Question

Given the following information, calculate the current value of the stock: current dividend is $3.00, projected super normal growth for three years at 20%, growth rate after year 3 should remain constant at 11% and you want to earn a 16% annual return. What should you pay for the stock?

A.$67.55

		B.$83.34
		C.$74.39
		D.$61.46

Answer 1

Calculation of the value of the Stock

Current Dividend (D₀) = $3.00

Super Normal growth for next 3 years (g₁) = 20% or 0.20

Growth Rate after 3 year (g₂) = 11% or 0.11

Required rate of Return (r) = 16% or 0.16

Value of Share (P₀) = [D₁/(1+r)] + [D₂/(1+r)²] + [D₃/(1+r)³] + [P₃/(1+r)³]

Where P₀ = Present Value of Share

D₁ = Dividend in year 1

D₂ = Dividend in year 2

D₃ = Dividend in year 3

P₃ = Value of share at the end of the year 3

Calculation of Value of P₃

P₃ = D₄/(r-g₂)

= D₀(1+g₁)³(1+g₂)/(r-g₂)

= $3.00(1+0.20)³(1+0.11)/(0.16-0.11)

= $115.0848

Value of Share (P₀) = [D₁/(1+r)] + [D₂/(1+r)²] + [D₃/(1+r)³] + [P₃/(1+r)³]

= [D₀(1+g₁)/(1+r)¹] + [D₀(1+g₁)²/(1+r)²] + [D₀(1+g₁)³/(1+r)³] + [P₃/(1+r)³]

= [$3.00(1+0.20)/(1+0.16)¹] + [$3.00(1+0.20)²/(1+0.16)²] + [$3.00(1+0.20)³/(1+0.16)³] + [$115.0848/(1+0.16)³]

= $3.10 + $3.21 + $ 3.32 + $73.72

= $83.34

Option B is the answer.