Introduction to Corporate Finance

5: Valuing Shares

rate. To find today’s value of a preferred share, PS 0 , we use the equation for the present value of a

perpetuity, dividing the preferred dividend, Dp, by the required rate of return on the preferred share, rp:

Eq. 5.1 PS 0 =

D

r

p

p

example

Aussie Company has preferred shares outstanding

that pay a dividend of $3.75 per share each year.

The share paid a dividend on 8 September 2015. If

investors require a 5.5% return on this investment,

what would you expect the price of these shares to

be on 9 September 2015?

Recognising that the next $3.75 dividend comes

one year in the future, we can apply Equation 5.1 to

estimate the value of Aussie Company’s preferred

shares:

PS 0

375

0 055

== 6818

$.

.

$.

Equation 5.1 is valid if dividend payments arrive annually and if the next dividend payment comes

in one year. Suppose the preferred shares pay dividends quarterly. How do we modify Equation 5.1 to

value a preferred share paying quarterly dividends? One approach is to divide both the annual dividend

and the required rate of return by four to obtain quarterly figures. If we apply that logic to Aussie

Company’s preferred shares, we obtain:

PS 0

3754

0 055

0 9375

0 01375

=

÷

÷

==

($.)

(. )

$.

.

$

4

668. 18

Our calculations so far indicate that Aussie Company’s preferred shares are worth $68.18 each,

whether it pays dividends annually or quarterly. That can’t be right. The time value of money implies

that investors are better off if they receive dividends sooner rather than later. In other words, if Aussie

Company’s preferred shares pay $3.75 in dividends per year, the value of that dividend should be greater

if it is paid in quarterly instalments rather than in one payment per year. In fact, Aussie Company shares

would be worth more than $68.18 each if it paid quarterly dividends, as the next example demonstrates.

example

When we attempted to adjust Equation 5.1 for

quarterly dividends, we assumed that investors

required a quarterly return of 1.375%, or one-quarter

of the 5.5% required return used in the example

with annual dividends. However, if the quarterly

required return is 1.375%, this translates into an

effective annual return that is higher than 5.5%. Using

Equation 3.14 (see page 98), we can calculate that a

quarterly rate of 1.375% translates into an effective

annual rate of about 5.6%:

=

 +







Effectiveannualrate −=

10 .055

4

10 .056

4

That means our examples with annual and

quarterly dividends are not making a true, ‘apples

with apples’ comparison, because we have assumed a

slightly higher effective discount rate in the quarterly

calculations. If the effective annual required return

is in fact 5.5%, then we can use Equation 3.14 to

determine that the quarterly rate is just 1.35%:

0055 1

4

1

4

0 0135

4

.

.

=+









−

=

r

r

Discounting the quarterly dividend at the

appropriate quarterly rate would result in a higher

value for Aussie Company preferred shares:

PS 0

0 937

0 0135

== 6944

$.

.

$.