In the tutorial on Present Value, we demonstrated that the greater the "riskiness" of a future cash flow, the lower its present value. We also explained that "riskiness" is measured by the percentage return expected from an alternative investment with the same amount of risk. The "Cost of Capital" calculation quantifies that risk.
What Does "Cost of Capital" Mean?
More specifically, "cost of capital" is defined as "the opportunity cost of all capital invested in an enterprise."
Let's dissect this definition:
- "Opportunity cost" is what you give up as a consequence of your decision to use a scarce resource in a particular way.
- "All capital invested" is the total amount of cash invested into a business.
- "In an enterprise" refers to the fact that we are measuring the opportunity cost of all sources of capital which include debt and equity.
How Do We Calculate a Company's Weighted Average Cost of Capital?
We calculate a company's weighted average cost of capital using a 3 step process:
1. Cost of capital components. First, we calculate or infer the cost of each kind of capital that the enterprise uses, namely debt and equity.
A. Debt capital. The cost of debt capital is equivalent to actual or imputed interest rate on the company's debt, adjusted for the tax-deductibility of interest expenses. Specifically:
The after-tax cost of debt-capital = The Yield-to-Maturity on long-term debt x (1 minus the marginal tax rate in %)
We enter the marginal tax rate in cell C10 of worksheet "Inputs."
B. Equity capital. Equity shareholders, unlike debt holders, do not demand an explicit return on their capital. However, equity shareholders do face an implicit opportunity cost for investing in a specific company, because they could invest in an alternative company with a similar risk profile. Thus, we infer the opportunity cost of equity capital.
We can do this by using the "Capital Asset Pricing Model" (CAPM). This model says that equity shareholders demand a minimum rate of return equal to the return from a risk-free investment plus a return for bearing extra risk. This extra risk is often called the "equity risk premium", and is equivalent to the risk premium of the market as a whole times a multiplier--called "beta"--that measures how risky a specific security is relative to the total market.
Thus, the cost of equity capital = Risk-Free Rate + (Beta times Market Risk Premium).
2. Capital structure. Next, we calculate the proportion that debt and equity capital contribute to the entire enterprise, using the market values of total debt and equity to reflect the investments on which those investors expect to earn a minimum return.
3. Weighting the components. Finally, we weight the cost of each kind of capital by the proportion that each contributes to the entire capital structure. This gives us the Weighted Average Cost of Capital (WACC), the average cost of each dollar of cash employed in the business.
Case Study: Gateway, Inc., as of April 21, 2000
To demonstrate how to calculate a company's cost of capital, we will use the Gateway case study developed in the book. Readers who want to calculate the Weighted Average Cost of Capital (WACC) may wish to download the accompanying spreadsheet.
1. Cost of capital components. Gateway draws upon two major sources of capital from the capital markets: debt and equity.
A. Cost of Gateway's debt capital. As of the end of 1999, Gateway only had debt of $8.5 million. Enter this figure in cell C25 of worksheet "Inputs." Because this amount is so small, it will not significantly affect our Weighted Average Cost of Capital calculation. For the purposes of this tutorial, however, let's run the numbers.
Our first step in calculating any company's cost of capital is to consult the relevant annual 10-K regulatory filings with the Security and Exchange Commission (SEC). For this case study, we can click here to see Gateway's 1999 10-K. This document tells us that Gateway has two components to its total debt of $8.488 million:
Because there are two kinds of debt with different interest rates, we have to weight the different interest rates associated with each kind of debt by the relevant proportion of debt that each comprises. In this case, the pre-tax cost of debt would be equivalent to (4.7% x 99.14%) + (6.5% x 0.86%), or 4.72%. Enter the pre-tax cost of debt in cell C5 of worksheet "Inputs."
- Regular debt. Gateway has $8.415 million of "Notes payable through 2002 with interest rates ranging from 3.9% to 5.5%." We can calculate that the middle of this range equals 4.7%. We can also calculate that Gateway's Notes Payable of $8.415 million comprises 99.14% of the company's total debt of $8.488 million.
- Capital leases. Gateway also has $73, 000 in "capital leases." A capital lease is a debt-like agreement in which a firm agrees to pay fixed amounts to someone who leases them land or equipment. Gateway's SEC filing tells us that this debt-equivalent capital lease has a "fixed rate of 6.5%" We can calculate that Gateway's $73,000 of capital leases comprises 0.86% of the company's total debt of $8.488 million.
However, we are not done yet. We noted above that we have to adjust for the tax-deductibility of interest expenses, which lowers the cost of debt according to the following formula:
After-Tax Cost of Debt Capital = The Yield-to-Maturity on long-term debt x (1 minus the marginal tax rate)
Given Gateway's marginal tax rate of 35%, the company's after-tax cost of debt equates to 4.72% x (100% minus 35%), or 3.1%. We see this calculation in cell C6 of worksheet "WACC."
Notably, Gateway has both near-zero debt levels and a near-zero after-tax cost of debt, which means it will have virtually no effect on the company's weighted average cost of capital. Thus, the purpose of this cost-of-debt calculation is purely instructional.
Also, plese note that in this example, we have used a company's actual cost of debt as a proxy for its marginal cost of long-term debt. A company's marginal cost of long-term debt may be better estimated by summing the risk-free rate and the "credit spread" that lenders would charge a company with a specific credit rating.
B. Cost of Gateway's equity capital. We noted above that:
Cost of Equity Capital = Risk-Free Rate + (Beta times Market Risk Premium).
To calculate any company's cost of equity capital, we need to find a reliable source for each of these inputs:
1. Risk-free Rate. We suggest using the rate of return on long-term (ten-year) government treasury bonds as a proxy for the risk-free rate. We enter this data point in cell C4 of worksheet "Inputs."
Sources for this include:
- CBS Marketwatch. Even unregistered users can use CBS MarketWatch's free bond quotes by clicking here.
- New York Times. Any user can see the "10yr. Tres. Yield" on the front page of the New York Time's web site by clicking here. To get further details, you can register free of charge.
- Wall Street Journal. Paid subscribers to the WSJ's online service can find quotes for key interest rate measures (including the ten-year T-Bond) by clicking here.
2. Beta coefficient. We enter this data point in cell C8 of worksheet "Inputs."
There are a variety of sources available for obtaining the beta coefficient for a particular company.
- Value Line Investment Survey. Paid subscribers to this service can obtain Value Line's estimates of a company's beta coefficient. Value Line can be accessed either online or offline through a paid subscription, as well as at most public libraries. Click here to see how to read a company-specific Investment Survey using Value Line. Arrow #1 points to where you can find Value Line's Beta estimate.
- Yahoo. Yahoo offers free beta estimates through its Company Profile service. Click here to see Gateway's Company Profile on Yahoo.
- Bloomberg. Free beta estimates from Bloomberg can be accessed online. Bloomberg's estimate of Gateway's current beta can be accessed here.
- Barra. Barra publishes the Barra Beta Book monthly to suscribers. You may be able to find this resource in a good business library. Click here to see the company's web site.
3. Equity Risk Premium. Forward looking approaches, as well as more recent historical data, suggest an equity risk premium in the 3 to 5 percent range. We use an Equity Risk Premium estimate of 3.2%. We enter this data point in cell C7 of worksheet "Inputs."
For those interested in looking at historical equity risk premia, we refer you to the following online resources:
- Ibbotson Associates. Ibbotson sells a report on historical risk premia over time on its website. The report can be purchased by clicking here.
- Aswath Damodaran. Valuation expert Professor Damodaran of NYU's Stern School of Business has published an informative article on equity risk premia that can be downloaded free of charge.
To continue with our Gateway case study, we used the following estimates for these three factors as of April 21, 2000:
- Risk-free rate of 5.85%.
- Beta coefficient of 1.3.
- Equity risk premium of 3.2%.
Using these estimates, Gateway's cost of equity capital = Risk-Free Rate + (Beta times Market Risk Premium).= 5.85% + (1.3 x 3.2%), or 10%. We see this calculation in cell G7 of worksheet "WACC."
3. Weighting the components. Finally, we weight the cost of each kind of capital by the proportion that each kind of capital contributes to the entire enterprise. This gives us the Weighted Average Cost of Capital (WACC), the average cost of each dollar of cash employed in the business.
To review, Gateway's after-tax cost of debt is 4.72% and its cost of equity is 10%. As of April 21, 200, the market value of Gateway's debt is equal to $8.5 million and the market value of Gateway's equity approaches $17 billion. We enter the shares outstanding and share price for this calculation in cells C12 and C13 in worksheet "Inputs."
Thus, debt contributes virtually 0% of Gateway's capital while equity contributes virtually 100%.
Gateway's weighted average cost of capital is thus 4.72% x 0% + 10% x 100%, or 10%. You can see this calculation in cell J13 of worksheet "WACC."