A stock just paid a dividend of $1.17. The dividend is expected to grow at 21.41% for three years and then grow at 4.10% thereafter. The required return on the stock is 14.60%. What is the value of the stock?
A stock just paid a dividend of $1.81. The dividend is expected to grow at 24.24% for five years and then grow at 3.81% thereafter. The required return on the stock is 12.06%. What is the value of the stock?
Requirement 1:
D0 = $ 1.17
D1= $ 1.17 + $ 1.17 x 0.2141 = $ 1.17 + $ 0.250497 = $ 1.420497
D2= $ 1.420497 + $ 1.420497 x 0.2141 = $ 1.420497 + $ 0.3041284077 = $ 1.7246254077
D3 = $ 1.7246254077 + $ 1.7246254077 x 0.2141 = $ 1.7246254077 + $ 0.36924229978857
= $ 2.09386770748857
D4 = $ 2.09386770748857 + $ 2.09386770748857 x 0.041
= $ 2.09386770748857 + $ 0.0858485760070314 = $ 2.1797162834956014
As per dividend discount model, price of stock on year 3rd,
P3 = D4 / (r – g)
D4 = Dividend on year 4 = $ 2.1797162834956014
r = Required return = 14.60 % or 0.146
g = Constant growth rate = 4.10 % or 0.041
P3 = $ 2.1797162834956014/ (0.146 – 0.041)
= $ 2.1797162834956014/0.105
= $ 20.7592026999581
Stock price today = D1/(1+r) + D2/(1+r)2 + D3/(1+r)3+ P3 /(1+r)3
= $ 1.420497/ (1+0.146) + $ 1.7246254077/ (1+0.146)2 + $ 2.09386770748857/ (1+0.146)3+
$ 20.7592026999581/ (1+0.146)3
= $ 1.420497/ (1.146) + $ 1.7246254077/ (1.146)2 + $ 2.09386770748857/ (1.146)3+
$ 20.7592026999581/ (1.146)3
= $ 1.420497/1.146 + $ 1.7246254077/ 1.313316 + $ 2.09386770748857/ 1.505060136 +
$ 20.7592026999581/ 1.505060136
= $ 1.23952617801047 + $ 1.31318388544722 + $ 1.39121863466097 + $ 13.7929390350673
= $ 17.73686773318596 or $ 17.74
Value of stock is $ 17.74
Requirement 2:
D0 = $ 1.81
D1= $ 1.81 + $ 1.81 x 0.2424 = $ 1.81 + $ 0.438744 = $ 2.248744
D2= $ 2.248744 + $ 2.248744 x 0.2424 = $ 2.248744 + $ 0.5450955456 = $ 2.7938395456
D3 = $ 2.7938395456+ $ 2.7938395456 x 0.2424 = $ 2.7938395456 + $ 0.67722670585344
= $ 3.47106625145344
D4 = $ 3.47106625145344 + $ 3.47106625145344 x 0.2424
= $ 3.47106625145344 + $ 0.841386459352314 = $ 4.31245271080576
D5 = $ 4.31245271080576 + $ 4.31245271080576 x 0.2424
= $ 4.31245271080576 + $ 1.04533853709932 = $ 5.35779124790508
D6 = $ 5.35779124790508 + $ 5.35779124790508 x 0.0381
= $ 5.35779124790508 + $ 0.20413184654518 = $ 5.56192309445026
As per dividend discount model, price of stock on year 5th
P5 = D6 / (r – g)
D6 = Dividend on year 6 = $ 5.56192309445026
r = Required return = 12.06 % or 0.1206
g = Constant growth rate = 3.81 % or 0.0381
P5 = $ 5.56192309445026/ (0.1206 – 0.0381)
= $ 5.56192309445026/0.0825
= $ 67.4172496297001
Stock price today = D1/(1+r) + D2/(1+r)2 + D3/(1+r)3+ D4/(1+r)4+ D5/(1+r)5+P5 /(1+r)5
= $ 2.248744/ (1+0.1206) + $ 2.7938395456/ (1+0.1206)2 + $ 3.47106625145344/ (1+0. 1206)3+
+ $ 4.31245271080576/ (1+0. 1206)4 + $ 5.35779124790508/ (1+0.1206)5 + $ 67.4172496297001/ (1+0.1206)5
= $ 2.248744/ (1.1206) + $ 2.7938395456/ (1.1206)2 + $ 3.47106625145344/ (1.1206)3+ $ 4.31245271080576/ (1.1206)4 + $ 5.35779124790508/ (1.1206)5 + $ 67.4172496297001/ (1.1206)5
= $ 2.248744/1.1206 + $ 2.7938395456/ 1.255744+ $ 3.47106625145344/ 1.407187129816
$ 4.31245271080576/ 1.57689389767181 + $ 5.35779124790508/ 1.76706730173103 + $ 67.4172496297001/1.76706730173103
= $ 2.00673210779939 + $ 2.2248473770569 + $ 2.46666998148804 + $ 2.7347767133685
+ $ 3.03202444109319 + $ 38.1520554218041
= $ 50.61710604261012 or $ 50.62
Value of stock is $ 50.62
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