Question

Your task is to value Shake Shack's (SHAK’s) stock. Shake Shack's next dividend (i.e., the dividend at t =
1) is expected to be $3.25. Across years 2 and 3 and 4, dividends will grow by 7%/year. After that, dividends
are projected to grow at a constant rate of 3% forever. SHAK has a debt-to-equity ratio (in market-value
terms) of 1.0. The yield to maturity on SHAK's bonds averages 4% and the company's tax rate is 30%. If the
risk-free rate is 2.2%, the market risk premium is 6%, and SHAK's equity beta is 1.25, what should the stock
sell for today based on a discounted valuation of its projected dividends?

Answer 1

Required rate of return of Shak's stock ( under CAPM)

Where,

Ke = Cost of equity (Required rate of return)

rf = risk free return

= Beta

Thus,

Ke = 9.7%

Sell Price of Stock using discounted discount model -

Growth rate (g) till 4th year = 7%

Growth rate after that = 3%

D1 = 3.25

D2 = 3.25*1.07 = 3.4775

D3 = 3.4775*1.07 = 3.720925

D4 = 3.720925*1.07 = 3.98138975

D5 = 3.98138975*1.03 = 4.1008314425

Therefore, Today's sell price of Shak's stock is $53.6841

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.