Question

4. Last year, a company paid a $2.50 per share dividend. The dividend is expected to grow at a constant rate of 8% per year. The stock currently sells for $50 a share. If the company issues additional stock, it must pay its investment banker a flotation cost of $3.5 per share. (1) What is the cost of external equity, re , (2) what will be the cost of external equity, re, if the flotation cost were 10%?

Answer 1

The cost of external equity, re, without flotation costs is 13.4%. With a flotation cost of $3.5 per share, the re is 13.81%. If the flotation cost were 10%, the re would be 14%.

Step-by-step explanation:

Last year, a company paid a $2.50 per share dividend, which is expected to grow at a constant rate of 8% per year. The stock currently sells for $50 a share. To calculate the cost of external equity, re, without flotation costs, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model is represented by the formula:

re = (D1 / P0) + g

where D1 is the dividend expected at the end of year one, P0 is the current stock price, and g is the growth rate of dividends.

First, calculate D1:

D1 = $2.50 * (1 + 0.08) = $2.70

Then substitute into the formula:

re = ($2.70 / $50) + 0.08 = 0.054 + 0.08 = 0.134 or 13.4%

For the cost of external equity including a 10% flotation cost, the stock price used should account for this cost:

P0 (adjusted) = $50 - ($50 * 0.10) = $50 - $5 = $45

Then calculate re:

re = ($2.70 / $45) + 0.08 = 0.06 + 0.08 = 0.14 or 14%

The cost of external equity with a flotation cost of $3.5 per share would be:

P0 (adjusted for $3.5) = $50 - $3.5 = $46.5

And so, re adjusted for $3.5 flotation cost:

re = ($2.70 / $46.5) + 0.08 = 0.05806 + 0.08 = 0.13806 or 13.81%