Question

11

Compute Ke and Kn under the following circumstances:

a. D1 = $4.60, P0 = $92, g = 6%, F = $5.00. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. D1 = $.26, P0 = $25, g = 6%, F = $2.50. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. E1 (earnings at the end of period one) = $5, payout ratio equals 40 percent, P0 = $29, g = 8.5%, F = $2.80. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

d. D0 (dividend at the beginning of the first period) = $4, growth rate for dividends and earnings (g) = 7%, P0 = $55, F = $5. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

a. D1 = $4.60, P0 = $92, g = 6%, F = $5.00

Cost of retained earnings = Ke = (D1 / P0) + g = (4.60 / 92) + 6% = 0.05 + 6% = 5% + 6% = 11.00%

Cost of new stock = Kn = [D1 / (P0 - F)] + g = [4.60 / (92 - 5)] + 6% = [4.60 / 87] + 6% = 0.052873 + 6% = 5.2873% + 6% = 11.2873% = 11.29% (rounded to two decimal places)

b. D1 = $0.26, P0 = $25, g = 6%, F = $2.50

Cost of retained earnings = Ke = (D1 / P0) + g = (0.26 / 25) + 6% = 0.01040 + 6% = 1.040% + 6% = 7.040% = 7.04% (rounded to two decimal places)

Cost of new stock = Kn = [0.26 / (25 - 2.50)] + g = [0.26 / (22.5)] + 6% = 0.011555 + 6% = 1.1555% + 6% = 7.1555% = 7.16% (rounded to two decimal places)

c. E1 (earnings at the end of period one) = $5, dividend payout ratio = 40%, P0 = $29, g = 8.5%, F = $2.80

D1 = E1 x Dividend payout ratio = 5 x 40% = $2

Cost of retained earnings = Ke = (D1 / P0) + g = (2 / 29) + 8.5% = 0.068965 + 8.5% = 6.8965% + 8.5% = 15.3965% = 15.40% (rounded to two decimal places)

Cost of new stock = Kn = [2 / (29 - 2.80)] + 8.5% = [2 / (26.20)] + 8.5% = 0.076335 + 8.5% = 7.6335% + 8.5% = 16.1335% = 16.13% (rounded to two decimal places)

d. D0 (dividend at the beginning of the first period) = $4, growth rate for dividends and earnings = g = 7%, P0 = $55, F = $5

D1 = D0 x (1 + g) = 4 x (1 + 7%) = 4 x 1.07 = 4.28

Cost of retained earnings = Ke = (D1 / P0) + g = (4.28 / 55) + 7% = 0.077818 + 7% = 7.7818% + 7% = 14.7818% = 14.78% (rounded to two decimal places)

Cost of new stock = Kn = [ 4.28 / (55 - 5)] + 7% = [4.28 / (50)] + 7% = 0.08560 + 7% = 8.56% + 7% = 15.56% (rounded to two decimal places)