Question

Crane Inc.’s common shares currently sell for $32 each. The firm’s management believes that its shares should really sell for $45 each. The firm just paid an annual dividend of $2 per share and management expects those dividends to increase by 8 percent per year forever (and this is common knowledge to the market).

What does management believe is the correct cost of common equity for the firm? (Round final answer to 2 decimal places, e.g. 15.25%.)

Answer 1

(a)(1)-Current cost of common equity for the firm

Dividend in year 0 (D0) = $2.00 per share

Dividend Growth Rate (g) = 8% per year

Current Selling price per share (P0) = $32.00 per share

Using Dividend Discount Model, Cost of Common Equity = [D0(1 + g) / P0] + g

= [$2.00(1 + 0.08) / $32.00] + 0.08

= [$2.16 / $32.00] + 0.08

= 0.0675 + 0.08

= 0.1475 or

= 14.75%

“The current cost of common equity for the firm = 14.75%”

(B)-Correct cost of common equity for the firm

Dividend in year 0 (D0) = $2.00 per share

Dividend Growth Rate (g) = 8% per year

Revised Selling price per share (P0) = $45.00 per share

Using Dividend Discount Model, Cost of Common Equity = [D0(1 + g) / P0] + g

= [$2.00(1 + 0.08) / $45.00] + 0.08

= [$2.16 / $4556.00] + 0.08

= 0.0480 + 0.0800

= 0.1280 or

= 12.80%

“The Correct cost of common equity for the firm = 12.80%”