Question

Your broker offers to sell you some shares of FFC a common stock that paid a dividend of Rs. 2 yesterday. FFC dividend is expected to grow at 5% per year for the next 3 years, and, if you buy the stock, you planned to hold it for 3 years and then sell it. The appropriate discount rate is 12 percent.

a. Find the expected dividend for each of the next 3 years; that is, calculate D₁, D₂, and D₃. (3M)

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 PV of D₁, D₂, and D₃, and then sum these PVs. (2M)

c. You expect the price of stock 3 years from now to be Rs. 34.73; Discounted at a 12 percent rate, what is the present value of this expected future stock price? (2M)

d. If you plan to buy the stock, hold it for three years and then sell it for Rs.34.73, what is the most you should pay for it today? (2M)

e. Calculate the present value of this stock. Assume that g = 5%, and it is constant. (1M)

Answer 1

a.

D1 = D0*(1 + Growth rate) = 2*(1.05) = 2.1

D2 = D1*(1+Growth Rate) = 2.1*1.05 = 2.2050

D3 = D2*(1+Growth rate) = 2.2050*1.05 =2.31525

b.

Hence, the present value of dividend is $5.28 (rounded off to two decimals)

c.

Present Value of Stock Price = Stock Price/(1+discount rate)^3 = 34.74/(1.12^3) = $24.73 (rounded off to two decimals)

d.

The most we should pay is the present value of future cash flows i.e. dividend and stock price.

Therefore, the most we should pay = PV of dividend + PV of stock price

= 5.28 + 24.73 = $30.01

e.

Assuming the stock pay dividend till perpetuity

Value of stock = D1/(Discount rate - Growth Rate) = 2.1/(12% - 5%) = 2.1/.07 = $30.00

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