Question

Triple X Company recently paid a $3 annual dividend. The company is projecting that its dividends will grow by 20 percent next 2 years, 10 percent annually for the following year after that, and then at 5 percent annually thereafter. Based on this information, how much should Triple X's common stock sell for today if her required return is 12%?

Answer 1

Step-1, Dividend per share for the first 3 years

Current Year Dividend per share (D0) = $3.00 per share

Dividend per share Year 1 (D1) = $3.60 per share [$3.00 x 120%]

Dividend per share Year 2 (D2) = $4.32 per share [$3.60 x 120$]

Dividend per share Year 3 (D3) = $4.75 per share [$4.32 x 120$]

Step-2, Calculation of Stock Price for the Year 3 (P3)

Dividend Growth Rate from 3^rd year (g) = 5%

Required Rate of Return (r) = 12%

Stock Price for the Year 3 (P3) = D3(1 + g) / (Ke – g)

= $4.75(1 + 0.05) / (0.12 – 0.05)

= $4.99 / 0.07

= $71.28 per share

Step-3, The Selling Price of the Common Stock today

The Selling Price of the Common Stock today is the Present Value of the future dividend payments and the present value the stock price for the year 3

Selling Price of the Stock Today = D1/(1 + r)¹ + D2/(1 + r)² + D3/(1 + r)³ + P3/(1 + r)³

= $3.60/(1 + 0.12)¹ + $4.32/(1 + 0.12)² + $4.75/(1 + 0.12)³ + $71.28/(1 + 0.12)³

= [$3.60 / 1.12] + [$4.32 / 1.25440] + [$4.75 / 1.40493] + [$71.28 / 1.40493]

= $3.22 + $3.44 + $3.38 + $50.74

= $60.78 per share

“Hence, the Triple X's common stock would be selling for $60.78 per share”