# The Cost of Capital

The cost of capital is the weighted average of the cost of equity and the 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:

cod = coe * (mve/((mvd + mve)) + cod * (1 – mtr) * (mvd/(mvd + mve))

Where:

• coc: Cost of Capital
• coe: Cost of Equity
• mve: Markest Value of Equity
• mvd: Market Value of Debt
• cod: Cost of Debt
• mtr: Marginal Tax Rate

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.

mv = p * s

Where:

• mve: Market Value of Equity
• p: Price
• s: 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:

mvd = aie * (((1 – (1/(1 + pcod)^t ))/pcod)) + (bvd/(1 + pcod)^t)

Where:

• mvd: Market Value of Debt
• aie: Annual Interest expense
• pcod: Pretax Cost of Debt
• bvd: Book Value of Debt

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, 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 nor 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

coct = (1 + cocu) * (1 + it/1+cocu) – 1

Where:

• coct: Target Country Cost of Capital
• cocu: Cost of Capital USD
• it: Target Country Inflation
• iu: Inflation USD