Question

1. A company’s stock is currently selling for $80 per share. The company has just paid a dividend of $3.75 per share. Investors expect this dividend to grow at the rate of 9% per year for the next 8 years and at a rate of 3% per year thereafter.

1. Calculate the cost of equity for this company.

Answer 1

current stock price (P₀) = $80

dividend growth rate for first 8 years (g₁) = 9%

From 9th year the dividend growth rate (g₂) = 3%

D_t = dividend paid in year t

Dividend paid in year 0 i.e. today (D₀) = $3.75 per share

Dividend in year 1 = Dividend in year 0 + ( dividend in year 0 * growth rate * t )

D₁ = D₀ + ( D₀ * g₁ * 1)

= $3.75 + ($3.75 * 9% * 1)

= $3.75 + $0.3375

D₁ = $4.0875

Similarly, D₈ = D₀ + ( D₀ * g₁ * 8)

D₈ = $3.75 + ($3.75 * 9% * 8)

D₈ = $3.75 + $2.7

D₈ = $6.45

Therefore, dividend in year 8 (D₈) = $6.45

Cost of equity (K_e) using dividend growth model:

K_e = (Dividend / current stock price) + growth rate

= ( D₈ / P₀ ) + g₂

= ($6.45 / $80) + 3%

= 0.080625 + 3%

= 8.0625% + 3%

K_e = 11.0625%