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%.

A. 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 = $

B. 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. $

C. 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. $

D. 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. $

E. 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.

Answer 1

A) Following table shows value of D1,D2 and D3

Year	Dividend
0	D0 = 1.25	1.2500
1	D1=1.25*1.06	1.3250
2	D2 = 1.325*1.06	1.4045
3	D3 = 1.4045*1.06	1.4888

B) Statement showing Present Value of Dividend

Year	Dividend		PVIF @ 11%	Present value= Dividend*PVIF
1	D1=1.25*1.06	1.3250	0.9009	1.1937
2	D2 = 1.325*1.06	1.4045	0.8116	1.1399
3	D3 = 1.4045*1.06	1.4888	0.7312	1.0886
Total				3.4222

C) Present value of expected selling price

= Expected selling price after 3 years *PVIF(11%,3years)

= 31.56*0.7312

=$23.08

D) Price to be paid for the stock

=PV of stock price + Sum of PV of dividend

=23.08+3.42

=26.5$

E) Stock price using formula Po = D0(1+g)/Ke-g

D0(1+g) = D1 = 1.325

g= growth rate =6%

Ke=Discount rate = 11%

Po= Price of stock today

Po = 1.325/11%-6%

=1.325/5%

=$26.5