In a previous post, we discussed a metric called return on invested capital (ROIC) and its variant, return on incremental invested capital (ROIIC). ROIC measures the after-tax operating earnings generated per dollar of average total capital, while ROIIC measures the incremental operating earnings generated per dollar of additional capital employed in the business.
These measures are interpreted as follows: when ROIC and ROIIC exceed the firm’s cost of capital, the company is creating value for the providers of those funds; when these measures generate less than the firm’s cost of capital, the company is destroying value for the providers of those funds.
So how do we determine the company’s cost of capital?
Weighted- Average Cost of Capital (WACC)
A firm’s cost of funds must represent the cost of both debt and equity capital. Thus, the cost of capital is a weighted average of the after-tax cost of debt and cost of equity. In other words, the company’s cost of capital is computed as the sum of (a) debt as a percentage of total capital times the after-tax cost of capital and (b) equity as a percentage of total capital times the cost of equity capital. For a company with a “simple” capital mix, total capital is the sum of outstanding debt and shareholders’ equity.
WACC = [(Debt ÷ total capital) x (interest rate x 1 – tax rate)] + [(equity ÷ total capital) x (cost of equity)]
Capital Structure
A firm’s capital structure refers to the amount of debt and equity the firm uses to finance its business. For smaller businesses, the capital structure is relatively straight forward – debt capital in the form of bank loans and working capital lines, and equity capital in the form of shareholder contributions and retained earnings.
For larger firms, the capital structure can get a bit complicated. Larger firms are more likely to have outstanding employee stock options, warrants, preferred shares, debt issued with an option to convert to equity, and other forms of securities, all of which can alter the capital structure. In addition, large firms generally issue multiple layers of debt with different terms and different rates. These complexities must be dealt with when calculating WACC for large firms.
When using the WACC to evaluate corporate projects, business expansion, or to value an entire business, we are implicitly assuming that the firm will maintain the capital structure used in the calculations. Whether this is a reasonable assumption depends on the company and the scenario. In addition, finance theory states that since the value of a firm is the sum of future cash flows discounted at the firm’s cost of capital, the firm should choose a capital structure which minimizes the firm’s cost of capital (the lower the discount rate, the greater the value of discounted future cash flows). This requires a capital structure with a greater level of debt than management may be comfortable with, or which limits the company’s strategic flexibility.
Smaller companies which rely on bank financing will be unlikely to be able to maintain a constant borrowing level. Banks are unlikely to lend additional amounts as loans are paid back, and any borrowings from other institutions will be subordinate (lower in protection and rank) to the bank debt and possibly cost prohibitive. The point being that smaller firms will likely have to operate with a greater level of equity in the capital structure than what is optimum for maximizing shareholder value.
The Cost of Debt
A company’s cost of debt refers to the interest rate which the firm must pay on borrowed funds. Interest is expensed on the income statement and reduces taxable income, so we have to reduce the interest charge by the tax savings (known as the “tax shield”). We do this by multiplying the interest rate by 1 minus the tax rate:
Cost of debt = Interest rate x (1 – tax rate)
Even smaller companies can have multiple forms of debt. For example, a company may regularly use a credit line to finance working capital, bank loans to finance equipment and vehicle purchases, and operating leases to finance real estate. Larger companies may use money market instruments, medium-term and long-term bonds, and senior bank debt.
When multiple forms of debt are used, the cost of debt must reflect these various sources. The cost of debt is thus a weighted average of the various forms of debt as a proportion of total debt.
One issue is how to handle convertible debt. A convertible debt security is a debt instrument which grants the holder the right to convert the security into equity at a stated price. Because of the conversion feature, convertible debt has a lower rate than a comparable bond lacking the conversion feature. Financial managers have differing views on how to handle convertible debt when calculating WACC. Rather than making the calculation unnecessarily complicated (in my opinion), I recommend treating convertible bonds as debt and using the rate on non-convertible bonds with similar terms.
Another issue concerns preferred shares. Preferred stock is not debt, but it does represent a claim senior to common equity (the equity which represents ownership in the company). Preferred shares pay a stated dividend which must be paid before any dividends are paid to the common shares. We treat the cost of preferred shares separately from debt and equity. The cost of preferred shares is thus the recognized value of preferred stock as a percentage of total capital times the stated yield of the shares. When preferred shares contain a conversion feature, we use the yield on similar preferred stock not containing a conversion feature.
The cost of debt must represent the cost of issuing new debt, so we have to rely on market interest rates for bonds and bank debt. If the company has historical debt outstanding at fixed rates, these rates may not reflect the cost of issuing new debt.
The Cost of Equity
While the cost of debt is an observable input, the cost of equity is much more difficult to calculate. The cost of equity represents the return needed to attract equity capital to the firm given available alternatives.
One formula for calculating equity cost which is taught in business schools and used by many corporate financial managers is the capital asset pricing model (CAPM). The CAPM starts with the risk-free rate. For businesses, this is usually the rate on the 10-year Treasury notes. To this rate, the CAPM adds a risk premium calculated as the product of (a) the market risk premium (the historical return on stocks over the risk-free rate) and (b) a measure of correlation between the stock’s returns and the returns on a market index, known as the beta coefficient.
Cost of Equity = Risk Free Rate + (Beta x Market Risk Premium)
The theory underlying the CAPM is that since investors in public securities can diversify their portfolios, they should not be compensated for the specific risk of investing in a business. Rather, investors should only be compensated for the general risk inherent in investing in common stocks or any other risky asset. This general risk is measured by a coefficient known as beta, represented by the Greek letter β. The beta coefficient measures a stock’s volatility against the volatility of a market benchmark, such as the S&P 500. Since the market’s correlation against itself is 1, a company is considered riskier than the market if its beta is greater than 1 and less risky than the market if its beta is less than 1.
Private firms can use the CAPM by calculating the average of the betas for publicly traded competitors. The private firm can then add an appropriate risk premium to compensate for the smaller size (if applicable) and lack of liquidity of its shares.
While the CAPM is an imperfect model, the difficulty of computing equity costs assures its continued use.
Some financial managers prefer to use “multi-factor” models. These models rely on statistical research which identities correlations between certain variables, such as a company’s size, and the stock’s price. The theory is that these variables represent risk factors which can be used to estimate a company’s cost of equity capital. In my opinion, however, these models are awkward and do not represent a viable alternative to the CAPM.
Other financial managers rely on various rules of thumb for estimating equity costs. For example, some managers and investors use the average rate of return on a benchmark, such as the S&P 500 or the Russell 2000. One CFO that I worked with used 2.5 times the interest rate on the firm’s long-term debt.
Regardless of the method used to calculate equity costs, the costs must reflect the expected returns on other investments with similar risks available to the equity holders.
Example
Joe is the CFO for a regional building supply company. The CEO has asked Joe to calculate the firm’s cost of capital for use in preparing the upcoming capital expenditure budget.
Joe estimates that the company can finance its working capital at 9% with a revolving credit line, and bank loans for equipment, vehicles, and other tangible assets can be borrowed at 7%. This rate on long-term bank borrowing is also used to calculate the present value of lease obligations. The company has outstanding preferred shares which are held by a private equity firm. The preferred shares pay 10% and are not convertible into common equity. The company’s tax rate is 28%.
The capital breakdown per the most recent balance sheet is:
Long-term debt = $8,500,000
Working capital = $1,000,000
Operating leases = $4,000,000
Preferred shares = $5,000,000
Shareholders’ equity = $9,200,000
Total capital = $27,700,000
Joe calculates the capital structure as follows:
% Debt = (8,500,000 + 1,000,000 + 4,000,000) ÷ 27,700,000 = 48.74%
% Preferred Stock = 5,000,000 ÷ 27,700,000 = 18.05%
% Common Equity = 9,200,000 ÷ 27,700,000 = 33.21%
Joe calculates the cost of debt as follows:
Cost of Long-term debt and capital leases = [(8,500,000 + 4,000,000) ÷ 13,500,000] x .07 = 6.48%
Cost of working capital = (1,000,000 ÷ 13,500,000) x .09 = .0067 = .67%
After-tax cost of debt = (6.48 + .67) x (1 – .28) = 5.148%
Weighted cost of debt = 5.148% x .4874 = 2.51%
For the cost of equity, Joe uses the capital asset pricing model and adds a size and liquidity risk premium of 3%. He estimates that the average beta for publicly listed competitors is 1.5. For the 10-year Treasury, he uses 4% (the most recent quote), and he uses 7% as the market risk premium. The company’s cost of equity capital under the CAPM is thus:
Cost of Equity = 4% + 1.5(7%) + 3% = 17.5%
Weighted cost of equity = 17.5% x .3321 = 5.81%
The company has $5 million in preferred stock, which is 18.05% of total capital. The preferred shares yield 10% on par (the price at which the company issues the shares). The cost of preferred is thus:
Weighted cost of preferred = 10% x .1805 = 1.81%
The company’s total weighted average cost of capital is thus:
WACC = 2.51% + 5.81% + 1.81% = 10.13%
Conclusion
A company’s cost of capital, weighted by the percentage of debt and equity in the capital structure, allows a business manager or investor to determine if the company is generating or destroying value for the firm’s capital providers.
Because a firm employs both debt and equity (and possibly preferred stock) in financing their business, the firm’s total cost of capital must represent a weighted average of the various forms of capital. The costs of both debt and equity capital must represent the costs the firm will incur to attract new capital.
A firm’s cost of capital is a “hurdle rate” used to measure the amount of value its business is providing to capital providers. When a firm’s operations generate returns in excess of the firm’s costs of capital, then the firm creates value for its capital providers. However, when a firm is generating returns which are less than the firm’s cost of capital, the firm is destroying value and its ability to attract capital (and stay in business!) will be diminished.
