Valuing a company

Valuing a target is the stage of a takeover where the price gets decided, and there is no single right answer. Several methods are available, they produce different numbers, and which number is relevant depends on what the buyer intends to do with the business.

The methods fall into two families.

The gap between the two families is where the argument lives. A profitable company is worth far more as a going concern than the sum of its assets, because the assets by themselves do not include the customers, the staff, the licences or the brand. A lossmaking one can be worth more broken up than kept alive.

This is why valuation is described as more art than science. The arithmetic in each method is straightforward; choosing the method, and defending the assumptions inside it, is the work.

For a listed company the market has already put a value on the equity every trading day. Market capitalisation is the number of issued ordinary shares multiplied by their market price.

A company with 5 million ZMW0.50 ordinary shares quoted at ZMW2.85 has a market capitalisation of 5m × ZMW2.85 = ZMW14.25 million. The ZMW0.50 nominal value plays no part — it is the traded price that matters.

What that figure gives a bidder is a floor, not a price. It is roughly the minimum the target’s shareholders will accept, because they can already sell at it in the market. To persuade them to hand over control, a substantial premium has to be added on top.

Two limitations are worth stating in any answer that uses it.

• It reflects marginal trading only. On any given day a small fraction of the shares change hands, and that price is what values the whole company — which is fine for a share and questionable for control of a business.
• It reflects the company as it is, not as the bidder intends it to be. Nothing in the share price knows about the synergies or the cost savings the buyer is planning, so it cannot say what the target is worth to this particular bidder.

Whether it is a fair value at all depends on how efficient the market is — and on the LuSE, where some counters trade rarely, a quoted price can be several weeks out of date. So look at how the share price has moved over a period rather than reading one day’s figure.

An asset-based valuation adds up what the company owns and deducts what it owes. The three versions differ only in how the assets are measured.

Book value is the one that is always available, and the one that is nearly always wrong. Its figures are factual, which is its whole appeal, but historical cost is not current value: a Lusaka warehouse bought in 2009 sits in the accounts at a fraction of what it is worth, while the inventory and receivables figures may be worth considerably less than stated.

The larger problem is what the accounts leave out entirely. Internally generated goodwill, brands, customer relationships and the skill of the workforce are not recognised as assets — and in a profitable company they are usually most of what the buyer is actually paying for.

Replacement cost and realisable value are more relevant than book value and much harder to obtain. A bidder can download the target’s published accounts; working out what its assets would really fetch, or really cost to replace, needs information only the target has.

The P/E basis values a company by multiplying its earnings by the multiple the market applies to companies like it. It is the quickest income-based method and the most widely used in practice.

The whole valuation turns on which P/E ratio is used, and there are three candidates. The bidder’s own, the target’s own, or an average for the sector. They can differ by a factor of five, and the choice has to be argued for rather than assumed.

PC plans to acquire 75% of the shares in Computer Co, whose share capital is ZMW2 million made up of 40 ngwee shares. Computer Co has just paid a dividend of 6 ngwee per share on a payout ratio of 40%, and the sector average P/E is 8 times.

Two things in that working catch people out. The dividend has to be turned back into earnings by dividing by the payout ratio, since P/E values earnings and not dividends. And the number of shares comes from dividing the share capital by the nominal value of 40 ngwee, not by the market price.

The dividend growth model values a share as the present value of every dividend it will ever pay. It is the cost of equity calculation from Lesson 2, rearranged: there you knew the price and solved for the return, here you know the return and solve for the price.

PH Co is considering a bid for HP Co. HP has 5 million ordinary shares, earnings per share of 40 ngwee and a payout ratio of 60%. It paid 23.0 ngwee a year ago and 20.0 ngwee the year before that. Its equity beta is 1.40, treasury bills yield 4.6%, the market returns 10.6% and the sector P/E is 10 times.

Take the P/E basis first, since it needs nothing but the earnings.

Then the dividend growth model, which needs three inputs built first: the cost of equity, the current dividend and the growth rate.

ZMW20 million on one basis and ZMW37.55 million on the other, from the same company on the same day. Nothing has been done wrong — the two methods are answering the question differently, and knowing why is worth more than either figure.

• The P/E basis says HP is an ordinary company in its sector and should be rated like one. It takes a single year’s earnings and a market multiple, and asks nothing about the future.
• The dividend growth model says HP will grow its dividend at 9.5% forever against a required return of 13%. That gap of 3.5 points is doing almost all of the work.

That is the fragility to watch. With re − g on the denominator, the answer explodes as growth approaches the required return: at 11% growth instead of 9.5% the same shares are worth ZMW13.32 and the company ZMW66.6 million. A growth rate estimated from two old dividends cannot carry that much weight.

So the practical answer is a range rather than a number. Net asset value sets the floor, market capitalisation sets what the shareholders will not go below, and the income methods mark out the ceiling — with the final price settled by negotiation somewhere inside it.