Introduction to Corporate Finance

PARt 2: VALUAtIoN, RISk ANd REtURN

example

Hewlett-Packard (HP), the US computer giant, paid a constant quarterly dividend of US$0.08 per share without

interruption from June 1998 to March 2011. Perhaps after receiving the same dividend for more than 12 years,

investors believed that HP’s dividend would remain at US$0.08 (or US$0.32 per year) forever. What price would

they be willing to pay for HP shares?

The answer depends on investors’ required rate of return. If investors demanded a 10% annual return, then

the share should be worth US$0.32 ÷ 0.10 or US$3.20 (making the simplifying assumption that the dividend is

paid annually).^5 In fact, in the first half of 2011, HP shares actually traded close to US$40 per share. This implies

one of two things: either investors required a rate of return that was very low (in fact, less than 1%) – which is

implausible – or they expected that dividends would eventually grow, even though they had remained steady

for many years. Expectations of higher dividends were realised when HP increased its dividend by 50% in the

spring of 2011 and announced its intention to make double-digit dividend increases during the next few years.

5-2d CoNStANt GRoWtH

Of all the relatively simple share valuation models that we consider in this chapter, the constant growth

model probably sees the most use in practice. The model assumes that dividends will grow at a constant

rate, g. If dividends grow at a constant rate forever, we calculate the value of that cash flow stream by

using the formula for a growing perpetuity, this is given in Chapter 3. Denoting next year’s dividend as D 1 ,

we determine the value today of a share that pays a dividend growing at a constant rate:^6

Eq. 5.4 P

D

rg

0

=^1

−

The constant growth model in Equation 5.4 is commonly called the Gordon growth model, after Myron

Gordon, who popularised this formula.

example

Cochlear Limited is undoubtedly an Australian corporate success story. Its value is based on its primary

product, a bionic ear implant that enhances hearing for those with impairments. The device is made up of two

main sections, an external sound processor and coil, and an internal implant. The sound processor captures

sound and converts it into digital code, while the sound processor transmits the digitally coded sound through

the coil to the implant. The implant converts the digitally coded sound to electrical impulses and sends them

along the electrode array, which is positioned in the cochlea. The company listed on the ASX in 1995 and is

still, as of 2015, growing in value.

Since 1997, Cochlear has paid an annual dividend, rising nearly every year. The compound annual average

growth rate of the dividend was about 1% over the period 2000–1, but clearly this could not remain the annual

growth rate forever, or even for each year. The payment for 2014 was $2.54 per share. Although the dividend is

normally paid semiannually, here we shall assume, for simplicity, that the dividend is paid annually, and that it is

5 You can apply the same formula to quarterly dividends as long as you make an appropriate adjustment in the interest rate. For example, if

investors expect a 10% effective annual rate of return on HP shares, they expect a quarterly return of (1.10)0.25 – 1, or 2.41%. Using this figure,

you can recalculate the share price by dividing $0.08, the quarterly dividend, by 0.0241 to obtain $3.32. Why are HP shares more valuable in

this calculation? Since HP’s dividends arrive more often than once a year, the present value of the dividend stream is greater.

6 To apply this equation, one must assume that r > g and that g itself is constant. Of course, some companies may grow very rapidly for a time,

so that g > r temporarily. We treat the case of companies that grow rapidly for a finite period later in the discussion. In the long run, it is

reasonable to assume that r must eventually exceed g. If the growth rate exceeded the discount rate forever, the value of the share would be

infinite, because it would grow faster over time than it would be discounted.

LO5.2

Gordon growth model
Values a share under the
assumption that dividends
grow at a constant rate
forever