**Unformatted text preview: **on the dividends and then pay brokerage fees before acquiring additional shares. By using pt as the average stockholder’s personal tax rate and bf as the average brokerage fees stated
as a percentage, we can specify the cost of retained earnings, kr, as kr ks (1 pt) (1 bf). Because of the difficulty in estimating pt and bf, only the simpler definition of kr given in Equation 11.7 is used here. CHAPTER 11 The Cost of Capital 481 offerings of common stock. Flotation costs paid for issuing and selling the new
issue will further reduce proceeds.
We can use the constant-growth valuation model expression for the cost of
existing common stock, ks, as a starting point. If we let Nn represent the net proceeds from the sale of new common stock after subtracting underpricing and
flotation costs, the cost of the new issue, kn, can be expressed as follows:7
D1
Nn kn g (11.8) The net proceeds from sale of new common stock, Nn, will be less than the
current market price, P0. Therefore, the cost of new issues, kn, will always be
greater than the cost of existing issues, ks, which is equal to the cost of retained
earnings, kr. The cost of new common stock is normally greater than any other
long-term financing cost. Because common stock dividends are paid from aftertax cash flows, no tax adjustment is required.
EXAMPLE In the constant-growth valuation example, we found Duchess Corporation’s cost
of common stock equity, ks, to be 13%, using the following values: an expected
dividend, D1, of $4; a current market price, P0, of $50; and an expected growth
rate of dividends, g, of 5%.
To determine its cost of new common stock, kn, Duchess Corporation has
estimated that on the average, new shares can be sold for $47. The $3-per-share
underpricing is due to the competitive nature of the market. A second cost associated with a new issue is flotation costs of $2.50 per share that would be paid to
issue and sell the new shares. The total underpricing and flotation costs per share
are therefore expected to be $5.50.
Subtracting the $5.50 per share underpricing and flotation cost from the current $50 share price results in expected net proceeds of $44.50 per share ($50.00
$5.50). Substituting D1 $4, Nn $44.50, and g 5% into Equation 11.8 results
in a cost of new common stock, kn, as follows:
kn $4.00
$44.50 0.05 0.09 0.05 0.140, or 14.0% Duchess Corporation’s cost of new common stock is therefore 14.0%. This is the
value to be used in subsequent calculations of the firm’s overall cost of capital. Review Questions
11–9 What premise about share value underlies the constant-growth valuation
(Gordon) model that is used to measure the cost of common stock
equity, ks? 7. An alternative, but computationally less straightforward, form of this equation is
kn P0 D1
(1 f) g (11.8a) where f represents the percentage reduction in current market price expected as a result of underpricing and flotation costs. Simply stated, Nn in Equation 11.8 is equivalent to P0 (1 f) in Equation 11.8a. For convenience, Equation 11.8 is used to define the cost of a new issue of common stock, kn. 482 PART 4 Long-Term Financial Decisions 11–10 Why is the cost of financing a project with retained earnings less than the
cost of financing it with a new issue of common stock? LG4 11.5 The Weighted Average Cost of Capital weighted average cost
of capital (WACC), ka
Reflects the expected average
future cost of funds over the long
run; found by weighting the cost
of each specific type of capital
by its proportion in the firm’s
capital structure. Now that we have calculated the cost of specific sources of financing, we can
determine the overall cost of capital. As noted earlier, the weighted average cost
of capital (WACC), ka, reflects the expected average future cost of funds over the
long run. It is found by weighting the cost of each specific type of capital by its
proportion in the firm’s capital structure. Calculating the Weighted Average
Cost of Capital (WACC)
Calculating the weighted average cost of capital (WACC) is straightforward:
Multiply the specific cost of each form of financing by its proportion in the firm’s
capital structure and sum the weighted values. As an equation, the weighted average cost of capital, ka, can be specified as follows:
ka (wi ki) (wp kp) (ws kr or n) (11.9) where
wi proportion of long-term debt in capital structure
wp proportion of preferred stock in capital structure
ws proportion of common stock equity in capital structure
wi wp ws 1.0 Three important points should be noted in Equation 11.9:
1. For computational convenience, it is best to convert the weights into decimal
form and leave the specific costs in percentage terms.
2. The sum of the weights must equal 1.0. Simply stated, all capital structure
components must be accounted for.
3. The firm’s common stock equity weight, ws, is multiplied by either the cost of
retained earnings, kr , or the cost of new common stock, kn. Which cost is
used depends on whether the firm’s common stock equity wi...

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