Question

(a) ABC Company has just paid a dividend of $1.00 per share. Dividends are paid annually. Analysts estimate that dividends per share will grow at a rate of 20% for the next 2 years, at 15% for the subsequent 3 years, and at 3% thereafter. If the shareholders’ required rate of return is 12% per year, then what is the price of the stock today? What will be the ex-dividend price at the end of the first year? What will be the capital gains yield in the first year? [10 points]

(b) Crazy Dividends Inc. has announced that it will pay dividends only in alternate years, starting 2 years from now. It has just paid a $1.00 dividend per share and the next dividend will be at the end of year 2, followed by dividends at the end of year 4, 6, etc. Each dividend amount is 10% higher than the last payment. So, the next dividend will be $1.10. The stock is selling for $22 right now. What is the shareholders’ required return per year? [5 points]

Answer 1

	ABC Company
	Last Dividend =$1
	Required return =12% pa
		Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
	Growth Rate of Dividend		20%	20%	15%	15%	15%	3% there after
	Dividend amount		$        1.200	$          1.440	$         1.656	$       1.904	$       2.190
	From Year 6 Dividend growth will be 3%
	PV( at year 5) of all dividends from Year 6 will be P0=d0(1+g)/(ke-g)						25.0633
	d0=2.190
	g=3%
	Ke=12%
	P0=2.190*(1.03)/(0.09)=25.0633
1	Sum of all future cash flows		$        1.200	$          1.440	$         1.656	$       1.904	$     27.253
2	Discount fcator @12%	1.0000	0.8929	0.7972	0.7118	0.6355	0.5674
3	PV of all cash flows in future=1*2		$      1.0714	$        1.1480	$       1.1787	$     1.2103	$ 15.4643

Sum of PV of all cash flows = Stock Value today=

$               20.07

	Stock Value after Year 1
1	Future cash flows after Year 1			$          1.440	$         1.656	$       1.904	$     27.253
2	Discount fcator @12%			0.8929	0.7972	0.7118	0.6355
	PV of all cash flows in future=1*2			1.285714286	1.32015306	1.3555143	17.320024
	Sum of all PV of cash flows = Stock value at Year 1		$        21.28
	So Capital Gain s in 1 Year =21.21-20.07	$                 1.21
	Capital Gains Yield =1.21/20.07=	6%

b	As the dividend growth is 10% each 2 year, we can assume that
	the annual growth is 5%
	Suppose the required return =ke
	So , P0=d0(1+g)/(ke-g)
	P0=22
	d0=1
	g=5%
	so, 22=1*1.05/(ke-0.05)
	22*(ke-0.05)=1.05
	Ke-0.05=0.04727
	Ke=9.7727
	Or Required rate of return =9.77%