The Weighted Average Cost of Capital: An Introduction
The story so far: So far, we have figured out the basic formulae we need to compute the NPV of any financial instrument. We have also derived the CAPM which tells us the discount rate for securities. In this final part of the course, we find out how to calculate the discount rate for the whole company. This first lesson will start with a basic introduction to the concept. Now read on ... Required Reading: My notes and HV Chapter 10-11
The Weighted Average Cost of Capital: A Definition
The WACC is the discount rate to be used to discount free operating cash flows. It reflects the • business risk and the • target debt capacity of the firm or project we are trying to value. It is a weighted average of the costs of various financing instruments. If we assume that debt and equity are the only source of financing, then the WACC is given by:
WACC= rs
where
B S+B
S B + rb(1− tc) S +B S+B
is the target debt to asset ratio and rs and rb(1-tc) are after tax costs of debt and equity.
Let us take an example to illustrate this:
Let rs = 24%, rb = 18%, tc = .50,
S = 1/3 S +B
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MGMT 611G: Financial Management Krannert School, Purdue University
Then the weighted average cost of capital is given by: WACC = 24% × (1/3) + 9% × (2/3) = 8% + 6% = 14% Assumption : Interest is tax deductible Where do we find rb? Simple, ask the bank! Where do we find rs? From the CAPM : rs = rf + (rm -rf)$s
Practical Implementation
• Betas are estimated assuming regression of return on the stock and the return on the “market” portfolio m. You can also buy them from data services (Datastream, Barra, …) rf = long term riskless rate rm - rf = is the expected risk premium. It is usually estimated employing past data. During the last 70 years investors who brought a diversified market portfolio in the U.S. have on average received a risk premium above long term government bonds of approximately 7.5 percent per year. Somewhat comparable numbers for other countries are: Japan U.K. 1973-1988 1929-1988 7.2 % 7.6 %
• •
Important note for project evaluation or valuation of individual divisions of a multibusiness firm
As the cost of capital is specific to the risk of the asset, which in turn is (negatively) related to the debt capacity of a project, you cannot use the “firm’s” cost of capital (which reflects the risks of all the assets of the firm, plus the firm’s capital structure) to discount the cash flows of a project or division. However, as “projects” or individual “divisions” are not traded, you need an alternative approach.
MGMT 611G: Financial Management Krannert School, Purdue University Raghavendra Rau Finance Department
MGMT 611G: Financial Management Krannert School, Purdue University
Raghavendra Rau Finance Department
How do we compute the cost of capital of a non-traded firm or project?
1. Find an undiversified firm, (comparable company) with equity traded on the stock market, in the same line of business as the firm/project you want to value. 2. Compute beta of the equity of this comparable firm, $LS . The “L” indicates that this beta will reflect the leverage of the comparable company. If the comparable company’s leverage is not very different from the target leverage of the firm/project you want to value, the $LS will reflect your target leverage. In that case, $LS is equal to $TS, your target beta. Hence you can go immediately to step 5. 3. Unlever $LS to get $US , “U” refers to unlevered firm. How do we do this? See the next section. 4. Lever up the $US with the target proposed debt capacity of the firm to arrive at new $TS. 5. Apply the weighted average cost of capital formula
S B WACC rs + rb = V V
with rs = rf + (rm - rf) × $TS
Unlevering Betas
Basic formula
B L U βS = βS 1+ (1 − tc) S
where $LS = beta of equity of levered firm • • $US = beta of equity of the firm if it had no debt. Note that this is also the beta of the assets of the unlevered firm • tc = corporate tax rate B/S = debt-equity ratio of the levered firm •
MGMT 611G: Financial Management Krannert School, Purdue University
Raghavendra Rau Finance Department
Where does this formula come from? We’ll discuss this in the next class.
Example of Unlevered Industry betas
Industry Electronic components Crude petroleum and natural gas Retail department stores Petroleum refining Motor vehicle parts Chemicals Metal mining Food Trucking Textile mill products Paper and allied products Retail grocery stores Airlines Steel Railroads Natural gas transmission Telephone companies Electric utilities Beta 1.49 1.07 0.95 0.95 0.89 0.88 0.87 0.84 0.83 0.82 0.82 0.76 0.75 0.66 0.61 0.52 0.50 0.46
Note: These are asset betas. The effect of financial leverage on beta has been removed. Source: U.S. Federal Energy Regulatory Commission, Testimony of Gerald A Pogue, Williams Pipe Line Co., Docket Nos OR79-1, et al., p 74. These were obtained by applying the unlevering formula to various different industry betas. Note that some of these industries’ risk characteristics have changed over time. The crucial formula here is the formula for unlevering beta. Where does this formula come from? Well, what this formula says is that risk (measured using beta) is different when a firm is levered (has debt) than when it does not. Why should this be so? Does risk go up or down with leverage? These are all questions we’ll answer in the next chapter.
MGMT 611G: Financial Management Krannert School, Purdue University
Raghavendra Rau Finance Department