II. Financial Leverage and Beta
Even firms within one industry have different levels of debt, and increasing debt increases leverage. Increasing leverage increases beta. Recall, in the APT arbitrage in expectations example, that we could "synthesize" a security with a beta of 1.3 by borrowing 30% of our wealth, and investing the total in an asset with a beta of one. We moved out the security market line by borrowing. Suppose, for instance, that investor A hold a portfolio of $100 invested in an S&P 500 index trust. In order to increase his expected return, investor B, who also has $100, borrows an additional $30 for one year at 0% interest, and invests $130 in the S&P 500 index trust. What will happen if the S&P goes up by next year? A will have $110, for a gain of 10%, while B will have $143 - $30, leaving a gain of 13%! What will happen if the market drops by 10% next year? A will have $90, a loss of -10%, while B will have a net loss of $87, a 13% loss. B's leverage increased his exposure to market risk. Leverage can be used by corporations as well as individuals to increase their expected returns, and in fact, this is exactly what some firms do. Even if they are in a low-beta business, such as a utility, they can increase expected return through leverage.
III. Leverage and the Cable T.V. Industry
The cable television industry is a utility. If we could observe an unlevered cable company, it would undoubtedly have a low beta. Good television reception is like food, people can't seem to live without it, even in a recession. Thus, it is not as cyclical as some other businesses. Empirical research has shown that the beta of the average all-equity cable TV company (called an asset beta) is .67, but most firms borrow more that their total equity value! Thus, the beta of their equity (that is, the beta measured by regression of stock returns on the market) is greater than one: 1.85. This increases the average expected return in the industry from 11.39 to 21.41.
IV. Capital Budgeting Applications of Levered Betas: Discounting Cash Flows
Leverage can have a huge effect on financial decisions. For instance, suppose that you ignored the effect of leverage in the cable television industry. You might draw the mistaken conclusion that cable t.v. assets are unusually sensitive to business cycle fluctuations, when in fact they are relatively stable. This has immediate implications for investment decisions.
Example 1: Project Valuation
Suppose you are an analyst working for AT&T, the telephone company. The company has a large cash "war chest" for investment in new opportunities and it is considering a move into providing local cable television service. It is currently evaluating the profitability of bidding on the franchise for the borough of Queens, in New York City. You have been asked to evaluate an all-equity investment in this new cable system.
Based upon estimates subscriber rates, you calculate that the project will have net cash flows of $234 million / year, and for simplicity, assume that this can be considered a perpetuity, with no future growth or decline in cash flows. What is your estimate of the value of the project?
You have the cash flows, but you need the discount rate. Obviously, since there is no existing Queens cable company you cannot observe the historical beta, but you can use the industry norms. In this case, the cable T.V. asset beta = .67. Assume the current riskless rate is: rf = 5.5, and you take the equity premium to be the long-term historical average: ERP = 8.5.
Project Value = Annual net cash flow / CAPM expected return
Project Value = $234/(.055 + .67*.085) = $2.09 Billion
Example 2: Merger and Acquisition Application
Another way firms move into a new industry is through acquisition -- that is to buy the outstanding stock of another firm. Suppose you are an AT&T analyst, and were considering the purchase of a successful cable television company Cable Vision, a firm with $3.6 billion in outstanding equity (that is, the price per share times the number of shares). Assume you know that you have estimated Cable Vision's beta as 2, and that the earnings are $150/year. Also, assume that Paul Kagan the media industry security analyst estimates the growth in earnings to by 18% per year.
To begin your analysis, assume earnings are a good estimate of net cash flow. Use analysts ' forecast of earnings growth to apply perpetuity model with growth:
Earnings = $150 million
Growth = 18%
Rf = 5.5
Estimate R from equity beta: R = .055 + 2*.085 = .225
P = 150/ (.225 - .18) = 3.33 Billion.
In other words, maybe Cable Vision is slightly overpriced.
Example 3: P/E Ratios as Approximate Discount Rates
There are many reasons why the perpetuity model is not an exact formula for corporate valuation. First, it assumes no uncertainty about future cash flows or future discount rates. Second, it is a highly stylized model of future cash flows. Third, it requires estimation of inputs that cannot always be correctly estimated, e.g. the growth of earnings. None-the-less, P/E ratios must have some relationship to discount rates. Note that if:
This Ri is calculated from earnings and price, not from beta, so it is an independent check on the level of systematic risk. Ri may be calculated and compared to CAPM/APT discount rate.
Matching the CAPM/APT discount rate pretty well.
Example 4: Project Choice
The firm itself may be thought of as a portfolio of projects, each with a project (i.e. asset) beta. In this setting, cash flows from each project should be discounted at the rate appropriate to that project. This is important, because the wrong discount rate may result in an incorrect capital budgeting decision. For instance, what if you discounted every project at the company cost of capital?
You will reject some worthwhile projects with low betas, and you accept high beta projects that make the firm riskier. You will end up selecting for exposure to systematic risk. What if you take projects below your company cost of capital? Doesn't this mean that you will be borrowing at a higher rate than your projects are yielding? No! Accepting lower beta projects will lower the expected return of the firm and thus lower the financing costs proportionally.
CAPM betas and APT factor loadings are more than inputs to estimates of expected returns. They are measures of the systematic risk of the company or the portfolio. Both asset pricing models are linear, which implies that the betas measure the amount that actual returns for a security are expected to change when the market (or macro-economic factor) changes. In practice, betas are estimated with historical data, using regression techniques. When historical data is not available, industry comparables are used, and adjustments are made for leverage.
Firms may use leverage to adjust their expected return and systematic risk exposure just as investors do. The beta of the underlying asset held by the firm may be much lower than the observed beta of the stock of the company, if the company is highly levered. We used the Cable T.V. industry to explore how to lever and unlever the beta of companies. This method can be applied to a number of corporate finance problems, including decisions about investment and acquisition.
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