Question

Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $1.25 yesterday. Bahnsen's dividend is expected to grow at 6% per year for the next 3 years. If you buy the stock, you plan to hold it for 3 years and then sell it. The appropriate discount rate is 11%.

1. Find the expected dividend for each of the next 3 years; that is, calculate D₁, D₂, and D₃. Note that D₀ = $1.25. Do not round intermediate calculations. Round your answers to the nearest cent.
   
   D₁ = $  
   D₂ = $  
   D₃ = $  
   
2. Given that the first dividend payment will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PVs of D₁, D₂, and D₃, and then sum these PVs. Do not round intermediate calculations. Round your answer to the nearest cent.
   $  
   
3. You expect the price of the stock 3 years from now to be $31.56; that is, you expect  to equal $31.56. Discounted at an 11% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $31.56. Do not round intermediate calculations. 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 $31.56, what is the most you should pay for it today? Do not round intermediate calculations. Round your answer to the nearest cent.
   $  
   
5. Use equation below to calculate the present value of this stock.
             
   Assume that g = 6% and that it is constant. Do not round intermediate calculations. Round your answer to the nearest cent.
   $  
   
6. Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period was 2 years or 5 years rather than 3 years, would this affect the value of the stock today,  ?
   
   1. 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  .
   2. 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  .
   3. 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.
   4. No. The value of the stock is not dependent upon the holding period unless the growth rate remains constant for the foreseeable future.
   5. Yes. The value of the stock is dependent upon the holding period as long as the growth rate remains constant for the foreseeable future.
   
   -Select-IIIIIIIVVItem 8

Answer 1

a]

dividend in each of next 3 years = D0 * (1 + dividend growth rate for next 3 years)^{number of years from today}

D1 = $1.25 * (1 + 6%)¹ = $1.33

D2 = $1.25 * (1 + 6%)² = $1.40

D3 = $1.25 * (1 + 6%)³ = $1.49

b]

present value of each dividend = dividend / (1 + discount rate)^{number of years after which dividend is paid}

Sum of PVs of next 3 years dividends = $3.42

А с 1 Year Dividend 1 1.33 1.40 1.49 Total mtin 2 PV of Dividend 1.19 1.14 1.09 3.42

1 Year Dividend 2 1 -1.25*1.06^A2 32 =1.25*1.06^A3 4 3 =1.25*1.06^44 Total PV of Dividend =B2/(1+11%)^A2 =B3/(1+11%)^A3 =B4/(1+11%)^A4 =SUM(C2:04)

c]

present value of expected future stock price = expected future stock price / (1 + discount rate)³

present value of expected future stock price = $31.56 / (1 + 11%)³

present value of expected future stock price = $23.08

d]

Most you should pay = Sum of PVs of next 3 years dividends + present value of expected future stock price

Most you should pay = $3.42 + $23.08 = $26.50