14.1 The Cost of Capital: Some Preliminaries
The cost of capital is the minimum required return that an investment must offer to be considered attractive. It represents the rate of return that a firm must earn on its capital investment to compensate its investors for the use of their capital. It is crucial to remember that the cost of capital depends on the risk of the investment, not the source of the funds.
A firm's overall cost of capital is a mixture of the returns needed to compensate its creditors and stockholders, reflecting its target capital structure. In this chapter, we will assume this capital structure is fixed, and our goal is to find the cost of each component and the overall weighted average cost.
14.2 The Cost of Equity
The cost of equity, \(R_E\), is the return required by the firm's equity investors. We must estimate it, as it cannot be directly observed. Two primary approaches are used for this.
The Dividend Growth Model Approach
This approach uses the assumption that a firm's dividends will grow at a constant rate, \(g\). The cost of equity is then estimated by rearranging the dividend growth model formula.
where \(D_1\) is the expected dividend next period and \(P_0\) is the current stock price. This method is simple but is only applicable to companies that pay dividends with a reasonably steady growth rate. It also does not explicitly account for risk.
The SML Approach (CAPM)
This approach explicitly adjusts for risk using the Capital Asset Pricing Model (CAPM). The cost of equity depends on the risk-free rate, the market risk premium, and the stock's beta (\(\beta_E\)).
This method has the advantage of explicitly accounting for risk and being more widely applicable. Its main drawback is that it relies on estimates of the market risk premium and beta, which can be inaccurate.
Textbook Example: The Cost of Equity
Alpha Air Freight stock has a beta of 1.2, a market risk premium of 7%, and a risk-free rate of 6%. Its last dividend was $2, growing at 8% indefinitely, and the stock sells for $30.
SML Approach: \( R_E = 6\% + 1.2 \times 7\% = \textbf{14.4\%} \)
Dividend Growth Model: \( D_1 = 2 \times (1.08) = \$2.16 \)
\( R_E = \frac{\$2.16}{\$30} + 8\% = 7.2\% + 8\% = \textbf{15.2\%} \)
The two estimates are reasonably close, so an average of 14.8% could be used as the cost of equity.
14.3 The Costs of Debt and Preferred Stock
Determining the cost of other capital sources is typically easier than for equity.
The Cost of Debt
The cost of debt, \(R_D\), is the return creditors demand on new borrowing. It can be observed directly by looking at the **yield to maturity** (YTM) on the firm's outstanding bonds. The coupon rate is irrelevant as it reflects the cost of debt when the bonds were originally issued, not today's market rate.
The Cost of Preferred Stock
Preferred stock is a perpetuity, so its cost, \(R_P\), is the fixed dividend divided by the current price per share.
This is simply the dividend yield on the preferred stock.
14.4 The Weighted Average Cost of Capital (WACC)
The WACC is the overall return a firm must earn on its existing assets to maintain the value of its stock. It is a weighted average of the costs of its various capital sources. When calculating the WACC, we must use market values for debt and equity, not book values, as they reflect the current value of the firm. Additionally, we use the aftertax cost of debt because interest payments are tax-deductible.
WACC Calculation
The WACC is calculated as follows, assuming a corporate tax rate, \(T_C\):
where \(E/V\) and \(D/V\) are the market value weights for equity and debt, and \(V = E + D\).
If preferred stock is also used, the formula expands to include its weight, \(P/V\), and cost, \(R_P\).
Textbook Example: Calculating the WACC
B.B. Lean Co. has 1.4 million shares at $20/share (total equity market value: $28M). Its debt has a face value of $5M, sells at 93% of face value (market value: $4.65M), and yields 11%. Beta is 0.74, the risk-free rate is 8%, the market risk premium is 7%, and the tax rate is 21%.
Cost of Equity: \( R_E = 8\% + 0.74 \times 7\% = 13.18\% \)
Total Value: \( V = \$28M + \$4.65M = \$32.65M \)
Weights: \( E/V = \frac{\$28M}{\$32.65M} \approx 0.8576 \), \( D/V = 1 - 0.8576 = 0.1424 \)
WACC: \( WACC = (0.8576 \times 13.18\%) + (0.1424 \times 11\% \times (1 - 0.21)) \)
\( WACC = 11.29\% + 1.25\% = \textbf{12.54\%} \)
14.5 Divisional and Project Costs of Capital
Using a firm's overall WACC is only appropriate when the proposed investment has the same risk as the firm's existing operations. Using the WACC as a blanket discount rate for all projects can lead to errors. It may incorrectly reject low-risk, profitable projects and incorrectly accept high-risk, unprofitable ones.
To address this, firms should use different costs of capital for projects or divisions with different risks. Two common methods are:
The Pure Play Approach
This method involves finding a publicly traded company (a pure play) that focuses exclusively on a business similar to the project in question. You then use that company's cost of capital as the discount rate for your project. This is often difficult to implement as finding a perfect pure play can be challenging.
The Subjective Approach
Firms can also make subjective adjustments to their overall WACC based on the project's risk. For example, they might add a premium for high-risk projects or subtract a factor for low-risk projects. While not perfect, a subjective adjustment is generally better than no adjustment at all.
14.6 Company Valuation with the WACC
When valuing an entire company, the process is similar to valuing a single project, but with an important adjustment. We must first calculate an adjusted cash flow from assets (CFA*) that excludes the effect of debt financing (specifically, the tax shield from interest payments).
The firm's value, \(V_0\), can then be found by discounting these adjusted cash flows at the WACC, often using a growing perpetuity formula for the terminal value, similar to the dividend growth model.
14.7 Flotation Costs and the Average Cost of Capital
When a company issues new securities (stocks and bonds), it incurs flotation costs. These costs are a relevant cash outflow that should be included in a project's NPV analysis.
The Basic Approach
The flotation cost should be treated as an initial project cost. We first calculate a weighted average flotation cost, \(f_A\), using the firm's target capital structure weights. The true cost of the project is then the initial investment divided by \((1 - f_A)\).
where \(f_E\) and \(f_D\) are the flotation costs for equity and debt, respectively. Even if a firm can finance a project with all debt, it should still use the target weights in this calculation to account for the need to maintain its target capital structure over time.
Chapter Summary and Conclusions
The weighted average cost of capital (WACC) is the overall required return on the firm, serving as an appropriate discount rate for projects of similar risk. We calculated it as a weighted average of the costs of equity, debt, and preferred stock. The cost of debt is adjusted to reflect the tax shield from interest payments.
We also learned that using a single WACC for all projects can lead to incorrect decisions. For projects with different risks, it is better to use the pure play approach or subjective adjustments to determine the appropriate discount rate. Finally, flotation costs are a real expense that must be included in a project's initial investment cost.
Chapter Review and Critical Thinking Questions
Solution: A firm's WACC of 12% means that the firm must earn a return of at least 12% on its investments to satisfy its investors (both creditors and stockholders). If the firm earns more than 12%, it is creating value for its investors; if it earns less, it is destroying value.
Solution: You would choose to use the book value of debt. The reason is that, for most large corporations, the market value of long-term debt is not drastically different from its book value, especially if the debt is relatively new. In contrast, the market value of equity can be significantly different from its book value due to the market-to-book ratio, making book value of equity a poor substitute for its market value in the WACC calculation.
Solution: No, this is a common pitfall. The cost of capital for a project depends on the **risk of the project**, not the source of the funds. The 6% interest rate only reflects the cost of debt. If the project's risk is higher than that of the firm's overall operations, its cost of capital would be higher than the firm's WACC, and certainly higher than the 6% cost of debt alone.
Solution: We use an aftertax figure for the cost of debt because interest payments on debt are tax-deductible for corporations. This tax shield reduces the effective cost of debt to the firm. Payments to equity holders (dividends), however, are not tax-deductible, so there is no tax adjustment for the cost of equity.
Solution: The advantages are its simplicity and ease of use. The disadvantages are that it's only applicable to dividend-paying firms with a stable growth rate, and the estimated cost is highly sensitive to the estimated growth rate. You need the expected growth rate, \(g\). You can estimate \(g\) using historical dividend growth rates or by relying on analysts' forecasts.
Solution: The advantages of the SML approach are that it explicitly adjusts for risk and is applicable to a wider range of companies. The disadvantages are that it requires two estimates: the market risk premium and the beta coefficient. These variables need to be estimated based on historical data or available market information. Estimates for the risk-free rate can come from Treasury bill yields, the market risk premium from historical data, and beta from financial services or by calculation using historical returns.
Solution: The appropriate cost of debt is the yield to maturity on new debt. It does not matter if the debt is publicly or privately placed, as the market-required rate of return is what matters. For privately held debt, you would need to find the yield on similarly rated bonds of other, publicly traded companies to estimate the firm's cost of debt.
Solution: a. Tom's conclusion is wrong because he has ignored the expected growth in dividends. The cost of equity is the sum of the dividend yield and the capital gains yield. b. Tom's conclusion is wrong because he is using book values to calculate the cost of debt, and not the market-required yield. c. Tom's conclusion is likely wrong. The cost of equity is almost always higher than the cost of debt because debt has a lower priority of claims on a firm's assets and earnings, and it is less risky than equity. The 10% figure for equity is likely understated, and the 12.5% figure for debt is likely overstated.
Solution: We need to determine the required return for each project using the CAPM, which is: $E(R_i) = R_f + \beta_i \times (E(R_M) - R_f)$. For both companies, the project's risk is determined by its exposure to the price of natural gas. Since both are investing in the same project, they have the same beta, which is a pure play on natural gas. Superior Oil's beta of 0.75 is a more accurate reflection of this project's risk. Dow's beta of 1.25 reflects its higher risk as a natural gas user. Therefore, Dow should use the 0.75 beta to evaluate the project. Required return for the project: $12\% + 0.75 \times 8\% = 18\%$. The NPV is positive at 18%, so both companies should proceed.
Solution: It is appropriate to use different costs of capital when a firm has divisions with distinctly different levels of risk. If the firm's overall WACC were used as the hurdle rate, riskier divisions would tend to get more investment projects because their higher expected returns would more easily exceed the average WACC. More conservative divisions would see their profitable, low-risk projects rejected. Problems in estimating a divisional cost of capital include finding pure play companies and having to make subjective adjustments. Two techniques are the **pure play approach** and the **subjective approach**.