The Cost of Capital
Timothy R. Mayes, Ph.D. FIN 3300: Chapter 11
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What is the “Cost” of Capital?
When we talk about the “cost” of capital, we are talking about the required rate of return on invested funds It is also referred to as a “hurdle” rate because this is the minimum acceptable rate of return Any investment which does not cover the firm’s cost of funds will reduce shareholder wealth (just as if you borrowed money at 10% to make an investment which earned 7% would reduce your wealth)
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The Appropriate Hurdle Rate: An Example
The managers of Rocky Mountain Motors are considering the purchase of a new tract of land which will be held for one year. The purchase price of the land is $10,000. RMM’s capital structure is currently made up of 40% debt, 10% preferred stock, and 50% common equity. This capital structure is considered to be optimal, so any new funds will need to be raised in the same proportions. Before making the decision, RMM’s managers must determine the appropriate require rate of return. What minimum rate of return will simultaneously satisfy all of the firm’s capital providers?
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RMM Example (cont.)
Because the current capital structure is optimal, the firm will raise funds as follows:
Source of Funds
Debt Preferred Common Total
Amount
$4,000 $1,000 $5,000 $10,000
Dollar Cost
$280 $100 $600 $980
After-tax Cost
7% 10% 12% 9.8%
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RMM Example (Cont.)
The following table shows three possible scenarios:
Rate of Return
Total Funds Available Less: Debt Costs Less: Preferred Costs = Remainder to Common
8%
9.8%
11%
$11,100 $4,280 $1,100 $5,720
$10,800 $10,980 $4,280 $4,280 $1,100 $1,100 $5,420 $5,600
Obviously, the firm must earn at least 9.8%. Any less, and the common shareholders will not be satisfied.
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The Weighted Average Cost of Capital
We now need a general way to determine the minimum required return Recall that 40% of funds were from debt. Therefore, 40% of the required return must go to satisfy the debtholders. Similarly, 10% should go to preferred shareholders, and 50% to common shareholders This is a weighted-average, which can be calculated as:
WACC w d k d w p k p w cs k cs
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Calculating RMM’s WACC
Using the numbers from the RMM example, we can calculate RMM’s Weighted-Average Cost of Capital (WACC) as follows:
WACC 0.40(0.07) 010(010) 050(012) 0.098 . . . .
Note that this is the same as we found earlier
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Finding the Weights
The weights that we use to calculate the WACC will obviously affect the result Therefore, the obvious question is: “where do the weights come from?” There are two possibilities:
• Book-value weights • Market-value weights
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Book-value Weights
One potential source of these weights is the firm’s balance sheet, since it lists the total amount of longterm debt, preferred equity, and common equity We can calculate the weights by simply determining the proportion that each source of capital is of the total capital
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Book-value Weights (cont.)
The following table shows the calculation of the book-value weights for RMM:
Source Long-term Debt Preferred Equity Common Equity Grand Totals
Total Book Value $400,000 $100,000 $500,000 $1,000,000
% of Total 40% 10% 50% 100%
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Market-value Weights
The problem with book-value weights is that the book values are historical, not current, values The market recalculates the values of each type of capital on a continuous basis. Therefore, market values are more appropriate Calculation of market-value weights is very similar to the calculation of the book-value weights The main difference is that we need to first calculate the total market value (price times quantity) of each type of capital
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Calculating the Market-value Weights
The following table shows the current market prices:
Source Debt Preferred Common Totals
Price per Units Total Market % of Unit Value Total $ 905 400 $362,000 31.15% $ 100 1,000 $100,000 8.61% $ 70 10,000 $700,000 60.24% $1,162,000 100.00%
WACC 0.31150.07 0.0861010 0.60240.12 01027 10.27% . .
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Market vs Book Values
It is important to note that market-values is always preferred over book-value The reason is that book-values represent the historical amount of securities sold, whereas marketvalues represent the current amount of securities outstanding For some companies, the difference can be much more dramatic than for RMM Finally, note that RMM should use the 10.27 WACC in its decision making process
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The Costs of Capital
As we have seen, a given firm may have more than one provider of capital, each with its own required return In addition to determining the weights in the calculation of the WACC, we must determine the individual costs of capital To do this, we simply solve the valuation equations for the required rates of return
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The Cost of Debt
Recall that the formula for valuing bonds is:
1 1 N 1 k d FV VB Pmt N kd 1 k d
We cannot solve this equation directly for kd, so we must use an iterative trial and error procedure (or, use a calculator) Note that kd is not the appropriate cost of debt to use in calculating the WACC, instead we should use the after-tax cost of debt
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The After-tax Cost of Debt
Recall that interest expense is tax deductible Therefore, when a company pays interest, the actual cost is less than the expense As an example, consider a company in the 34% marginal tax bracket that pays $100 in interest The company’s after-tax cost is only $66. The formula is:
After tax k d Before tax k d 1 t
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The Cost of Preferred Equity
As with debt, we calculate the cost of preferred equity by solving the valuation equation for kP:
D kP VP Note that preferred dividends are not tax-deductible, so there is no tax adjustment for the cost of preferred equity
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The Cost of Common Equity
Again, to find the cost of common equity we simply solve the valuation equation for kCS:
k CS D 0 1 g VCS D1 g g VCS
Note that common dividends are not tax-deductible, so there is no tax adjustment for the cost of common equity
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Flotation Costs
When a company sells securities to the public, it must use the services of an investment banker The investment banker provides a number of services for the firm, including:
• Setting the price of the issue, and • Selling the issue to the public
The cost of these services are referred to as “flotation costs,” and they must be accounted for in the WACC Generally, we do this by reducing the proceeds from the issue by the amount of the flotation costs, and recalculating the cost of capital
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The Cost of Debt with Flotation Costs
Simply subtract the flotation costs (F) from the price of the bonds, and calculate the cost of debt as usual:
1 1 N 1 k d FV VB F Pmt N kd 1 kd
Note that we still must adjust this calculation for taxes
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The Cost of Preferred with Flotation Costs
Simply subtract the flotation costs (F) from the price of preferred, and calculate the cost of preferred as usual:
D kP VP F
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The Cost of Common Equity with Flotation Costs
Simply subtract the flotation costs (F) from the price of common, and calculate the cost of common as usual:
k CS
D1 g g VCS F VCS F
D 0 1 g
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A Note on Flotation Costs
The amount of flotation costs are generally quite low for debt and preferred stock (often 1% or less of the face value) For common stock, flotation costs can be as high as 25% for small issues, for larger issue they will be much lower Note that flotation costs will always be given, but they may be given as a dollar amount, or as a percentage of the selling price
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The Cost of Retained Earnings
The firm may choose to finance new projects using only internally generated funds (retained earnings) These funds are not free because they belong to the common shareholders (i.e., there is an opportunity cost) Therefore, the cost of retained earnings is exactly the same as the cost of new common equity, except that there are no flotation costs:
k RE D 0 1 g VCS D1 g g VCS
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