends.
Step-1:Present value of dividends of first 2 years
Year	Dividend	Discount factor	Present value
a	b	c=1.12^-a	d=b*c
1	1.10D0	0.892857	0.982143	D0
2	1.21D0	0.797194	0.964605	D0
Total			1.946747	D0
Working:
# 1	As per Capital Asset Pricing model,
	Required return	=	Risk free rate	+	Beta	*	(Market return - Risk free return)
		=	6%	+	1.2	*	(11%-6%)
		=	6%	+	1.2	*	5%
		=	12.00%
# 2	Dividend of year:
	1	D0*(1+0.10)^1	=	1.10	D0
	2	D0*(1+0.10)^2	=	1.21	D0
Step-2:Present value of dividend after year 2
Present value		=	D2*(1+g)/(K-g)*DF2			Where,
		=	17.04135	D0		D2	1.21	D0
						g	6%
						K	12%
						DF2	0.797194
Step-3:Sum of present value of dividends
Sum of present value of dividends		=	1.946747	D0	+	17.04135	D0
		=	18.9881	D0
As pe dividend discount mode, current price of stock is the sum of present value of dividends.
28.48		=	18.9881	D0
D0		=	$       1.50