Question

Ragan, Inc. was founded nineteen years ago by brother and sister Carrington and Genevieve Ragan. The company manufactures and installs commercial heating, ventilation, and cooling (HVAC) units. Ragan, Inc. has experienced rapid growth because of a proprietary technology that increases the energy efficiency of its units. The company is equally split between the two siblings. The original partnership agreement between them gave each 500,000 shares of stock. The company has since gone public. At that time, the siblings retained their shares and 1,000,000 shares of new stock were issued. The firm anticipates needing to raise a large amount of capital ($10 million) in the coming year to facilitate further expansion and are evaluating several financing options. The first option is to issue zero-coupon bonds that mature in 20 years. Similar zero-coupon bonds currently have a YTM of 4.5%. The second option is to issue 4% coupon bonds that mature in 20 years. Similar bonds have a YTM of 4%. The third option is to issue preferred stock with a fixed dividend of $0.85 per share. These preferred stock would have a required return of 7.5%. The firm currently has no preferred stock outstanding. The fourth option is to issue common stock.The stock is currently trading on the market for $20 per share. The firm most recently paid a dividend on common stock of $0.50 and plans to increase that dividend by 25% per year for the next five years. After that, the firm will level off at the industry average of 5% per year, indefinitely. Carrington and Genevieve estimate the required return on the stock to be 15%. 5. What do you think about the estimate of a 15% required return? What does the current stock price suggest about the required return? 6. If they can sell new shares of common stock at the current stock price of $20, how many would they have to issue? 7. Based on your answer above (#6), what would be the increase in the dividend expenses for the firm in future years?

Answer 1

	Required Return=15%=0.15
	Present value(PV) of cash flow=(cash flow)/(1+i)^N
	i=Required return=0.15, N=Year of Cash flow
	Current Price P0=Sum of PV of future cash flows
	Dividend in year N+1=1.25*Dividend in yearN, when N is less than or equal to 4
	Dividend in year 1=1.25*(dividend in year 0)
	Dividend in year N+1=1.05*Dividend in yearN, when N is greater than 4
	Dividend in year6=1.05*(Dividend in year 5)
	Price at year 5=(Dividend in year6/(i-g)
	i=Required return=0.15, g= constant growth rate up to infinity=5%=0.05
		Year	Dividend
		0	$0.50
		1	$0.63
		2	$0.78
		3	$0.98
		4	$1.22
		5	$1.53
		6	$1.602
		N	A	B=A/(1.15)^N
		Year		Present Value
	D1=Dividend in year1	1	$0.63	0.543478261
	D2=Dividend in year2	2	$0.78	0.59073724
	D3=Dividend in year3	3	$0.98	0.642105696
	D4=Dividend in year4	4	$1.22	0.697940974
	D5=Dividend in year5	5	$1.53	0.758631493
	P5=Price at year 5=1.6/(0.15-0.05)=	5	$          16	7.954827765
			Total	11.18772143
	As per dividend growth model Current priceP0=	$            11.19
	Required Return of 15% appears to be high
	Since current market price is$20
	If required return is 11%
	The calculation of current price is given below
		N	A	B=A/(1.11)^N
		Year		Present Value
	D1=Dividend in year1	1	$0.63	0.563063063
	D2=Dividend in year2	2	$0.78	0.634080026
	D3=Dividend in year3	3	$0.98	0.714054083
	D4=Dividend in year4	4	$1.22	0.804114959
	D5=Dividend in year5	5	$1.53	0.905534863
	P5=Price at year 5=1.6/(0.11-0.05)=	5	$          27	15.82536875
			Total	19.44621574
	P0=Current price	$            19.45
	Hence , the required rate of return is close to 11%, if market price is fair
C	Amount of capital needed	$10,000,000
D	selling price of each share	$20
E=C/D	Number of shares required to be issued	500,000
	Increase in dividend expense		F	G=F*500000
				Increase in Dividend
		Year	Dividend	Expense
		1	$0.63	$312,500
		2	$0.78	$390,625
		3	$0.98	$488,281
		4	$1.22	$610,352
		5	$1.53	$762,939
		6	$1.60	$801,086
		7	$1.68	$841,141
		8	$1.77	$883,198
		9	$1.85	$927,358
		10	$1.95	$973,726