Answer:
current stock price, [tex]P_{0}[/tex] = $26.84
Explanation:
Given,
Most recent dividend, [tex]D_{0}[/tex] = $1.50
Growth rate, [tex]g_{1}[/tex] = 15% = 0.15 (Next 2 years)
[tex]g_{2}[/tex] = 5% = 0.05 (remain constant after 2 years)
required rate of return , [tex]r_{s}[/tex] = 12% = 0.12
We know,
Current stock price, [tex]P_{0}[/tex] = [[tex]D_{1}[/tex] ÷ (1 + [tex]r_{s}[/tex])] + [tex]\frac{D_{2} + P_{2}}{(1 + r_{s})^{2}}[/tex]
or, [tex]P_{0}[/tex] = [{[tex]D_{0}[/tex] × (1 + [tex]g_{1}[/tex])} ÷ (1 + [tex]r_{s}[/tex])] + [tex]\frac{D_{0} (1 + g_{1})^{2} + \frac{D_{3}}{r_{s} - g_{2}}}{(1 + r_{s})^{2}}[/tex]
or, [tex]P_{0}[/tex] = [{$1.50 × (1 + 0.15)} ÷ (1 + 0.12)] + [tex]\frac{1.50*(1+0.15)^{2} + \frac{D_{2} (1 + g_{2})}{(0.12 - 0.05)}}{(1+0.12)^{2}}[/tex]
or, [tex]P_{0}[/tex] = ($1.725 ÷ 1.12) + [tex]\frac{1.98375 + \frac{1.98375*(1 + 0.05)}{0.07}}{1.2544}[/tex]
or, [tex]P_{0}[/tex] = $1.5402 + [(1.98375 + 29.75625) ÷ 1.2544]
or, [tex]P_{0}[/tex] = $1.5402 + (31.74 ÷ 1.2544)
or, [tex]P_{0}[/tex] = $1.5402 + 25.3029
Therefore, current stock price, [tex]P_{0}[/tex] = $26.84
