UoK (FM) – Valuation of Securities (VoS) – Lecture 5

Online Certificate Course

Introduction

In theory, determines the market value of equity and of debt.

The valuation of equity – constant dividends

The market value of a share is effectively determined by the shareholders – it is the price that
shareholders are prepared to pay for a share on the stock exchange.

In theory, the amount that shareholders are prepared to pay depends on two factors:
1. The dividends that they expect to receive in the future
2. The rate of return that shareholders require

Alpha plc has in issue $1 shares and has just paid a dividend of 20c per share. Dividends are
expected to remain constant. Shareholders required rate of return is 10% p.a.
What will be the current market value per share?

Beta plc has in issue $0.50 shares and has just paid a dividend of 15c per share. Dividends are
expected to remain constant. Shareholders required rate of return is 12%.
What will be the current market value per share?

Cum div / ex div values

In both the above examples, the company had just paid a dividend, and therefore anyone buying the
share would have to wait for a year until they were to receive their first dividend (in the
examination we ignore the possibility of interim dividends).
We call this situation an ‘ex div’ valuation.

Suppose, however, that the company was about to pay a dividend. This would mean that someone
buying the share would receive a dividend virtually immediately (in addition to all the future
dividends). Therefore the price that they will be prepared to pay will be higher by the amount of the
dividend about to be paid.
We call this situation a ‘cum div’ valuation.

Market value cum div = market value ex div + dividend about to be paid

The valuation of equity – non-constant dividends

The arithmetic in the previous section is very simple, but in practice it is unlikely that the
shareholders will be expecting constant dividends in the future. They will usually be expecting
them to change – hopefully to grow! The full dividend valuation model, which copes with any
expected future stream of dividends, is the following:

The market value of a share is the present value of future expected dividends,
discounted at the shareholders required rate of return.
This will deal with any future dividend stream – including of course the simple situation in the
previous section of constant dividends.

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 UoK (FM) – Valuation of Securities (VoS) – Lecture 5
Online Certificate Course
The valuation of equity – constant growth rate in dividends

In this situation it is possible to use the dividend valuation model to derive a formula for the market
value of a share. The proof of this is not in the examination syllabus – you are only expected to be
able to use the formula.
The formula is:

The valuation of debt

Here we are talking about traded debt. This is debt borrowing that is traded on a stock exchange
and therefore has a market value. Unless you are told otherwise, debt is traded in units of $100
nominal and is referred to as ‘debentures’, ‘loan stock’, or ‘bonds’ – they are different words for the
same thing. Debt (in the examination) carries a fixed rate of interest, but this is based on the
nominal value of the debt. This rate of interest is known as the coupon rate. The market value at any
time will depend on the rate of return that investors are currently requiring.

The basis of valuation is, in theory, exactly the same as for equity:

The market value of debt is the present value of future expected receipts discounted at the
investors required rate of return.

The valuation of debt – irredeemable debt

Irredeemable debt is debt that is never repaid. The holder of this debt will simply receive interest
each year for ever (unless they choose to sell it on the stock exchange, in which case the purchase
will continue to receive the interest).

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 UoK (FM) – Valuation of Securities (VoS) – Lecture 5
Online Certificate Course
The valuation of debt – redeemable debt
In practice, debt is not irredeemable but redeemable which means that the company will repay the
borrowing at some specified date in the future.

The valuation of redeemable debt is the one place where there is no formula and where we have no
choice but to use first principles.

Limitations of the dividend valuation model

Although expected future dividends and the shareholders required rate of return certainly do
impact upon the market value of shares, it would be unrealistic to expect the theory to work
perfectly in practice.

Main reasons for this include:

1. The stock exchange is not perfectly efficient, and therefore the market value of a share may
be distorted from day-to-day by factors such as rumors about a takeover bid.
2. In practice, market values do not change instantly on changes in expectations – the speed at
which the market value changes depend on the volume of business in the share.
3. The model only deals with constant growth in dividends. In practice this may not be the
case. However, do appreciate that the growth used in the model is the future growth that
shareholders are expecting – this is perhaps more likely to be at a constant rate. The big
problem is determining the rate of growth that shareholders expect! It is clearly impossible
to ask them and to any estimate that we make for our calculations is only an estimate and
course is completely different from the rate of growth that shareholders are in fact
expecting.

Financial Accounts based valuations of equity

Other common, practical approaches to valuing shares in unquoted companies are:

Net assets basis

On this approach the value per share is calculated as:

Value of net assets / Number of shares

A problem is on what basis to value the net assets:

1. Realizable value – this would only be sensible if the company was about to be wound up
2. Replacement value – this would be more sensible from the point of view of another
company considering making an offer for the shares in our company. However, it would be
ignoring the value of any goodwill.
3. Book value – this is normally of little relevance, since the book values of assets are unlikely
to even approximate to the actual values.

Earnings basis
This approach uses the price earnings ratio of a similar quoted company.
PE ratio = Market value per share / Earnings per share

For example, if the latest set of accounts for a publishing company shows earnings per share of 50c,
and quoted publishing companies currently have PE ratios of 18, then the price per share for our
company would be 50c × 18 = $9.

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