Question

Micah is investing in the stocks of the company KNS. KNS just paid a dividend of $1 per share (D0 = 1). Micah expects the dividend growth rate to be -10% for Year One and 5% for Year Two. Afterwards, Micah believes the growth rate to be constant at g forever. Micah uses CAPM model to determine the discount rate (expected rate of return). And he calculates the following: E(rm) = 6%, rf = 1%, and βKNS = 0.6. (a) If g = 3%, what is Micah’s estimate of the current price using the Dividend Discount Model?

(b) Suppose that the current price of KNS is $120 and Micah decides to short sell 100 shares of KNS stock using margin. The initial margin requirement is 50%. How much does Micah have to deposit into the margin account?

(c) If the price goes up to $140 per share and the maintenance margin is 35%, will Micah receive a margin call?

(d) Suppose Micah receives a margin call under 2(c). What is the minimum amount of cash that Micah can use to bring the margin back to 35%?

Answer 1

		CAPM Equation:
		R=rf+Beta*(rm-rf)
		R=Expected Rate of Return
		Beta=0.6
		rf=Risk Free Rate=1%
		rm=Expected Market Return=6%
		R=Expected Rate of Return=1+0.6*(6-1)	4%
		Dividend Discount Model:
		D0=1
		D1= dividend of year 1	1.1	(1*(1+0.1)	(Growth Rate =10%=0.1
		D2= dividend of year 2	1.155	(1.1*(1+0.05)	(Growth Rate =5%=0.0.05
		D3= dividend of year 3	1.18965	1.155*(1+0.03)	(Growth Rate =g=3%=0.0.03
		R=Expected Return=4%=0.04
		Price in year2=P2
		P2=D3/(R-g)
		P2=1.18965/(0.04-0.03)	118.97
		Current Price =Present Value of Future Cash Flows
		Present Value of future cash flows=(Cash Flow)/((1+R)^N)
		R=Discount Rate =4%=0.04, N=Year of cash flows
		N	CF	PV=CF/(1.04^N)
		Year	Cash Flow	Present Value
	D1	1	1.1	1.057692308
	D2	2	1.155	1.067862426
	P2	2	118.97	109.9898299
			SUM	112.1153846
		P0=Estimated Current Price	$112.12
	(b)	Current Price Per Share	$120
		Total Value of shares shorted=100*120	$12,000
		Initial Margin Requirement	50%
		Amount of initial margin required=50%*12000	$6,000
		Amount to be deposited as initial margin	$6,000
	.(c)	If Price goes up to $140,
		Loss =(140-100)*100	$4,000
		Balance available in margin account=6000-4000	$2,000
		Total value =140*100	$14,000
		Maintenance Margin	35%
		Margin Required =14000*35%	$4,900
		Available Margin	$2,000
		Micah will receive Margin Call
	(d)	Minimum amount to be deposited in margin account	$2,900	(4900-2000)