Question

Compute K_e and K_n under the following circumstances:

a. D₁ = $5.00, P₀ = $70, g = 8%, F = $7.00. (Round your intermediate and final answers to 2 decimal places.)

Ke:

Kn:

b. D₁ = $.22, P₀ = $28, g = 7%, F = $2.50. (Round your intermediate and final answers to 2 decimal places.)

?Ke:

Kn:

c. E₁ (earnings at the end of period one) = $7, payout ratio equals 40 percent, P₀ = $30, g = 6.0%, F = $2.20. (Round your intermediate and final answers to 2 decimal places.)
Ke:

Kn:

d. D₀ (dividend at the beginning of the first period) = $6, growth rate for dividends and earnings (g) = 7%, P₀ = $60, F = $3. (Round your intermediate and final answers to 2 decimal places.)

Ke:

Kn:

Answer 1

In order to solve this question, we will use Gordon model formula:

a.1. P₀ = D₁ / (K_e - g)

70 = 5 / (K_e - 0.07)

K_e = 5 / 70 + 0.07 = .1414

K_e = 14.14%

a. 2. P₀ - F = D₁ / (K_n - g)

70 - 7 = 5 / (K_n - 0.07)

K_n = 5 / 63 + 0.07 = .1494

K_e = 14.94%

b.1. P₀ = D₁ / (K_e - g)

28 = 0.22 / (K_e - 0.07)

K_e = .22 / 28 + 0.07 = .0779

K_e = 7.79%

b. 2. P₀ - F = D₁ / (K_n - g)

28 - 2.5 = .22 / (K_n - 0.07)

K_n = .22 / 25.5 + 0.07 = .0786

K_e = 7.86%

c. D₁ = E₁ X payout ratio = 7 X 0.40 = 2.8

c.1. P₀ = D₁ / (K_e - g)

30 = 2.8 / (K_e - 0.06)

K_e = 2.8 / 30 + 0.06 = .1533

K_e = 15.33%

c. 2. P₀ - F = D₁ / (K_n - g)

30 - 2.2 = 2.8 / (K_n - 0.06)

K_n = 2.8 / 27.8 + 0.06 = .1607

K_e = 16.07%

d.1. P₀ = D₀ X (1+g) / (K_e - g)

60 = 6 x (1+0.07) / (K_e - 0.07)

K_e = 6.42 / 60 + 0.07 = 0.177

K_e = 17.7%

d.2. P₀ - F = D₀ X (1+g) / (K_e - g)

60 - 3 = 6 x (1+0.07) / (K_e - 0.07)

K_e = 6.42 / 57 + 0.07 = 0.1826

K_e = 18.26%