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the way that high economic gearing leads to a higher company premium and

hence a higher overall cost of debt. I will therefore carry out three assess-

ments of the typical WACC. Initially I will study a low case, a mid point and

a high case all for a company with a Î² of 1. I will investigate changes in Î² at a

subsequent stage in my analysis.

Initial cost of capital assessment

Low Mid point High

Cost of debt â€“ %

Inflation 2.0 2.5 3.5

Real risk-free 0.75 1.75 2.75

413 First view: The cost of capital

Table (cont.)

Low Mid point High

Risk-free rate 2.8 4.3 6.3

Company premium 1.0 2.0 3.0

Company CoD 3.8 6.3 9.3

Tax rate 40 40 27

After-tax CoD 2.3 3.8 6.8

Cost of equity â€“ %

Risk-free rate 2.8 4.3 6.3

Beta factor 1 1 1

Market risk premium 3 4.5 6

Cost of equity 5.8 8.8 12.3

Debt/equity 10/90 25/75 30/70

Weighted average cost of capital 5.4% 7.5% 10.7%

Now although the individual ranges for the various components of the cal-

culation are, I believe, quite reasonable, it is not justified simply to combine a

series of â€˜realisticâ€™ downside assumptions and then describe the overall result as

realistic.24 It is highly unlikely that all low-case assumptions will turn out to be

good long-run assumptions at the same time. Likewise the high-case estimate is

almost certainly too high. I will return to this point in a few pages time. There are,

however, two other features of the numbers which I believe require adjustment.

The first feature concerns the approach which this initial assessment has

taken in regard to inflation. I have assumed a range of 2â€“3Â½%. I believe that

it would be better to remove this uncertainty from the initial CoC assessment

and to base the assessment on a single assumed rate of inflation. It would

then be possible to ensure that the assumptions behind the CoC were con-

sistent with the assumptions behind the assessment of future cash flow. If

a different rate of inflation were required, this could be used but the CoC

would also need to be changed.25 So it would be more meaningful to show a

table with just a single rate of inflation and accept that if this were to change

there would be a need to change the CoC.

There remains a second adjustment to be made to the calculation of the CoC

in order to remove one remaining inconsistency. This concerns the Î² factor.

Remember, for example, that if something has a 20% chance of happening and something else also

24

has a 20% chance of happening, if the two outcomes are uncorrelated the chance of them both hap-

pening is just 4%.

When working in a large company the best approach would be for there to be a single company-wide

25

assumption about inflation with this linked into the cost of capital assessment. The inflation assump-

tion would not be changed without reviewing also the cost of capital assumption.

414 Three views of deeper and broader skills

At present I have used a Î² assumption of 1 in all three columns even though

the economic gearings are different. Now the Î² factor quoted in the table is an

equity Î². This means that if the gearings are different the implied asset Î²s are

different. It would be better to remove this effect so that we were dealing with

the CoC for a set of assets of equal risk in all three columns. My mid point has

an equity Î² of 1 but with 25% debt. Now the asset Î² is the weighted average of

the debt and equity Î²s. This means that its asset Î² must be 0.75 since the Î² for

debt should be zero. My low-case column has only 10% economic gearing so

if its asset Î² was 0.75, its equity Î² would be 0.83. A similar calculation would

suggest that the Î² for the right-hand column should be 1.07.

The updated CoC assessment would then be as follows:

Cost of capital assessment â€“ fixed inflation assumption and

constant asset Î²

Low Mid point High

Cost of debt â€“ %

Inflation 2.5 2.5 2.5

Real risk-free 0.75 1.75 2.75

Risk-free rate 3.3 4.3 5.3

Company premium 1.0 2.0 3.0

Company CoD 4.3 6.3 8.3

Tax rate 40 40 27

After-tax CoD 2.6 3.8 6.1

Cost of equity â€“ %

Risk-free rate 3.3 4.3 5.3

Beta factor for equity 0.83 1 1.07

Market risk premium 3 4.5 6

Cost of equity 5.8 8.8 11.7

Debt/equity 10/90 25/75 30/70

Weighted average cost of capital 5.4% 7.5% 10.0%

One should, I suggest, remove the apparent precision of these numbers

and call the range 5Â½%â€“7Â½%â€“10%.

We are now ready to return to the problem that this assessment has com-

bined several low-case assumptions together to arrive at the low estimate. It is

my view that it is very unlikely that all of the low or all of the high assumptions

will come about together. I therefore suggest that the range needs to be cropped

somewhat. This is necessary particularly at the upper end of the range.

415 First view: The cost of capital

Overall, therefore, my assessment of the CoC for a typical set of assets is a

range of 6â€“9% with the mid-point being 7Â½%. Readers who started as begin-

ners and so read the financial foundation section might recall my earlier very

rough estimate of a typical CoC of 9% from page 58. There are several small

differences between the way that I derived that number and this revised esti-

mate but it is within my latest range. This one and a half percentage point

range for the CoC for a typical company is, in my view, more realistic than

the Â±0.5% range which other experts claim. Perhaps the one and a half per-

centage points which I suggest is too great but I cannot see how the reason-

able range can be less than Â±1%.

Having completed this analysis for a typical company one can then con-

sider the range that is possible between high- and low-risk companies. My

mid-point assumptions applied to a low-risk company with an equity Î² of 0.5

would produce a WACC of about 6%. If the Î² rose to 1.75, which would be

high for a major company, the WACC would be about 10%.

The cost of capital for a project

So far we have been considering how to assess a companyâ€™s WACC. This is

what one should use in order to value the activities of an entire company.

The CoC is, however, often used while evaluating individual projects within

a company. These projects will have their own unique risk characteristics. So

what CoC should we use in these situations?

The theory tells us to assume that shareholders look through the company

to its projects. We ought, therefore, to be computing project costs of cap-

ital based on the diversified shareholdersâ€™ views on the risk that accompan-

ies the project. This requirement to take the diversified shareholdersâ€™ view

gives a strong message about one thing that we should not be doing. This

is basing our project CoC on the total risk that is inherent in any project. I

deliberately referred to projects as having unique risk characteristics. Our

portfolio diversification approach tells us that risks which can be diversified

should not result in shareholders requiring additional returns. This means

that unique risks will not impact on the CoC. What impacts on the CoC is a

projectâ€™s exposure to risks which are held in common with many other com-

panies on the market.

It may well be difficult in practice, but in principle what our theories tell

us is that the approach should be that one builds up a project CoC based on

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