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453 First view: The cost of capital

The decision to invest in Project B should be simple. If the numbers are

correct it creates value. The NPV is small and the use of any fudge factor

or hurdle rate would serve to rule it out because the IRR is less than one

percentage point above the CoC and I am assuming that the fudge factor is

always at least one percent.

Let us now reflect on the returns which shareholders will earn at the point

at which the choice of projects is announced and believed by the market and

also the returns which will be earned in the following 23-year build-up to

steady state and finally the return which will be earned by shareholders at

steady state.

The return at the point of acceptance by the market of the strategy will

equal the present value of future NPVs. If either Project A or Optimised A

are announced the value gain will be $7m divided by the CoC of 9%. This is

$77.8m. If the decision to invest in A and B is announced the value created

will be $92.2m. It is the owner of the company before the announcements

are made that will gain this value. Once the announcements are made share-

holders will then earn just the CoC if the company implements the plans in

line with expectations. This means that throughout the 23-year build-up and

then through to perpetuity shareholders will earn just the CoC. The only

difference is that more money will have been invested in the larger company.

CoC theory tells us that shareholders are happy with this. This is why the

company should be content to invest in a project which earns exactly the

CoC. This is, on average, all the shareholders ever expect to get.

I hope that this example has helped to explain why investing in a zero-NPV

project is quite acceptable. Of course the shareholders would love it if the pro-

ject were better. If this happens, however, it is the existing shareholders who

reap the benefit and not any new shareholders who invest after the new value

is reflected in the share price. So the model is that shareholders are investing

in the company to earn their CoC. The best way to align company decision-

making with this fact is not to incorporate a fudge factor in the CoC.

Within a company, growth can bring some subtle benefits. It may, for

example, have created better employment opportunities which could have

attracted better quality staff. The increased size might also lower risk,

although if Project B is in the same business area as Project A the strong cor-

relation between the two projects will mean that the reduction in risk is only

small. The companyâ€™s status and position in many published league tables

will be enhanced and the additional market capitalisation may be enough

to cause its inclusion within a stock exchange index. This can enhance the

liquidity of the companyâ€™s shares which should benefit shareholders.

454 Three views of deeper and broader skills

What I have shown is that the inclusion of a fudge factor or a hurdle rate of

just 1% over the CoC can cause material effects when they play out over many

years. If the company had adopted a hurdle rate of just 1% above the CoC it

would reach steady state with a market value of $525m. Without the hurdle

rate it reaches $920m.

The solution, in my view, is to have a clear perception of the difference

between what is the correct marginal CoC and what projects must earn on

average. Fudge factors usually represent what projects need to earn on aver-

age if a company is to remain healthy. This is an important number to know.

If a companyâ€™s projects on average fail to deliver a sufficient return to cover

things like search costs then its strategy was wrong and it needs to learn les-

sons. It will not, however, solve its problems by setting an artificially high

CoC for marginal decision taking.

Topic 8: Pre- or post-tax?

This topic should, in my view, not merit a mention in this book! It has to, how-

ever, thanks to some accounting standards which require asset impairment

valuations to be carried out on a pre-tax basis. It is also necessary because I

have seen pre-tax value calculations carried out.

The dogma of the economic value model is that the CoC is applied to after-

tax cash flows. In this approach tax is, quite correctly in my view, treated as

just another cost which serves to lower funds flow. This simple statement of

approach is very clear. Now nobody asks that, for example, a valuation should

be done based on only variable costs and with fixed costs incorporated in the

discount rate. So why might the treatment of tax be different?

The reason, I think, is that in some situations one can ignore tax and

work with a pre-tax discount rate. A classic example is with debt. Here the

usual approach is that tax is only applied to interest receipts and the lender

of money is not taxed on the repayment of the principal. Hence with a loan

paying 6% interest in a country with a 33.3% tax rate the valuation numbers

on a two year loan would work like this:

Time zero: lend $100

Year 1: receive interest of $6

Year 2: receive interest of $6 plus the principal of $100

If we work pre-tax and use a 6% discount rate the present value of the year 2

flow is $94.34 while the present value of the year 1 flow is $5.66. Overall the

loan is worth exactly the amount which is lent.

455 First view: The cost of capital

If we work post-tax the discount rate is reduced by an amount equal to one

minus the tax rate. The relationship is:

Pre-tax cost of debt Ã— (1 â€“ tax rate) = Post-tax cost of debt

So in this situation the discount rate is 4%. The post-tax cash flows are $4 in

year 1 and $104 in year 2. So once again, the value is exactly $100.

It is this relationship between pre- and post-tax costs of debt which has, I

am sure, led to the idea of it being acceptable to have pre- and post-tax costs of

capital. This relationship also works with businesses which will endure to per-

petuity with no growth. In this situation value is equal to funds flow divided by

CoC. Funds flow is, however, also equal to profit. Hence value is equal to profit

divided by post tax CoC. Since profit is equal to pre-tax profit times one minus

the tax rate the correct pre-tax discount rate is also given by the above formula.

Now the problem is that most valuations do not concern the valuation

of debt or of companies that will remain in steady state with no growth to

perpetuity. Real life businesses and real life tax are both too complicated to

expect this situation to be maintained. My experience is that many taxes

start with a set of very simple principles. Then, however, loopholes are found

or unfair anomalies emerge. So the tax authorities bring in more complex

laws to address these problems. Within a few years, tax is back to its usual

complexity. Against this backdrop I find it hard to believe that the effect of

tax can be so simple as to multiply by one minus the tax rate.

If one accepts that the right way to calculate value is by discounting post-

tax funds flows at the post-tax CoC, what might the necessary rate be in

order to achieve the same result when discounting pre-tax funds flows? The

answer to this question is that the rate can vary greatly. I will illustrate this

through two examples.

At one extreme, some companies have large carried-forward losses such

that they do not expect to pay tax for many years. For these companies the

pre- and post-tax CoC would need to be the same because pre-tax funds flow

is equal to post-tax funds flow.

At the other extreme, consider an asset that has already used up all of its

tax allowances and that has just one year left to go before it is wound up. It

expects to generate, say, $10m of pre-tax cash and the tax rate is, say, 30%.

The post-tax cash flow is $7m. If the CoC is 7.5% the value of the business is

$6.5m. Now if we want to arrive at a value of $6.5m but starting with the pre-

tax cash flow of $10m, the pre-tax discount rate must be 53.8%.

So in this situation we have a post-tax CoC of 7.5% which would under the

usual formula have suggested a pre-tax CoC of 10.7%. In reality, however, the

actual rate may be as low as 7.5% or as high as 53.8%!

456 Three views of deeper and broader skills

This is a rather extreme example but in my experience, the requests for pre-

tax valuations do tend to be focused on confirming that assets are worth at

least book value. This is exactly the sort of situation where there is the great-

est uncertainty about what pre-tax discount rate will give the same answer as

would come from applying the correct post-tax rate to post-tax cash flows. If

the only way to establish the correct rate is to do the valuation post-tax first,

then why bother to do it pre-tax I wonder?

My simple message is that one should only use pre-tax discounting for

debt. Project cash flows should be assessed after tax and discounted at the

after-tax CoC. Tax can be hard to assess, but no harder than other elements

of future cash flow.

Topic 9: Country risk

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