Question

Janet Ludlow’s firm requires all its analysts to use a two-stage dividend discount model (DDM) and the capital asset pricing model (CAPM) to value stocks. Using the CAPM and DDM, Ludlow has valued QuickBrush Company at $63 per share. She now must value SmileWhite Corporation. a. Calculate the required rate of return for SmileWhite by using the information in the following table: Quick Brush SmileWhite Beta 1.35 1.15 Market price $45.00 $30.00 Intrinsic value $63.00 ? Notes: Risk-free rate 4.50% Expected market return 14.50% b. Ludlow estimates the following EPS and dividend growth rates for SmileWhite: First 3 years 12% per year Years thereafter 9% per year Estimate the intrinsic value of SmileWhite by using the table above, and the twostage DDM. Dividends per share in the most recent year were $1.72. c. Recommend QuickBrush or SmileWhite stock for purchase by comparing each company’s intrinsic value with its current market price. d. Describe one strength of the two-stage DDM in comparison with the constantgrowth DDM. Describe one weakness inherent in all DDMs.

Answer 1

a)	Required rate of return for SmileWhite per CAPM = 4.50%+1.15*(14.50%-4.50%) =	16.00%
b)	The intrinsic value of the stock of SmileWhite is the sum
	of the PV of the dividends for the next 3 years growing
	at 12% and the PV of the continuing value of dividends
	from year 4 to infinity, which grow at 9%.
	Year	Dividends	PV at 16%	PV at 16%
	0	$                1.72	1
	1	$                1.93	0.86207	$            1.66
	2	$                2.16	0.74316	$            1.61
	3	$                2.42	0.64066	$            1.55
	PV of dividends t1 to t3			$            4.82
	Continuing value of dividends = 2.42*1.09/(0.16-0.09) =	$              37.68
	PV of continuing value of dividends = 37.68*0.64066 =			$          24.14
	Intrinsic value of SmileWhite share			$          28.96
c)		QuickBrush	SmileWhite
	Intrinsic value	$              63.00	$             28.96
	Market value	$              45.00	$             40.00
	QuickBrush is undervalued by the market and SmileWhite is over price by the market.
	Hence, the undervalued stock is to be bought.
d)	The two stage model estimates the dividends more rationally by estimating the
	dividends of the immediately succeeding years and then assuming a constant growth
	rate (a lower rate) after the period of high growth rate.
	The weakness of all DDMs is that it assumes a perpetual growth rate into the future
	which may not hold.