Cost of Capital
Readings: Chapter 9
At the end of this unit students should be able to:
Explain what is meant by a firm’s weighted average cost of capital.
Define and calculate the component costs of debt and preferred stock.
Explain why retained earnings are not free and use three approaches to estimate the component cost of retained earnings.
Briefly explain why the cost of new equity is higher than the cost of retained earnings, calculate the cost of new equity, and calculate the retained earnings breakpointwhich is the point where new equity would have to be issued.
Briefly explain the two alternative approaches that can be used to account for flotation costs.
Calculate the firm’s composite, or weighted average, cost of capital.
Identify some of the factors that affect the overall, composite cost of capital.
Cost of capital components
When we speak of the 'Cost of Capital' we are referring to the cost of the capital that a company uses. As we have seen in our introductory classes, capital comes in two forms, Debt Capital & Equity Capital. For our purposes Equity Capital is broken down into Common Equity and Preferred Equity (Preferred Stock), while Common Equity is broken down into New Common Stock (external common equity) and Retained Earnings (internal common equity).
For the reason that companies often times raise funding from more than one sources of capital, we are interested in the Weighted Average Cost of Capital (WACC) i.e. the weighted total cost of each source of capital, where the associated weights represent the proportion of total funding that each source provides. The equation for the WACC is as follows:
or

Where:
k_{d} = the beforetax cost of debt; w_{d} = the weight of debt
T = the tax rate (in decimals)
k_{p} = the cost of preferred equity; w_{p} = the weight of preferred equity
w_{c} = the weight of common equity
k_{ic} = the cost of retained earnings (internal common equity);
k_{ec} = the cost of new common stock (external common equity);
* Note  our focus is on the weighted average cost of raising new capital.
Should we focus on beforetax or aftertax costs of capital?
Stockholders focus on aftertax cash flows. Therefore, we should focus on aftertax cash flows, i.e., use aftertax costs in determining the WACC. However, only the cost of debt requires adjustment, because the related interest expense is tax deductible.
Cost of debt  k_{d}
Companies borrow money in a variety of ways. However, unless otherwise stated, we will assume that companies raise debt capital by issuing bonds. We will now look at an example of how to determine the cost of debt. Before proceeding though, it is important to note that the beforetax cost (k_{d}) of a bond, is the same as the bond's yield to maturity.
E.g. With a tax rate of 40%, compute the beforetax cost of debt given the following information:
A 15year, 12% semiannual bond selling for $1,153.72.
Using the Rodriques formula: The beforetax cost of debt K_{d = }9.95%. However the aftertax cost of debt = 9.95(1T) = 9.95(0.60) = 5.97% 
Cost of preferred equity  k_{p}
The cost of preferred equity is same as the rate of return on preferred stock. (See topic # 7  Stock Valuation)
E.g.  The current market price of a preferred stock is $111.10. The par value of each stock is $100 and the dividend rate is 10%. Compute the cost of preferred stock.

Note  since preferred dividends are not tax deductible, no tax adjustment is required..
Cost of common equity  Retained Earnings  k_{ic}
Why is there a cost for retained earnings?
Opportunity cost in this sense refers to the return that stockholders could earn on alternative investments of equal risk. Stockholders could buy similar stocks and earn a particular rate k_{ic} , therefore this rate, k_{ic} is the cost of retained earnings.
There are three ways to determine this cost of internal common equity, k_{ic}:
1. Capital Asset Pricing Model (CAPM) approach.
2. OwnBondYieldPlusRisk Premium approach
3. Discounted Cash Flow (DCF) approach.
1. Capital Asset Pricing Model (CAPM) approach.
We may recall that theCapital Asset Pricing Model (CAPM) approach utilises the Security Market Line Equation to the determine the required rate of return for a stock given its beta.
Example: Given the information below determine the cost of internal common equity, k_{ic}, based on the CAPM?
k_{rf} = 7%, k_{rm} = 13% and beta, b = 1.2.
Recall that: k = k_{rf} + (k_{m} – k_{rf} )b
Note  There a few limitations of this approach. If a company's stock holders are well diversified, they may be concerned with standalone risk rather than just market risk. In that case, the company's true investment risk would not measured by its beta, and the CAPM procedure would understate the correct value of k_{ic}. Further, even if the CAPM is valid, it is hard to obtain correct estimates of the inputs required to make it operational because (1) there is controversy about whether to use short term or long term Treasury yields for k_{rf} , (2) it is hard to estimate the beta that investors expect the company to have in the future, and (3) it is difficult to estimate the market risk premium.
2. The ownbondyieldplusriskpremium approach
This approach stems from the theory that it is logical to think that companies with risky lowrated, and consequently highinterestrate debt will also have risky, highcost equity. This logic is utilised to estimate the cost of equity by adding a judgmental risk premium (of say 3 to 5 percentage points) to the interest rate on the company's own longterm debt. This subjective and adhoc approach is often times used by analysts who have little confidence in the CAPM approach.
Example: The company's beforetax cost of debt, k_{d} = 10% and the appropriate risk premium, RP, for common stock = 4%. Compute the cost of existing common equity, k_{ic}.
This approach also illustrates an important feature: The cost of debt (k_{d })is normally lower than the cost of equity (k_{c}). This is so because of the taxdeductability benefit of debt interest payments.
3. Discounted Cash Flow (DCF) approach.(also known as the 'DividendYieldPlusGrowthRate' approach)
The is the same approach we had used to compute the rate of return on a common stock (See topic # 7  Stock Valuation)
Recall that:
Example: What is the DCF cost of internal common equity, k_{ic}, given that D_{0} = $4.19; P_{0} = $50 and g = 5%.?
What’s a reasonable final estimate of k_{ic?}
Looking at our previous results we see that:
Method  Estimate 
CAPM  14.2% 
k_{d} + RP  14.0% 
DCF  13.8% 
A reasonable estimate would be to average these three figures thereby resulting in 14.0%. However, because of the limitations of the other approaches we will stick with the DCF method unless otherwise stated, in which case k_{ic} is 13.8%
Cost of common equity  New common stock  k_{ec}
When a company issues new common stock they have to pay floatation costs to the underwriter. Floatation costs basically refer to all those administrative and processing costs that are incurred when issuing new securities.
Two approaches that can be used to account for floatation costs:
Include the flotation costs as part of the project’s upfront cost. This reduces the project’s estimated return.
Adjust the cost of capital to include flotation costs. This is most commonly done by reducing the sale proceeds by the flotation costs to arrive at a net selling price. (applicable in the DCF approach).  We will stick to this approach!.. therefore:
Where: F = floatation costs. 
Example: using the previous DCF data and floatation costs of 15% of the sale proceeds, determine the cost of new/external common equity.
F = 15% x $50 = $7.50, therefore: 
Why is the cost of retained earnings cheaper than the cost of issuing new common stock?
1. When a company issues new common stock they have to pay flotation costs to the underwriter
2. Issuing new common stock may send a negative signal to the capital markets, which may depress stock price.
Comments about flotation costs:
Example of computing total WACC: (Using the previously accumulated data and DCF approach for Common Equity)
Assuming that the company wished to raise $300,000 from debt, $100,000 from preferred stock and $600,000 from common equity, what is
(a) the company's WACC using internal/existing common equity?
We will first have to compute the weights: w_{d} = 300,000/1,000,000 = 0.3 w_{p} = 100,000/1,000,000 = 0.1 w_{c } = 600,000/1,000,000 = 0.6 then:
WACC = 0.3(9.95%)(1  0.40) + 0.1(9%) + 0.6(13.8%) = 0.3(10.19%)(0.60) + 0.1(9%) + 0.6(13.8%) = 1.79% + 0.9% + 8.28% = 10.97% 
(b) what’s the firm’s WACC using external common equity ?
WACC = 0.3(9.95%)(1  0.40) + 0.1(9%) + 0.6(15.35%) = 0.3(9.95%)(0.60) + 0.1(9%) + 0.6(15.35%) = 1.79% + 0.9% + 9.21% = 11.90% 
What factors influence a company’s composite WACC?
Should the company use the composite WACC as the hurdle rate for each of its projects?
Breaks in the company's weighted average cost of capital
The company's WACC will increase when one of the individual component cost increases. This normally occurs when the cost of a component of capital increases whenever an increase in such capital is required. For example, issuing bonds to raise $10 million may attract a higher cost than issuing bonds to raise $7 million.
This breakpoint in the company's WACC can be computed as follows:
The component's limit The component's weight

Note  the result refers to that point in the total financing where the WACC will change. This is commonly used to determine the retained earnings 'breakpoint'.
Example:
Company X needs to raise financing for another of its typical projects. The company's capital structure is as follows:
Preferred Equity: 30%
Debt: 50%
Common Equity 20%
If the company only has $500,000 of Retained Earnings available and wishes to maintain its current capital structure, calculate the point at which the company's WACC will change.
Solution:
$500,000 0.20 = $2,500,000 