The valuation of securities – theoretical approach

1 Introduction

In this chapter we will look at what, in theory, determines the market value of equity and of debt. It is this theory which forms the basis for most of the arithmetic that is generally required in the examination in questions on this area.

In practice many other factors are likely to be relevant. These will be covered in the next chapter, and although important they are more relevant for discussion questions than for computations.

2 The valuation of equity – constant dividends

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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:

• the dividends that they expect to receive in the future

• the rate of return that shareholders require

3 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

In the examination you will only be asked to deal with the situation where a dividend has either just been paid (ex div) or is about to be paid (cum div). In practice, the next dividend might be due in 3 months time – this would make the arithmetic a little more involved, but will not be required in the examination.

In the examination, you always assume that market values are ex div, unless you are told otherwise.

4 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:

This will deal with any future dividend stream – including of course the simple situation in the previous section of constant dividends.

Although we can use this model for any future dividend stream, you will only be expected to deal with constant dividends, or (more likely) the situation where dividends are expected to grow at a constant rate.

5 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. (If you are interested in the proof, then you can find it in the Study text).

The formula is:

where:

  D₀ = the current dividend

  r_e = the share holders required rate of return

  g = the expected rate of growth in dividends p.a.

In practice, it is unlikely that dividends will grow at a constant rate. However, appreciate that the market value is based on the dividends that shareholders expect to receive. Shareholders are perhaps more likely to expect an average rate of growth p.a. than expect that the dividends will grow at different specific rates each year.

In the examination you will only be expected to deal with constant rate of growth and therefore to use the formula.

6 The valuation of debt

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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.

7 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).

The answer that we have calculated is an ex int market value – as before, the cum int value would be the ex int value plus any interest about to be received. However, again, we always assume values to be ex int unless told otherwise.

The market value of irredeemable debt can be expressed as a formula as follows:

where:
  I = the interest p.a. on $100 nominal
  k_d = the investors required rate of return

8 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.