Introduction to Corporate Finance

3: The Time Value of Money

preferred dividends, it usually must make up lost dividends before it can pay dividends on ordinary

shares. The following example illustrates that, even when companies pay extra preferred dividends to

make up for dividends that they previously skipped, preferred shareholders must endure some loss in

value of their shares.

Big Mining Pty Ltd (BM) is a large mining company
that has had preferred shares outstanding for many
years. BM’s preferred shares promise an annual
dividend payment of $4 per share. Assuming that
investors require an 8% return on those shares, the
share market price should be $50:

PV = $4 ÷ 0.08 = $50

Unfortunately, BM recently suffered large losses
and has had to suspend its preferred dividends for
the next two years. The company says that it expects
to begin paying preferred dividends again three
years from now. To make up for the dividends that
it skipped, BM will pay a one-time dividend of $12
in three years ($8 for the dividends it skipped plus
$4 for the normal dividend in year 3), and after that,
preferred shareholders will continue to receive the
annual $4 dividend that they have come to expect.
What is the present value of the dividend stream
that BM is now promising? Stated differently, what
price would investors be willing to pay today for BM
preferred shares (assume that their required return is
still 8%)?
The best way to approach this problem is
to break it into two parts. First, there is the $12
dividend payment expected in three years. Second,
there is a perpetuity paying $4 per year starting
four years from now. We need to take the present
value of each part and then add them together.
The market value of the preferred equity should
equal the present value of the entire dividend
stream.

We can find the present value of the $12

dividend by using Equation 3.1:

PV = $12 ÷ (1 + 0.08)^3 = $9.53

Next, we will use Equation 3.10 to find the

present value of the perpetuity. However, remember

that Equation 3.10 calculates the present value of a

perpetuity that makes its first payment one year in

the future. If we apply this equation to the perpetuity

that begins in year 4, we will actually be calculating

the value of the perpetuity as of year 3. Once we

have that value, we must discount it 3 more periods

to find the present value of the perpetuity.

PV(year 3) = $4 ÷ 0.08 = $50

PV = $50 ÷ (1 + 0.08)^3 = $39.69

At last we are ready to calculate the present

value of the entire BM preferred dividend stream,

or equivalently, the market value of BM’s preferred

shares.

Value of preferred shares = value of $12 dividend +

value of $4 perpetuity

Value of preferred shares = $9.53 + $39.69

= $49.22

Under normal circumstances, when BM’s

preferred shareholders expect to receive their $4

dividend annually, the preferred shares sell for $50.

In this case, even though BM promises to eventually

make up for the dividend payments that it must skip

in the next two years, the value of the preferred

shares dips slightly.

example

You might wonder why anyone would continue to hold BM preferred shares if it pays no dividends for

three years. It turns out that as time goes by, and the date on which BM’s dividend stream will begin again

draws near, the market value of the preferred shares will rise. In other words, a preferred shareholder can

expect the shares to increase in value even if they are not paying dividends.