Principles of Corporate Finance_ 12th Edition

338 Part Four Financing Decisions and Market Efficiency

bre44380_ch13_327-354.indd 338 09/11/15 07:55 AM

For example, imagine that in December 2014 you wanted to check whether the stocks

forming Standard & Poor’s Composite Index were fairly valued. As a first stab you might use

the constant-growth formula that we introduced in Chapter 4. In 2014, the annual dividends

paid by the companies in the index were roughly $350 billion. Suppose that these dividends

were expected to grow at a steady rate of 4.0% and that investors required a return of 6.0%.

Then the constant-growth formula gives a value for the common stocks of

PV common stocks = _____DIV

r − g

= __________^350

.060 − .040

= $17,500 billion

which was roughly their value in December 2014. But how confident could you be about

these figures? Perhaps the likely dividend growth was only 3.5% per year. In that case your

estimate of the value of the common stocks would decline to

PV common stocks = _____DIV

r − g

= __________^350

.060 − .035

= $14,000 billion

In other words, a reduction of just half a percentage point in the expected rate of dividend

growth would reduce the value of common stocks by 20%.

The extreme difficulty of valuing common stocks from scratch has two important conse-

quences. First, investors find it easier to price a common stock relative to yesterday’s price

or relative to today’s price of comparable securities. In other words, they generally take

◗ FIGURE 13.5 Log deviations from Royal Dutch Shell/Shell T&T parity.

Source: Mathijs van Dijk, http://www.mathijsavandijk.com/dual-listed-companies. Used with permission.

–40

–30

–20

–10

0

10

20

30

01/01/198001/01/198201/01/198401/01/198601/01/198801/01/199001/01/1992

Deviation, %

01/01/199401/01/199601/01/199801/01/200001/01/200201/01/2004