Question

The last dividend paid by Coppard Inc. was $1.50. The dividend growth rate is expected to be constant at 35% for 3 years, after which dividends are expected to grow at a rate of 6% forever. If the firm's required return (rs) is 11%, what is its current stock price?

Answer 1

D0 = $ 1.50

D1 = D0 x (1 + growth rate) = D0 x (1+0.35) = D0 x 1.35 = $ 1.50 x 1.35 = $ 2.025

D2 = D1 x (1 + growth rate) = D1 x (1+0.35) = D1 x 1.35 = $ 2.025 x 1.35 = $ 2.73375

D3= D2 x (1 + growth rate) = D2 x (1+0.35) = D2 x 1.35 = $ 2.73375 x 1.35 = $ 3.6905625

D4= D3 x (1 + growth rate) = D3 x (1+0.6) = D3 x 1.06 = $ 3.6905625 x 1.35 = $ 3.91199625

As per Dividend Discount model, stock price at the end of year 3 is;

P3 = D4/ (rs – g)

rs = Rate of return = 11 %

g = Constant growth rate = 6 %

P3 = $ 3.91199625/ (0.11 – 0.06)

    = $ 3.91199625/ 0.05

    = $ 78.239925

Current stock price = D1/(1+r) + D2/(1+r)2 + D3/(1+r)3+ P3/(1+r)3

           = $ 2.025/ (1+0.11) + $ 2.73375/ (1+0.11)2 + $ 3.6905625/ (1+0.11)23+ $ 78.239925/ (1+0.11)3

           = $ 2.025/ (1.11) + $ 2.73375/ (1.11)2 + $ 3.6905625/ (1.11)3 + $ 78.239925/ (1.11)3

           = $ 2.025/1.11 + $ 2.73375/ 1.21 + $ 3.6905625/ 1.331 + $ 78.239925/ 1.331

             = $ 1.84090909090909 + $ 2.25929752066116 + $ 2.77277422990233 + $ 58.7828136739294

           = $ 65.65579451540198 or $ 65.66

Current stock price is $ 65.66