# Valuation

## Learning outcomes

After studying this text the learner should / should be able to:

1. Explain the "balance sheet approach" to equity valuation.

2. Explain the "discounted cash flow approach" to equity valuation.

3. Explain the "relative valuation approach" to equity valuation.

## Introduction

The mathematics of the equity market is concerned with the valuation of ordinary shares. Preference shares of course also trade and need to be valued. However, those with fixed maturity dates and fixed rates are valued the same way as bonds. Preference shares with floating rates are usually valued at 100%, because the rate floats in line with market rates35. Perpetual preference shares (which are found in many other countries) are valued as perpetual bonds are:

In the case of the valuation of ordinary shares three approaches are generally followed. These are shown in Figure 1.

We discuss each of these methods in some detail and end with a section of inflation and the valuation on equities.

## Balance sheet valuation approach

### Introduction

There are three balance sheet valuation methods:

• Book value per share

• Liquidation value

• Replacement cost.

### Book value per share

The book value per share of a company is also called the net asset value per share. This is simply calculated as follows:

BVps = (A - L) / NOS = SF / NOS

where

A = assets

L = liabilities

SF = shareholders' funds

NOS = number of shares in issue.

 Equity and liabilities Stock (inventory) Bank deposits Debtors 3 563 050 1 035 092 3 216 925 Authorised share capital (5 000 000 shares of LCC1 each) Issued share capital (4 000 000 shares of LCC1 each) Distributable reserves Total shareholders' funds Liabilities (bank overdraft and creditors) 4 000 000 2 564 500 6 564 500 1 250 567 Total assets 7 815 067 Total equity and liabilities 7 815 067

Table 1: Balance sheet of NEWCO (Pty) Limited (LCC)

In the example shown in Table 1, the NAVps of the company is:

BV = (A - L) / NOS

= LCC7 815 067 - LCC1 259 567 / 4 000 000 = LCC6 564 500 / 4 000 000 = LCC1.64.

This analysis indicates that each share is worth LCC1.64, that any higher market price means that the share is overvalued, and that a market price below LCC1.64 means that the share is undervalued.

It should be apparent that the book value approach is crude and is based on the balance sheet that is drawn up on the basis of certain accepted accounting rules, which may or may not value the assets and liabilities of the company at market value (an example is the valuing of certain assets at historical cost).

The questions that arise here are: Can the share price he higher than the NAVper share, and does the NAV per share represent a "floor" price? The answers are yes and no, respectively. As regards the first question, it is apparent that a share price is indicative of the market participants' perception of past and future cash flows (dividends), which means that if the company has performed well and is expected to perform well in future, the share price can be substantially higher than the NAV per share.

As regards the latter question, there are many examples where the share price of a company is lower that the NAV per share. This could indicate that the cash flows expected by the market are low or that the company is in trouble.

It is notable that in instances where a share price is lower than the NAV per share, this represents an opportunity for the company to repurchase its own shares in order to improve the NAV per share. This action of course amounts to a "message" from the directors of the company to the market that they are incorrect in their assessment of the company.

 Assets Equity and liabilities Stock (inventory) Bank deposits Debtors 3 563 050 635 092 3 216 925 Authorised share capital (5 000 000 shares of LCC1 each) Issued share capital (3 600 000 shares of LCC1 each) Distributable reserves Total shareholders' funds Liabilities (bank overdraft and creditors) 3 600 000 2 564 500 6 164 500 1 250 567 Total assets 7 415 067 Total equity and liabilities 7 415 067

Table 2: Balance sheet of NEWCO (Pty) Limited (LCC)

An example may be useful: If the market price of the share in the above example is LCC1.00, and the directors decide to buy 10% of the issued shares back (i.e. 400 000 shares for which they used bank deposits), and cancel the shares, the NAV per share of the remaining shares improves to:

BV = SF / NOS

= LCC6 164 500 / 3 600 000 = LCC1.71.

As noted, this action sends a powerful message to the market, and it is likely that the share price will improve. The actual market activity of purchasing the 400 000 shares would most likely also have pushed up the share price.

Although this valuation method is crude, it is used to identify cheap shares, particularly if the market price is substantially below the NAV per share, and to identify companies for the purpose of a takeover. This method of valuation is rarely used in isolation.

### Liquidation value

This method is not foolproof because it is not easy to value assets and liabilities. Usually an austere valuation of assets and liabilities is undertaken and a proportion of the value is lopped off in order to allow for errors.

As in the case of the book value per share method, the liquidation value method is used to identify companies for takeover and/or liquidation in order to profit from the difference between market price and liquidation price. For example, if Newco (Pty) Limited is "raided" prior to the repurchase of its own shares, and all the shares are purchased at an average price of LCC1.00, the raider will profit as follows:

Profit per share = [(VA- VL) / NOS] - Pps where

Pps = price paid per share

VA = value of assets

VL = value of liabilities

NOS = number of shares in issue.

If VA is LCC6 000 000 and VL is LCC1 200 000, and number of shares is 4 000 000, then the profit per share made by the raider is:

Profit per share = [(VA- VL) / NOS] - Pps

= [(LCC6 000 000 - LCC1 200 000) / 4 000 000] - LCC1.00 = (LCC4 800 000 / 4 000 000) - LCC1.00 = LCC1.20 - LCC1.00

= LCC0.20.

As the raider bought all the shares, the total profit is LCC800 000 (4 000 000 x LCC0.20).

The alternative to this long-winded calculation is simply the NAV after liquidation (LCC4 800 000) less the mount paid by the raider for all the shares (LCC4 000 000), i.e. LCC800 000.

This method is rarely used in isolation.

### Replacement cost

Replacement cost amounts to the valuation of a company according to the replacement cost of its assets and liabilities. This method is premised on the notion that the market value of a company cannot be too removed (upwards) from the replacement cost of the assets and liabilities, because this will enable competitors to duplicate the company.

The economic logic of this approach is that if the market value of the company is substantially higher than the replacement cost of the company's assets and liabilities, many competitors will enter the relevant field of business. This will drive the market value of the firm down (lower profits and larger supply of shares of companies in this field) and increase the replacement value of the assets and liabilities (larger demand), until the market value of the companies becomes close to the replacement cost.

It is notable that James Tobin developed the concept of the ratio of market value to replacement value (known as Tobin's q). In terms of this view, the value of q will tend toward 1 in the long-term. In the short-run, however, the ratio may differ from 1.

### Concluding remark

The balance sheet valuation methods have a place, because they provide information on the replacement and liquidation value of a company. This information can be used to identify companies for takeover or raiding with the purpose of profiting from the breaking-up and sale of the assets.

However, these opportunities are rare, and analysts are mainly concerned with the value of a company as a going concern. They are interested in the cash flows generated by the company. For this, quantitative valuation methods are employed. These follow.