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

a. Beta of OSC = 1.70, Risk free rate = 5%, Expected return on market = 12%

Required rate of return using Security Market line of CAPM = Risk free rate + Beta of OSC (Expected return on market - risk free rate) = 5% + 1.70(12%-5%) = 5% + 1.70 x 7% = 5% + 11.90% = 16.90%

b. Last dividend = $1.60 , Constant growth rate = g = 8%, Required rate of return on stock = r = 16.90%

Next dividend = D₁ = Last dividend x (1 + Constant growth rate) = 1.60 x (1+8%) = 1.72

Let P be current fair value of stock and then applying constant growth rate model

P = 1.72 / 8.90% = $19.32

c. Current stock price = $18

Expected rate of return = (Next Dividend / Current stock price) + Expected constant growth rate

= (1.72/18,5) + 8% = 9.29% + 8% = 17.29%

d. Growth rate for first 3 years = 12%

Next dividend = D₁ = Last dividend (1+12%) = 1.60 (1+12%) = 1.79

Dividend after 2 years = D₂ = D₁ (1 + 12%) = 1.79 (1+12%) = 2.0048 = 2.00

Dividend after 3 years = D₃ = D₂ (1+12%) = 2.00 (1+12%) = 2.24

Constant Growth rate after 3 years = g = 7%

Dividend after 4 years = D₄ = D₃ (1+7%) = 2.24 (1+7%) = 2.39

We will find the terminal value of stock at the end of 3 using constant growth rate model

Let T be the terminal value of stock

T = 2.39 / 9.90% = 24.14

Let P be fair value of stock

P = 1.53 + 1.46 + 16.51 = $19.50

e. Based on the above parts stock should be purchased because of following reasons

i) Price of the stock calculated using constant growth rate model in part b is $19.32 , whereas current price of stock is $18.50. Hence current price is below the intrinsic value of stock.Thus the stock is currently undervalued and should be purchased

ii) Price of the stock calculated using non constant growth rate model in part d is 19.50, whereas current price of stock is $18.5. Hence the current price is below the intrinsic value of stock.Thus the stock is currently undervalued and should be purchased.

iii) Required return of stock on the basis of SML calculated in part a is 16.90% whereas expected return of the stock on the basis of current market price calculated in part c is 17.29%. Thus the stock will generate a higher return than the one predicted by the SML for the given Beta. Thus stock is undervalued and should be purchased.