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Cost Chapter of Capital
Slides developed by:
Pamela L. Hall, Western Washington University
The Purpose of the Cost of Capital
The cost of capital is the average rate paid for the use of capital funds
Primarily used in capital budgeting
Use as the hurdle rate, or benchmark for projects
Compare IRR to this rate Discount cash flows at this rate to find NPV
If a project cannot earn above this return, it is not worthwhile
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The Purpose of the Cost of Capital
A firm can only estimate what it will cost to raise future funds, so cost of capital will always be subject to uncertainty
Important to estimate this cost as accurately as possible in order to effectively manage the firm
The firms cost of capital can be viewed as the firms required rate of return on projects of average risk
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Capital Components
Components of a firms capital are
Debt
Borrowed money, either loans or bonds
Common equity
Ownership interest
Preferred stock
Cross between debt and equity
Capital structure is the mix of the three capital components
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Capital Structure
Target Capital Structure
A mix of components that management considers optimal and strives to maintain
Raising Money in the Proportions of the Capital Structure
An exact capital structure cant be maintained constantly
Sometimes, if interest rates are low, a firm might issue more debt (to take advantage of the low cost) Increases the weight of debt relative to equity Next time need more capital, issue equity to bring mix back into balance
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Capital Structure
However, cost of capital calculations assume that capital is raised in the exact proportions of some capital structure
Assumption is unrealistic but produces little distortion
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Returns on Investments and the Costs of Capital Components
Investors provide capital to companies by purchasing their securities
The returns to investors represent the costs to the firms in which investments are made
Opposite sides of the same coin
Since equity is riskier than debt, generally the return on an equity investment is higher than that of debt (or preferred stock), thus the cost to the firm is higher
Cost and return are not exactly equal, but are related
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The Weighted Average CalculationThe WACC
A firms WACC is the average of the costs of the separate sources weighted by the proportion of each source used
WACCfirm =
weight sourcecost source source = 1
n
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The Weighted Average Calculation Example
Q: Calculate the WACC for the Zodiac Company given the following information about its capital structure.
Capital Component Debt Preferred Stock Common stock Value $60,000 50,000 90,000 $200,000 Cost 9% 11 14
Example
A: First we need to calculate the capital structure weights based on the value given. For debt this weight is $60,000 $200,000 = 30%. Next, each components cost is multiplied by its weight and the results are summed as shown below:
Capital Component Debt Preferred Stock Common stock Value $60,000 50,000 90,000 $200,000 Weight 30% 25% 45% 100% Cost 9% 11 14 WACC = 2.70% 2.75% 6.30% 11.75%
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Capital Structure and Cost Book Versus Market Value
Book values reflect the cost of capital already spent Market value estimates the cost of capital to be raised in the near future
Market values are appropriate because new projects are generally funded with newlyraised equity
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Calculating the WACC
Step 1: Develop a market-based capital structure Step 2: Adjust the market returns on the securities underlying the capital components to reflect the company's true component costs of capital Step 3: Put the values obtained in Steps 1 and 2 together to determine the WACC Developing Market-Value-Based Capital Structures
Involves determining the percentage each source of capital makes up of the firm's overall capital structure based on market values
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Developing Market-Value-Based Capital StructureExample
Q: The Wachusett Corporation has the following capital situation. Debt: Two thousand bonds were issued five years ago at a coupon rate of 12%. They had 30-year terms and $1,000 face values. They are now selling to yield 10%. Preferred stock: Four thousand shares of preferred are outstanding, each of which pays an annual dividend of $7.50. They originally sold to yield 15% of their $50 face value. They're now selling to yield 13%. Equity: Wachusett has 200,000 shares of common stock outstanding, currently selling at $15 per share. Develop Wachusett's market-value-based capital structure.
Example
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Developing Market-Value-Based Capital StructureExample
A: To determine the market value of each source of capital, the market value (total) of each source must be calculated and then its percentage determined. The price of Wachusett's bonds in the market must be determined. We know the bonds have 25 years remaining until maturity, pay interest of $120 annually ($60 semi-annually) and are yielding 10% annually (5% semi-annually). Thus, each bond is selling for $1,182.55 in the market, calculated as shown below.
Pb = PMT[PVFAk,n] + FV[PVFk,n] = $60[PVFA5,50] + $1,000[PVF5,50] = $60(18.2559) + $1,000(0.0872) = $1,182.55
Example
Because there are 2,000 bonds outstanding, the market value of the firm's debt is $2,365,100, or $1,182.55 x 2,000. 13
Developing Market-Value-Based Capital StructureExample
The firm's preferred stock represents a perpetuity that pays $7.50 annually and is yielding 13%. Thus, the value of each share of preferred stock is $57.69, or $7.50 .13. Because there are 4,000 shares outstanding, the total market value of Wachusett's preferred stock is $230,760, or $57.69 x 4,000.
Example
Each share of Wachusett's common stock is trading for $15, thus the total market value of the firm's equity is $3,000,000, or $15 x 200,000 shares. Next, we calculate the portion of the the firm's total capital that each source represents: Debt Preferred Equity $2,365,100 230,760 3,000,000 $5,595,860 42.3% 4.1 53.6 100.0%
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Calculating Component Costs of Capital
We'll look at the market return received by new investors in each component Then make adjustments to reflect practical reality AdjustmentsThe Effect of Financial Markets and Taxes
The amounts effectively paid to investors and received by a corporation when raising capital are impacted by taxes and transaction costs Taxesinterest expense on debt is tax deductible which makes the debt cheaper than it would be otherwise
Thus, a dollar paid in interest results in a lower taxable income and lower taxes Therefore, the after-tax cost of debt is Interest (1 - tax rate)
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Calculating Component Costs of Capital
Flotation costsadministrative and fees expenses incurred in the process of issuing and selling securities
Lower the amount received when a security is issued, increasing the cost of the capital raised Thus, when a firm issues securities it will only net a portion of the total amount issued, as the remainder must be paid as issuance costs A firm's component cost of capital will be higher than the investor's return by the ratio of 1 (1 - flotation cost percentage)
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The Cost of Debt
The cost of debt is the investor's return adjusted for the tax deductibility of interest payments
Most debt is placed privately (not initially sold to the public) and flotation costs are minimal
The cost of debt is the market return on debt (kd) net of taxes or
Kd (1 - tax rate)
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The Cost of Preferred Stock
The cost of preferred stock is the investor's return adjusted for flotation costs
A preferred stockholder's return is the dividend received divided by the current price of the stock Adjusting this for the fact that a firm will only net the portion of the issuing price after flotation costs (f) results in
Dp (1 - f)Pp or kp (1 - f)
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The Cost of Preferred Stock Example
Q: The preferred stock of the Francis Corporation was issued several years ago with each share paying 6% of a $100 par value. Flotation costs on new preferred are expected to average 11% of the funds raised. (a) What is Francis's cost of preferred capital if the interest rate on similar preferred stock is 9% today? (b) Calculate Francis's cost of preferred stock if the stock is selling at $75 per share today.
Example
A: Questions (a) and (b) are both asking the same question; however with (a) we have the market return provided and with (b) we are given the information needed to calculate the market return. (a) Using the formula kp (1 - f) we simply adjust the market return by flotation costs: 9% (1 - .11) = 10.1%. (b) Using the formula Dp (1 - f) Pp we calculate the cost using the dividend and current price of preferred stock: (6% $100) (1-.11)$75 = 9%.
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The Cost of Common Equity
Debt and preferred stock offer investors known stream of payments so calculating returns are easy The cost of equity is imprecise because of the uncertainty of future cash flows
Thus, market return on an equity investment has to be estimated
We'll use the CAPM, the Gordon model and risk premiums
Equity sources include stock sales and retained earnings, which have different costs
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The Cost of Retained Earnings
Retained earnings (RE) are not free to the company because they represent reinvested earnings for the stockholders
Thus, retained earnings represent money stockholders could have spent if it had been paid out as dividends
Stockholders deserve a return on retained earnings The market return on new shares is an appropriate starting point for estimating the cost of retained earnings
No adjustments are needed between the return earned by new buyers and the cost of RE because RE are generated internallyno need to adjust for flotation costs or taxes
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The Cost of Retained Earnings
The CAPM ApproachThe Required Rate of Return
The market return on a stock can be approximated by estimating the required or expected return
CAPM offers a method of estimating the required return using beta as a measure of risk Kx = KRF + (Km - KRF) bX
The Dividend Growth ApproachThe Expected Rate of Return
The Gordon model is normally used to calculate the intrinsic value of a stock However, we can use the Gordon model to solve for the expected return by plugging in the current price of the stock
P0 = D0(1 + g) ( ke g)
Solve for ke, which represents expected return.
Use actual price
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The Cost of Retained Earnings
The Risk Premium Approach
It's possible to estimate the return on a firm's equity by adding 3 to 5 percentage points to the market return on its debt, or
Ke = kd + equity risk premium
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The Cost of New Common Stock
Firms often need to raise more equity than that generated by retained earnings
Accomplish this by issuing new common stock
Equity from new stock is just like equity from RE, with the exception that raising it involves incurring flotation costs Thus the market return estimates for RE must be adjusted for flotation costs to determine the cost of issuing new common stock
Easiest to do with the Gordon model because the price of the stock appears in that equation ke = [D0(1 + g) (1 f)P0] + g
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Putting the Weights and Costs Together
Once the component costs are calculated and the target weights are determined, the calculation of the weighted average cost of capital is simple
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The Marginal Cost of Capital (MCC)
A firm's WACC is not independent of the amount of capital raised WACC typically rises as the firm raises more capital The Marginal Cost of Capital (MCC) is graph of the WACC showing abrupt increases as larger amounts of capital are raised in a planning period
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The Break in MCC When Retained Earnings Run Out
Breaks (jumps) in the MCC occur when a cheap source of financing are used up First increase in MCC usually occurs when the firm runs out of RE and starts raising external equity by selling stock Locating the Break
The first breakpoint is always found by dividing the amount of RE available by the fractional proportion of equity in the capital structure
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The MCC Schedule
Other Breaks in the MCC Schedule
For most companies the WACC is reasonably constant aside from the break into external equity However, low-cost funds cannot be raised without limit For instance, as more debt is issued the firm becomes more risky and the investors' required rates of return rise The investment opportunity schedule (IOS) is a plot of the IRRs of available projects arranged in descending order The MCC and IOS plotted together show which projects should be undertaken
Because it represents the cost of raising funds relative to the expected return of the projects
Combining the MCC and IOS
Interpreting the MCC
The firm's WACC for the planning period is at the intersection of the MCC and the IOS 28
Figure 12.2: MCC Schedule and IOS
Projects A, B and C should be undertaken because their expected returns exceed the expected costs.
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A Potential MistakeHandling Separately Funded Projects
Sometimes a project is funded entirely by a single source of capital Should the cost of capital used to evaluate that project be the cost of the single source, or the firm's overall WACC?
It should be the firm's overall WACC because firms cannot continue to raise a single source of capital indefinitely, such as cheap debt
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