Question

Janet Ludlow’s firm requires all its analysts to use a two-stage DDM and the CAPM to value stocks. Using these measures, Ludlow has valued QuickBrush Company at \(63 per share. She now must value SmileWhite Corporation.

a. Calculate the required rate of return for SmileWhite using the information in the following table:

	December 2010
	Quick brush	Smile white
Beta	1.35	1.15
Market price	\)45	\(30
Intrinsic value	\)63	?

b. Ludlow estimates the following EPS and dividend growth rates for SmileWhite:

First three years	12% per year
Years thereafter	9% per year

Estimate the intrinsic value of SmileWhite using the table above and the two-stage DDM. Dividends per share in 2010 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 constant-growth DDM. Describe one weakness inherent in all DDMs.

Short answer

a.16%

b. $28.89

c. QuickBrush has potential for abnormal returns while SmileWhite has below market risk adjusted returns.

d.Strength: It allows for separate valuation of two distinct periods in company’s future.

Weakness: They are very sensitive to input values.

Step-by-step solution

Calculation of required rate of return ‘a’

Formula: k =r_f + β [E(r_M) –r_f ]

= 0.045 + 1.15 x (0.145 - 0.045)

= 0.16 or 16%

Estimation of intrinsic value ‘b’

Year Dividends

2007 $1.722014

2008 $1.72 x 1.12 = $1.932015

2009 $1.72 x (1.12)² = $2.162016

2010 $1.72 x (1.12)³ = $2.422017

2011 $1.72 x (1.12)³ x 1.09 = $2.63

Present value (PV) of dividends paid in years 2014 to 2016:

Year PV of Dividends

2008 $1.93/1.16 = $1.662014

2009 $2.16/(1.16)² = $1.61

2010 $2.42/(1.16)³ = $1.55

Total: $4.82

P₂₀₁₀ = D₂₀₀₃/ k－g = $ 2.630 / 0.16－0.0 9 = $37.57

PV (in 2013) of P₂₀₁₀ = $37.57/(1.16)³ = $24.07

Intrinsic value of stock = $4.82 + $24.07 = $28.89

Calculation of intrinsic values of two companies ‘c’

From the comparison of the Intrinsic values of two companies, it is noted that QuickBrish is selling below while QuickSmile is selling above intrinsic value. This implies that QuickBrush has the potential for abnormal returns while SmileWhite has slightly below market risk adjusted returns.

Explanation of one strength and one shortcoming of two-stage DDM compared to constant growth DDM

Strength: It allows for separate valuation of two distinct periods in company’s future.

Weakness: They are very sensitive to input values.