Question

Sara Smith is a surgical nurse at Orlando Surgery Centers (OSC), a small for-profit ambulatory surgery center whose stock is traded in the OTC market. A few nights ago, Sara received a call from her mother asking for some advice regarding a stock recommendation. Her mother said that her broker had recommended adding 1,000 shares of WSC stock to the family’s retirement portfolio. Because Sara worked at OSC, her mother thought that Sara might have some special insights.

            Sara was finishing up her master’s degree in healthcare administration at AdventHealth University, so she thought this would be a good opportunity to apply some of the stock valuation concepts she had learned. To begin, she looked up some basic data:

• OSC beta coefficient= 1.70
• Yield on treasury bonds (risk-free rate) = 5 percent
• Required rate of return on the market portfolio= 12 percent
• Last dividend paid= $1.60
• Expected growth rate= a constant 8.0%, or alternatively, 12% for 3 years and 7% constant growth thereafter.
• Current stock price= $18.50

Now, she must use this information to make some judgements about whether or not her mother should follow he broker’s advice.

Part a

Use the Security Market Line (SML) of the capital asset pricing model (CAPM) to estimate the required rate of return on the stock.

Part b

Estimate the current fair value of the stock using the constant growth valuation model.

Part c

Calculate the expected rate of return.

Part d

Use the non-constant growth model to estimate OSC’s fair value.

Part e

Based on parts a – d, should the stock be purchased? Please explain

Answer 1

Part (a)

OSC beta coefficient, beta = 1.70
Yield on treasury bonds = risk-free rate = 5 percent
Required rate of return on the market portfolio= 12 percent

As per the Security Market Line (SML) of the capital asset pricing model (CAPM), the required rate of return on the stock, K_e = Risk free rate + beta x (Required rate of return on the market portfolio - risk-free rate) = 5% + 1.7 x (12% - 5%) = 16.90%

Part (b)

Last dividend paid, D₀ = $1.60
Expected constant growth rate, g = 8.0%

Hence, the current fair value of the stock using the constant growth valuation model = D₀ x (1 + g) / (K_e - g) = 1.60 x (1 + 8%) / (16.90% - 8.00%) = $  19.42

Part (c)

Current price, = $ 18.50.

If K_exp = expected rate of return on this stock then,

$ 18.50 = = D₀ x (1 + g) / (K_exp - g) = 1.60 x (1 + 8%) / (K_exp - 8.00%)

Hence, K_exp = 1.60 x (1 + 8%) / 18.50 + 8.00% = 17.34%

Part (d)

Under non constant growth model,

g₁ = growth in first phase = 12% for 3 years

and, terminal growth rate, g = 7% constant thereafter

Hence, D₁ = D₀ x (1 + g₁) = 1.6 x (1 + 12%) = $ 1.792

D₂ = D₁ x (1 + g₁) = 1.792 x (1 + 12%) = $ 2.007

D₃ = D₂ x (1 + g₁) = 2.007 x (1 + 12%) = $ 2.248

and, D₄ = D₃ x (1 + g) = 2.248 x (1 + 7%) = $ 2.405

Terminal value of all the future dividends, at the end of year 3 = TV₃ = D₄ / (K_e - g) = 2.405 / (16.90% - 7.00%) = $  24.30

Hence, Price today = PV of all future dividends + PV of TV₃ = D₁ / (1 + K_e) + D₂ / (1 + K_e)² + D₃ / (1 + K_e)³ + TV₃ / (1 + K_e)³ = 1.792 / (1 + 16.90%) + 2.007 / (1 + 16.90%)² + 2.248 / (1 + 16.90%)³ + 24.30 / (1 + 16.90%)³ = $ 19.62

Part (e)

Since the current share price = $ 18.50 is lesser than the intrinsic share price calculated under constant growth model or non constant growth model, the stock is under priced as of now. Hence, it should be purchased.