The Cost of Capital

The cost of capital is the weighted average of the cost of equity and cost of debt. It’s the rate both equity and debt investors demand as a return or the hurdle rate if you’re on the other side of the table.

Calculating the Cost of Capital

The formula for calculating the cost of capital is straightforward:

\[CostOfCapital = CostOfEquity * \frac{MarketValueOfEquity}{(MarketValueOfDebt + MarketValueOfEquity)} +\ldots\\ CostOfDebt * (1 - MarginalTaxRate) * \frac{MarketValueOfDebt}{(MarketValueOfDebt + MarketValueOfEquity)}\]

Market weights are used when computing the cost of capital for a publicly traded firm as it’s what you would have to pay right now to purchase the company.

Estimating the Market Weight for Equity

Getting the market value for equity is easy. Just multiply the share price by the number of shares.

\[MarketValueOfEquity = Prices * Shares\]

Estimating the Market Weight for Debt

Estimating the market value for debt is generally more complicated. We determine the annual interest expense that is being paid today, and use the firm’s current cost of debt to back into the market value of debt. The best way to do this is to convert the book value of interest-bearing debt to market value using the bond pricing equation:

\[MarketValueOfDebt = AnnualInterestExpense * \Bigg[ \frac{\Big( 1 - \frac{1}{(1 + PreTaxCostOfDebt)^t}\Big)}{PreTaxCostOfDebt} \Bigg] + \frac{BookValueOfDebt}{(1 + PreTaxCostOfDebt)^t}\]

What About Hybrids?

Hybrids are instruments that are part debt and equity. Examples include:

  • Convertible Bonds
  • Preferred Stock

Convertible Bonds

Estimate the value of the straight bond and treat it as debt, and estimate the value of the conversion option and treat it as equity, and then add both to the market value of debt and equity.

Preferred Stock

Unlike preferred stock in many other countries, preferred stock in the U.S. is more challenging as it pays dividends that are contractually obligated. Preferred stock in the U.S. is neither debt or equity, so it will need its own cost of financing. It’s simple to estimate, however, as it’s just the dividend yield.

Converting Currencies

What if you want to convert the cost of capital to a different currency? There are two ways with the second being the preferred:

  1. Replace US risk-free rate with local currency nominal risk-free rate
  2. Add the difference in inflation to the local currency
\[CostOfCapital = (1 + CostOfCapital_{USD}) * \frac{1 + Inflation_{BR}}{1+Inflation_{USD}} -1\]

Additional Resources

  • [Debt and the Cost of Capital](http://people.stern.nyu.edu/adamodar/podcasts/Webcasts/debt.mp4 “Debt and the Cost of Debt”)
  • [Converting Leases to Debt](http://people.stern.nyu.edu/adamodar/podcasts/Webcasts/Leases.mp4 “Converting Leases to Debt”)
  • Cost of Capital by US Sector
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Leo Smigel

Based in Pittsburgh, Analyzing Alpha is a blog by Leo Smigel exploring what works in the markets.