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**Unformatted text preview: **ss Corporation example into
the approximation formula given in Equation 11.1, we get
I
kd $1,000 $960
20
$960 $1,000
2 $92
$980 $90 2
$980 9.4% This approximate before-tax cost of debt is close to the 9.452% value calculated
precisely in the preceding example. After-Tax Cost of Debt
However, as indicated earlier, the specific cost of financing must be stated on
an after-tax basis. Because interest on debt is tax deductible, it reduces the
firm’s taxable income. The after-tax cost of debt, ki, can be found by multiplying the before-tax cost, kd, by 1 minus the tax rate, T, as stated in the following
equation:
ki kd (1 T) (11.2) 476 PART 4 Long-Term Financial Decisions EXAMPLE Duchess Corporation has a 40% tax rate. Using the 9.4% before-tax debt cost
calculated above, and applying Equation 11.2, we find an after-tax cost of debt
of 5.6% [9.4% (1 0.40)]. Typically, the explicit cost of long-term debt is less
than the explicit cost of any of the alternative forms of long-term financing, primarily because of the tax deductibility of interest. Review Questions
11–5 What are the net proceeds from the sale of a bond? What are flotation
costs and how do they affect a bond’s net proceeds?
11–6 What three methods can be used to find the before-tax cost of debt?
11–7 How is the before-tax cost of debt converted into the after-tax cost? LG2 11.3 The Cost of Preferred Stock
Preferred stock represents a special type of ownership interest in the firm. It gives
preferred stockholders the right to receive their stated dividends before any earnings can be distributed to common stockholders. Because preferred stock is a
form of ownership, the proceeds from its sale are expected to be held for an infinite period of time. The key characteristics of preferred stock were described in
Chapter 7. However, the one aspect of preferred stock that requires review is
dividends. Preferred Stock Dividends
Most preferred stock dividends are stated as a dollar amount: “x dollars per
year.” When dividends are stated this way, the stock is often referred to as “xdollar preferred stock.” Thus a “$4 preferred stock” is expected to pay preferred
stockholders $4 in dividends each year on each share of preferred stock owned.
Sometimes preferred stock dividends are stated as an annual percentage rate.
This rate represents the percentage of the stock’s par value, or face value, that
equals the annual dividend. For instance, an 8 percent preferred stock with a $50
par value would be expected to pay an annual dividend of $4 a share (0.08 $50
par $4). Before the cost of preferred stock is calculated, any dividends stated as
percentages should be converted to annual dollar dividends. Calculating the Cost of Preferred Stock
cost of preferred stock, kp
The ratio of the preferred stock
dividend to the firm’s net
proceeds from the sale of
preferred stock; calculated by
dividing the annual dividend, Dp ,
by the net proceeds from the sale
of the preferred stock, Np. The cost of preferred stock, kp, is the ratio of the preferred stock dividend to the
firm’s net proceeds from the sale of the preferred stock. The net proceeds represents the amount of money to be received minus any flotation costs. Equation
11.3 gives the cost of preferred stock, kp, in terms of the annual dollar dividend,
Dp, and the net proceeds from the sale of the stock, Np:
kp Dp
Np (11.3) CHAPTER 11 The Cost of Capital 477 Because preferred stock dividends are paid out of the firm’s after-tax cash flows,
a tax adjustment is not required.
EXAMPLE Duchess Corporation is contemplating issuance of a 10% preferred stock that is
expected to sell for its $87-per-share par value.4 The cost of issuing and selling
the stock is expected to be $5 per share. The first step in finding the cost of the
stock is to calculate the dollar amount of the annual preferred dividend, which is
$8.70 (0.10 $87). The net proceeds per share from the proposed sale of stock
equals the sale price minus the flotation costs ($87 $5 $82). Substituting the
annual dividend, Dp, of $8.70 and the net proceeds, Np, of $82 into Equation
11.3 gives the cost of preferred stock, 10.6% ($8.70 $82).
The cost of Duchess’s preferred stock (10.6%) is much greater than the cost
of its long-term debt (5.6%). This difference exists primarily because the cost of
long-term debt (the interest) is tax deductible. Review Question
11–8 How would you calculate the cost of preferred stock? LG3 11.4 The Cost of Common Stock
The cost of common stock is the return required on the stock by investors in the
marketplace. There are two forms of common stock financing: (1) retained earnings and (2) new issues of common stock. As a first step in finding each of these
costs, we must estimate the cost of common stock equity. cost of common stock equity, ks
The rate at which investors
discount the expected dividends
of the firm to determine its share
value.
constant-growth
valuation (Gordon) model
Assumes that the value of a share
of stock equals the present value
of all future dividends (ass...

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