Question

Compute K_e and K_n under the following circumstances:

a. D₁ = $5.50, P₀ = $94, g = 3%, F = $6.00. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Ke = ?

Kn = ?

b. D₁ = $.28, P₀ = $32, g = 7%, F = $3.00. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
  

Ke = ?

Kn = ?

c. E₁ (earnings at the end of period one) = $6, payout ratio equals 15 percent, P₀ = $36, g = 9.5%, F = $1.20. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Ke = ?

Kn = ?

d. D₀ (dividend at the beginning of the first period) = $5, growth rate for dividends and earnings (g) = 4%, P₀ = $57, F = $4. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Ke = ?

Kn = ?

Answer 1

We can use the dividend growth model to compute the required return on retained earnings (Ke) and required return on new stock (Kn), as follows:

• Ke = D1 / P0 + g
• Kn = D1 / (P0 - F) + g

where D1 is expected dividend per share, P0 is current stock price, g is dividend growth rate, and Fis flotation costs.

a. Applying the dividend growth model,

• Ke= 5.5 / 94 + 3% = 8.85%
• Kn = 5.5 / (94 - 6) + 3% = 9.25%

b. Applying the dividend growth model,

• Ke= 0.28 / 32 + 7% = 7.87%
• Kn = 0.28 / (32 - 3) + 7% = 7.97%

c. Expected dividend per share = earnings per share * dividend pay out ratio = 6*15% = 0.90 . Applying the dividend growth model,

• Ke = 0.90 / 36 + 9.5% = 12%
• Kn = 0.90 / (36 - 1.2) + 9.5% = 12.09%

d. Expected dividend per share = current dividend per share * (1 + dividend growth rate) = 5*(1 + 4%) = 5.2. Applying the dividend growth model,

• Ke = 5.2 / 57 + 4% = 13.12%
• Kn = 5.2 / (57 - 4) + 4% = 13.81%.