Question

Problem 8-23 Dividend Initiation and Stock Value (LG8-6) A firm does not pay a dividend. It is expected to pay its first dividend of $0.22 per share in three years. This dividend will grow at 7 percent indefinitely. Use an 8 percent discount rate. Compute the value of this stock. (Round your answer to 2 decimal places.) Stock value

Answer 1

Solution :

D0 = D1 = D2 = 0,

D3 = 0.22

g = 7% = 0.07 = constant for ever.

r = 8% = 0.08

So,

P0 = P2 = D3/(r - g)

=> P0 = 0.22/(0.08 - 0.07) = 22.00 ($) 

Hence, 

Value of the stock = $ 22.00 (ANSWER)

Answer 2

Solution :

D0 = D1 = D2 = 0,

D3 = 0.22 ($)

g = 7% = 0.07 = constant for ever from year 3 onwards.

r = 8% = 0.08

=> 1 + r = 1.08

So,

P2 = D2/(r - g)

=> P2 = 0.22/(0.08 - 0.07) = 22.00 ($) 

=> P0 = P2/(1 + r)^2 = 22.00/1.08^2 = 18.86 ($)

Hence, 

Value of the stock = $18.86  (ANSWER)

Answer 3

Value after year 3=(D3*Growth rate)/(Discount rate-Growth rate)

=(0.22*1.07)/(0.08-0.07)=$23.54

Hence value of stock=Future dividends*Present value of discounting factor(8%,time period)

=0.22/1.08^3+23.54/1.08^3

which is equal to

=$18.86(Approx).