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The after-tax interest rate is the interest rate paid on a firm‟s debt less the impact of the tax break it
gets from issuing debt. For example, suppose that a firm pays 10% interest on its debt and the firm‟s
income tax rate is 40%. If the firm issues $100,000 of debt, then the annual interest expense will be
$10,000 (10% × $100,000). But this $10,000 of interest expense is tax deductible, so the firm would
save $4,000 in taxes (40% × the $10,000 interest). Thus, net of the tax break, this firm would be
paying $6,000 to service a $100,000 debt. Its after-tax interest rate is 6% ($6,000 ÷ $100,000
principal).
The formula for after-tax interest rate (R D, after-tax ) is:
where R D is the firm‟s pretax interest rate, and τ is the firm‟s income tax rate.
Borrowing from a bank or selling bonds to raise funds is known as “debt financing.” Issuing stock
to raise funds is known as “equity financing.” Equity financing is an alternative to debt financing, but
it is not free. When a firm sells equity, it sells ownership in the firm. The return earned by the new
shareholders is a cost to the old shareholders. The rate of return earned by equity investors is found by
adding dividends to the change in the stock price and then dividing by the initial stock price:
where R E is the return on the stock and also the cost of equity financing, D is the dollar amount of
annual dividends per share paid by the firm to stockholders, P 0 is the stock price at the beginning of
the year, and P 1 is the stock price at the end of the year.
For example, suppose the stock price is $100 per share at the beginning of the year and $112 at the
end of the year, and the dividend is $8 per share. The stockholders would have earned a return of 20%,
and this 20% is also the cost of equity financing:
The capital asset pricing model (CAPM) is often used to estimate a firm‟s cost of equity financing.
The idea behind the CAPM is that the rate of return demanded by equity investors will be a function
of the risk of the equity, where risk is measured by a variable beta (β). According to the CAPM, β and
cost of equity financing are related by the following equation:
R F is a risk-free interest rate, such as a Treasury bill rate, and R M is the expected return for the stock
market as a whole. For example, suppose the expected annual return to the overall stock market is
12%, and the Treasury bill rate is 4%. If a stock has a β of 2, then its cost of equity financing would be
20%, computed as follows:
Analysts often use the Standard & Poor‟s 500 index stock portfolio as a proxy for the entire stock
market when estimating the expected market return. The βs for publicly traded firms are available
from a wide variety of sources, such as Bloomberg, Standard & Poor‟s, or the many companies that
provide equity research reports. How β is computed and the theory behind the CAPM are beyond the