Question

A company’s current ROE is 12%. It pays out one-half of its earnings as cash dividends. Current book value is $20 and all reinvestments in the business will also produce a 12% return.

If the cost of capital is 8%, what is the appropriate current share price? What is the expected share price after five years?

If the cost of capital is 15%, what is the appropriate current share price? What is the expected share price after five years?

Answer 1

Answer:

Book value per share = $20

ROE = 12%

Hence Earning per share (EPS) = Book value per share * ROE = $20 * 12% = $2.40

It pays out one-half of its earnings as cash dividends. Hence dividend payout ratio = 50% and retention ratio is = 1 - dividend payout ratio = 1 - 50% = 50%

Hence current dividend per share = EPS * Dividend payout ratio = $2.40 * 50% = $1.20

Growth rate = ROE * Retention ratio = 12% * 50% = 6%

Hence dividend per share next year = Current dividend per share * (1 + growth rate)

= $1.20 * (1 + 6%) = $1.272

Cost of capital = 8%

Current share price with constant growth of 6% = Dividend next year / (Cost of capital - growth rate)

= $1.272 / (8% - 6%)

= $63.60

Expected share price after five years = Dividend of 6th Year / (Cost of capital - growth rate)

= $1.20 * (1 + 6%) ⁶ / (8% -6%)

= $85.11

Cost of capital = 15%

If the cost of capital is 15%, current share price = $1.20 * (1+6%) / (15% - 6%) = $14.13

Expected share price after five years = = $1.20 * (1+6%) ⁶ / (15% - 6%) = $18.91