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D Ã— (1 + g ) D Ã— (1 + g )

2 3

V Ã— (1 + CoE ) = D Ã— (1 + g ) + + â€¦

(1 + CoE ) (1 + CoE )2

The right hand side of this equation can be simplified by extracting the term

(1 + g). We then see that:

D Ã— (1 + g ) ï£¶ D Ã— (1 + g )

2

ï£«

V Ã— (1 + CoE ) = (1 + g ) Ã— ï£¬ D + + +â€¦

(1 + CoE ) ï£· (1 + CoE )2

ï£ ï£¸

Now note that all of the terms to the right of the final expression are exactly

the same25 as the original equation for V. This means that:

V Ã— (1 + CoE ) = (1 + g ) Ã— ( D + V )

The sum can either be done for ever into the future, which is referred to as a perpetuity valuation,

24

or to a point at which it is assumed the company is liquidated. However, since the liquidation value

should equal the value of the future cash flows that the remaining assets should produce, this too

should give a value equal to the present value of the stream of dividends to perpetuity.

This is true provided the growth rate g is less than the cost of equity.

25

43 Building block 2: Financial markets

Hence

V + V Ã— CoE = D + V + g Ã— D + g Ã— V

Which simplifies to:

(1 + g )

V =DÃ—

(CoE âˆ’ g )

This is an extremely useful formula allowing almost instant share valuation.

It does not matter if you do not follow the derivation, what matters is the

equation itself. To value a share all you need is a set of assumptions about

three things: the dividend, the growth rate and the cost of equity. With no

growth one gets an even more simple relationship that value is equal to the

dividend divided by the cost of equity. We first met this equation in the first

building block, now we should understand its derivation.

The term D Ã— (1 + g) is equal to the anticipated dividend receivable in one

yearâ€™s time. Hence the equation states that a share should be worth this antici-

pated dividend divided by cost of equity less growth.26 I refer to this relation-

ship as the perpetuity valuation formula. It is also called the Gordon Growth

model in recognition of its original â€˜inventorâ€™.

There is one final rearrangement of the formula which I like to make.

The dividend divided by the value is what is termed the dividend yield. This

means that:

Cost of equity = dividend yield + anticipated growth

The cost of equity is the return an investor requires and it is achieved through

a combination of dividend yield plus growth. When written this way the

equation is almost self evident.

The relationship between dividends and funds flow

The valuation formula which we have just derived is based purely on divi-

dends paid. We now need to consider the relationship between dividends

and a companyâ€™s actual generation of cash. The directors of a company are

allowed, subject to certain rules,27 to declare any dividend they consider

Once again, remember that a valuation is only as good as the assumptions on which it is based. In this

26

case the key assumptions concern constant growth to perpetuity and a constant cost of equity.

These rules are set by the prevailing company law. The usual rule is that dividends can only be paid

27

out of profits that have already been earned. So if more cash is available than the accumulated profit

44 The five financial building blocks

appropriate. So if a company is valued based on its dividend, why not always

pay as high a dividend as possible in order to achieve the highest possible

value?

The answer is that shareholders can see through such a simple approach.

If shareholders think a dividend is not sustainable then they will not be

prepared to assume that it is actually paid out for ever into the future. The

value they will place on the company will be lower than this would have

implied.

Shareholders will even place a value on a company that is paying no divi-

dend at all simply because they believe that at some stage in the future the

company will pay a dividend. Microsoft was an extreme example of this. It

managed to build a huge market capitalisation28 before it ever paid a cash

dividend. Its first cash dividend was paid in 2003 by which time it had gener-

ated a cash holding of almost $50bn.29

What was happening was that shareholders were buying shares in the

anticipation that at some stage in the future, dividends would be paid out. So

shareholders, as they set the share price, were looking beyond the actual divi-

dend to potential dividends. In Microsoftâ€™s case, the shareholders knew there

was $50bn in the bank and also all of the worth of the existing Windows suite

of software. The implication had to be of huge dividends in the future.

A simple way to think about a future dividend is to assume that cash held

by the company can either be paid out now or invested in a new project. If

money is invested in a new project then this will simply defer the dividend

because the project will return ever more money in the future. Indeed, if

the project earns a return equal to the time value of money then the present

value of that future cash will exactly equal the dividend that is foregone today

in order to fund the project. So paying a dividend or investing should both

yield the same value. If the project earns above the cost of capital then retain-

ing the cash will create more value than paying a dividend and not investing

in the project.

Cash raised from new share sales tends to be a significant source of finance

only for new or very fast growing companies. For most other companies the

main source of finance is the existing flow of cash generation. This is usu-

ally referred to as retained earnings. It might be tempting for established

this cannot be paid out as a dividend. Situations such as this can occur when companies stop growing

and see their need for capital start to fall.

Market capitalisation is the aggregate value of all shares that have been issued.

28

This was a highly unusual position and was probably at least in part a function of Bill Gatesâ€™ lack of

29

need for cash.

45 Building block 2: Financial markets

companies to consider that they have three sources of finance: debt, equity

and retained earnings. This would be wrong because companies belong to

shareholders and should always consider that retaining earnings means pay-

ing lower dividends to shareholders and that they are already the owners of

the company. Hence there are just two sources of finance.

Do dividends matter?

The answer to this question can be either yes or no. At the most obvious level,

dividends matter because, ultimately, a company is only worth the present

value of its future dividends. Dividends donâ€™t matter because a company is

valued on the assumption that its cash resources already belong to sharehold-

ers. This is equivalent to assuming that the payment of a dividend simply

moves money from one account of a shareholder (money held by the com-

pany) to another (money held directly by the shareholder).

Dividends donâ€™t matter only when shareholders trust the management of

a company to invest their money wisely. If shareholders think that cash can

be reinvested by a company and earn an NPV of zero or more then the share-

holders would, logically, be happy to see this happen even if it meant a com-

pany paying no dividend today. In theory, if a company has cash equivalent

to, say, $1 per share then if it pays this out as a dividend or retains it to invest

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