Question

PCS just paid a $3 dividend. Expected annual dividend growth is 3% per year from Year 1 to 3; 4% per year from Year 4 to 6 and 6% constant dividend. Required rate of return is 12%. What is the current share price of PCS? Price at Year 5?

Answer 1

Present Value of Dividend = D0 = $3

Growth for year 1 to 3 = g1 = 3%

=> D1 = D0(1+g1) = 3(1+0.03) = $3.09

D2 = D1(1+g1) = 3.09(1+0.03) = $3.18

D3 = D2(1+g1) = 3.18(1+0.03) = $3.28

Growth from Year 4 to 6 = g2 = 4%

=> D4 = D3(1+g2) = 3.28(1+0.04) = $3.41

D5 = D4(1+g2) = 3.41(1+0.04) = $3.55

D6 = D5(1+g2) = 3.55(1+0.04) = $3.69

Growth after year 6 = g = 6%

Hence, D7 = D6(1+g) = 3.69(1+0.06) = $3.91

Required Return = r = 12%

Using Gordons Growth model,

Price of Stock in Year 6 = P6 = D7/(r - g) = 3.91/(0.12 - 0.06) = $65.17

Hence, Price of stock now = P0 = D1/(1+r) + D2/(1+r)² + D3/(1+r)³ + D4/(1+r)⁴ + D5/(1+r)⁵ + D6/(1+r)⁶ + P6/(1+r)⁶

= 3.09/(1+0.12) + 3.18/(1+0.12)² + 3.28/(1+0.12)³ + 3.41/(1+0.12)⁴ + 3.55/(1+0.12)⁵ + 3.69/(1+0.12)⁶ + 65.17/(1+0.12)⁶

= $46.70

Price of Stock in Year 5 = P5 = D5/(1+r) + D6/(1+r)² + P6/(1+r)²

= 3.55/(1+0.12) + 3.69/(1+0.12)² + 65.17/(1+0.12)² = $58.06