Question

Based on the following information for Builtrite, calculate the current value of its stock if the current dividend is $3.00, a projected super normal growth for three years at 20%, the growth rate after year 3 should remain constant at 9% and you want to earn a 16% annual return. What would you be willing to pay for Builtrite stock?

Answer 1

$61.35

Step-by-step explanation:

The computation of the current value of the stock is shown below:

Current Dividend = D0 = $3.00

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

Growth Rate after 3 year = g2 = 9% or 0.09

Required rate of Return = r = 16% or 0.16

Now

as we know that

Value of Share (P0) is

= [D1 ÷ (1 + r)] + [D2 ÷ (1 + r)^2] + [D3 ÷ (1 + r)^3] + [P3 ÷ (1 +r )^3]

Where

D1 = Dividend in year 1

D2 = Dividend in year 2

D3 = Dividend in year 3

P3 = Value of share at the end of year 3

Now first we have to compute the P3 value which is

P3 = D4 ÷ (r - g2)

= D0 × (1 + g1)^3 (1 + g2) ÷(r - g2)

= $3.00 × (1 + 0.20)^3 (1 + 0.09) ÷ (0.16-0.09)

= $5.65056

Now

Value of Share (P0) is

= [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] + [$5.65056 ÷ (1 + 0.16)^3]

= $3.10 + $3.21 + $ 3.32 + $51.72

= $61.35