Question

You are analyzing Jillian’s Jewelry (JJ) stock for a possible purchase. JJ just paid a dividend of $1.00 yesterday. You expect the dividend to grow at the rate of 5% 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 = $1.00. Round your answers to the nearest cent.

1. D₁ = $   
   

2. D₂ = $   
   

3. D₃ = $   

2. JJ's stock has a required return of 11%, 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 $20.26 3 years from now (i.e., you expect  = $20.26). Discounted at a 11% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $20.26. 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 $20.26, 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 = 5%, and it is constant. Round your answer to the nearest cent.
   $   

Answer 1

a. D1 =1*(1+5%) =1.05
D2=1*(1+5%)^2 =1.1025 or 1.10
D3=1*(1+5%)^3=1.1576 or 1.16

b. PV of Dividend =1*1.05/1.11+1*1.05^2/1.11^2+1*1.05^3/1.11^3=2.69

c. PV of Future Price =20.23/(1+11%)^3=14.79

d. The most you should pay =PV of Dividends +PV of Par Value=1*1.05/1.11+1*1.05^2/1.11^2+1*1.05^3/1.11^3+20.23/(1+11%)^3 =17.48

e.
PV of this Stock =Dividend*(1+g)/(Required Rate-g) =1*(1+5%)/(11%-5%) =17.50