Question

Federal Biochem's preffered stock pays a fixed annual dividend of $2.4. The company's common stock just paid a dividend of $1 and this dividend is expected to grow at 4% every year starting from today. The required rate of return for both securities is 12%. If you were to buy the preffered stock today and convert it to common stock in 5 years, what would be the approximate conversion ratio from preferred stock to common stock that would allow you to earn annual rate of return of 14.77% on your investment on the preferred stock over the five year investment horizon?

Answer 1

	a	Annual on Preferred stock	$2.40
	b	Required Return	12%	0.12
	c=a/b	Price of Preferred Stock	$20.00
	D0	Current dividend of common stock	$1.00
	g	Dividend growth rate=4%	0.04
	D1=D0*(1+g)	Dividend in Year 1=1*1.04	$1.04
	R	Required Return=12%	0.12
	P0	Current Market price =P0=D1/(R-g)=1.04/(0.12-0.04)	$13.00
	P5=P0*(1+g)^5	Market Price of Common Stock at end of year5	$15.82	13*(1.04^5)
	A	Intestment in Preferred Stock now	$20.00
	B	Required return from investment =14.77%	0.1477
	C=A*(1+B)^5	Required Price of conversion =20*(1.1477^5)	$39.83	$79.66
	D	Market Price of Common Stock at end of year5	$15.82	$79.10
	E=C/D	Number of Common Shares to be received on conversion for one Preferred Share	2.51804	(39.83/15.82)
		Approximate Conversion Ratio:
		2 Preferred Shares Converted to 5 Common Shares