ABC is a profitable firm not paying a dividend on its common stock. Frank, a ana
ID: 2664314 • Letter: A
Question
ABC is a profitable firm not paying a dividend on its common stock. Frank, a analyst believes the ABC will begin paying a $3.00 per share dividend in two yrs and that the dividend will increase 4% annually thereafter. Kent, a colleague of Frank at the same firm is less optimistic. Brett thinks the ABC company will begin paying a divident in 4 yrs and it will be $2.50 and it will grow at a rate of 3% annually. John and James agree that the required return for ABC is 11%.
a. what value would Frank estimate for the firm
b. what value will Kent assign to ABC stock
Explanation / Answer
a) Calculating the present value of the firm: The formula for calculating the current price per share is P0 = D1 / (1+r)^1 + D2 / (1+r)^2 + D3 / (1+r)^3 + P3 / (1+r)^3 where r is the required return = 11% D1 is the Dividends in the year-1 = $3 P0 is the present value of the stock= ? g is the growth rate = 4% The value of Dividend per share in the years 1 and 2 is $3.00 and the dividend in the year-3 will increase 4% annually. Dividend in the year-3 = $3.00 (1.04) = $3.12 Dividend in the year-4 = $3.12 (1.04) = $3.25 Calculating the price of the share in the year-3: P3 = D4 / (r - g) = $3.25 / (0.11 - 0.04) = $3.25 / 0.07 = $46.43 Substituting the values in the above formula, we get P0 = ($3 / 1.11) + ($3.00 / 1.2321) + ($3.12 / 1.37) + ($46.43 / 1.37) = $2.7 + $2.43 + $2.27 + $33.89 = $41.29 Therefore, the present value of the stock is $41.29 b) Calculating the value of the stock: The formula for calculating the current price per share is P0 = D1 / (1+r)^1 + D2 / (1+r)^2 + D3 / (1+r)^3 + P3 / (1+r)^3 where r is the required return = 11% D1 is the Dividends in the year-1 = $2.50 P0 is the present value of the stock = ? g is the growth rate = 3% The value of Dividend per share in the years 1 ,2, 3 & 4 is $2.50 and the dividend in the year-5 will increase 3% annually. Dividend in the year-5 = $2.50 (1.03) = $2.575 Dividend in the year-6 = $2.575 (1.034) = $2.65 Calculating the price of the share in the year-3: P5 = D6 / (r - g) = $2.65 / (0.11 - 0.03) = $2.65 / 0.08 = $33.125 Substituting the values in the above formula, we get P0 = ($2.5 / 1.11) + ($2.5/ 1.2321) + ($2.5/ 1.37) + ($2.5 / 1.518) + ($2.575 / 1.685) + ($33.125/ 1.685) = $2.25 + $2.03 + $1.82 + $1.647 + $1.53 + $19.66 = $28.937 or $29 Therefore, the present value of the stock is $29 = $2.7 + $2.43 + $2.27 + $33.89 = $41.29 Therefore, the present value of the firm is $41.29