Question

Compute K_e and K_n under the following circumstances:

a. D₁ = $9.20, P₀ = $100, g = 7%, F = $2.00. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
  

b. D₁ = $.18, P₀ = $35, g = 10%, F = $2.50. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
  

c. E₁ (earnings at the end of period one) = $9, payout ratio equals 30 percent, P₀ = $37, g = 3.4%, F = $1.80. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
  

d. D₀ (dividend at the beginning of the first period) = $7, growth rate for dividends and earnings (g) = 5%, P₀ = $63, F = $4. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
  

Answer 1

This question applies use of constant growth dividend discount model. For existing stock, Cost of Equity Ke is mathematically represented as:

For new issuance, Cost of new equity issuance Kn is mathematically represented as:

a) D1 = $9.20, P0 = $100, g = 7%, F = $2.00.

Substituting these values in both the mathematical relations above,

100Ke - 7 = 9.20

100ke = 16.20

Ke = 16.20%

98Kn - 6.86 = 9.20

98Kn = 16.06

Kn = 16.39%

b) D1 = $0.18, P0 = $35, g = 10%, F = $2.50.

Substituting these values in both the mathematical relations above,

35Ke - 3.5 = 0.18

35Ke = 3.68

Ke = 10.51%

32.5Kn - 3.25 = 0.18

Kn = 10.55%

c) D1 = $9 * 30% = $2.7

P0 = $37, g = 3.4%, F= $1.80

Substituting these values in both the mathematical relations above,

37Ke - 1.258 = 2.7

Ke = 10.70%

35.2Kn - 1.1968 = 2.70

Kn = 11.07%

c) D1 = D0 * (1 + g) = 7 * (1 + 5%) = $7.35

P0 = $63, g = 5%, F= $4

Substituting these values in both the mathematical relations above,

63Ke - 3.15 = 7.35

63Ke = 10.50

Ke = 16.67%

59Kn - 2.95 = 7.35

Kn = 17.46%