Question

Constant Growth Stock Valuation

You are analyzing Jillian’s Jewelry (JJ) stock for a possible purchase. JJ just paid a dividend of $1.25 yesterday. You expect the dividend to grow at the rate of 7% per year for the next 3 years, if you buy the stock; you plan to hold it for 3 years and then sell it.

1. What dividends do you expect for JJ stock over the next 3 years? In other words, calculate D₁, D₂ and D₃. Note that D₀ = $1.25. Round your answers to the nearest cent.
   1. D₁ = $  
      
   2. D₂ = $  
      
   3. D₃ = $  
   
   
2. JJ's stock has a required return of 10%, and so this is the rate you'll use to discount dividends. Find the present value of the dividend stream; that is, calculate the PV of D₁, D₂, and D₃, and then sum these PVs. Round your answer to the nearest cent.
   $  
   
3. JJ stock should trade for $54.62 3 years from now (i.e., you expect = $54.62). Discounted at a 10% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $54.62. Round your answer to the nearest cent.
   $  
   
4. If you plan to buy the stock, hold it for 3 years, and then sell it for $54.62, what is the most you should pay for it? Round your answer to the nearest cent.
   $  
   
5. Use the constant growth model to calculate the present value of this stock. Assume that g = 7%, and it is constant. Round your answer to the nearest cent.
   $  
   
6. Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, ? Explain your answer.
   -Select-IIIIIIIVV
   I. Yes. The value of the stock is dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is not equal to the value calculated in Part e. Any other holding period would produce a different value of .
   II. Yes. The value of the stock is dependent upon the holding period due to the fact that the value is determined as the present value of all future expected dividends.
   III. No. The value of the stock is not dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is equal to the value calculated in Part e. Any other holding period would produce the same value of .
   IV. No. The value of the stock is not dependent upon the holding period unless the growth rate remains constant for the foreseeable future.
   V. Yes. The value of the stock is dependent upon the holding period as long as the growth rate remains constant for the foreseeable future.

Answer 1

a.Expected Dividend

D1 = 1.25(1.07) = $1.3375

D2 = 1.25(1.07)² = $1.43

D3 = 1.25(1.07)³ = $1.53

b.Present value = 1.34/1.10 + 1.43/(1.10)² + 1.53/(1.1)³

= $3.55

c.Present value = 54.62/(1.10)³

= $41.04

d.Most to be paid = 3.55+41.04

= $44.59

e.Stock Price = 1.3375/(10%-7%)

= $44.58

f.III No, does not depend