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has to be left to the analyst to ensure that the costs which are implicit in the

plan are consistent with the assumed rate of growth to perpetuity. The num-

bers assumed, however, are specifically highlighted as assumptions along-

side the steady-state capital employed and so are brought to the attention of

senior decision makers rather than left as implicit assumptions.

The problem with this method is that it does require judgement and cannot

simply be included as a standard part of the valuation methodology but the

assumptions are made explicit to decision-takers and hence overall I believe

this is the best method introduced so far.

The sustainable return on capital method is another variant on the per-

petuity valuation formula that also automatically adjusts for the consequence

of having to subtract growth times capital employed from profit in order to

arrive at funds flow. It depends on the accounting relationship that:

Funds Flow = Profit âˆ’ Growth Ã— Capital Employed

If one then substitutes this relationship for funds flow in the original TV for-

mula the logic can be worked through to an equation that I like to call â€˜the

magic formulaâ€™ because it looks so amazing!13 The formula is:

(Return on Capital âˆ’ Growth )

TV

=

(Cost of Capital âˆ’ Growth )

Book Value

Now the terminal value divided by book value is equal to a ratio that is called

the market-to-book ratio. If this is greater than 1 a company has created value

whereas if it is less than 1 a company must have destroyed value.

We can test this approach on the YMCC plan. The final-year capital

employed is $101.3 and the ROCE in that year was 13.0%. If we assume this is

maintained to perpetuity with 1% growth the market-to-book ratio would be

0.12 Ã· 0.08 = 1.5, so the TV would be $152.0m. This is very close to the figures

which I calculated using the two adjusted profit methods.

The derivation goes as follows:

13

TV = funds flow Ã· (CoC â€“ growth). (I am ignoring the small (1 + growth) part of the numerator.)

But funds flow = profit â€“ growth Ã— capital employed.

Hence funds flow Ã· capital employed = return on capital â€“ growth.

Hence TV Ã· capital employed = (return on capital â€“ growth) Ã· (CoC â€“ growth).

361 The third pillar: What sets the share price?

What I particularly like about this approach is the way that the assump-

tions are explained in ways that are easily tested against benchmarking

data. One of my earlier TV calculations had suggested that 4% growth could

equate with a TV of $310m. We can use the sustainable return on capital

formula to calculate what return on capital is implied by this TV and then

see if this is consistent with what we believe the companyâ€™s performance

might be. The TV is a market-to-book ratio of 3.06. Given that the CoC is

9% and the growth assumption which gave us the $310m TV was 4% we

know that:

3.06 Ã— (9 âˆ’ 4 ) = Return on Capital âˆ’ 4%

Hence the implied return on capital to perpetuity is 19.3%. In my opinion

senior decision-makers will find it easier to decide whether or not they

believe a figure such as this rather than a growth assumption of 4% applied

to the final-year funds flow. The danger of the method, in my view, is that it

can sometimes make the justification of a high TV too easy. Some companies

can achieve high returns on capital by sacrificing growth and so it is possible

that benchmarking data may even suggest that a company could sustain the

above return on capital of 19.3%. What would be difficult would be achieving

the return and growing at 4% pa. The formula is good, in my view, only as

long as growth rates are low.

I have called the next TV calculation method the two-stage growth to

perpetuity method. The title should be self explanatory. Rather than assum-

ing a single growth rate to perpetuity, one assumes a two-stage model with,

typically, higher growth in the period immediately following the plan period.

A new TV is introduced at the end of the first stage, typically based on a

much lower growth rate.14 The approach is best explained via an example.

I will take the YMCC plan and assume 5% growth in funds flow for five

years followed by zero growth thereafter. The final-year funds flow was

$15.5m and I will use this figure in this example. Clearly any of the adjusted

numbers could have been used as well.

The first step is to calculate what $15.5m growing at 5% to perpetuity would

have been worth. We will then subtract from this the part of this value which

is caused by higher growth beyond the fifth year of the post plan period.

$15.5m growing at 5% is worth:

$15.5 Ã— (1.05) Ã· 0.04 = $406.9m

The second part can even be one of the other methods such as book value or liquidation.

14

362 The three pillars of financial analysis

Now after five years the original $15.5m funds flow will have grown by five

lots of 5%. So it will be $19.8m. The value of this amount growing at 5%

to perpetuity is $519.3m. We want to adjust the growth down to zero. The

value of $19.8m with zero growth is $219.8m. So the extra 5% growth beyond

year 5 of the post-plan period is contributing $299.5m of value. This figure is

five years into the future so its present value is calculated by discounting it

for five years at 9%. The present value effect is $194.7m. We need to subtract

this from our original $406.9m in order to arrive at our two-stage valuation

of $212.2m.15

One useful feature of this calculation is that it is not difficult to programme

it into a spreadsheet with the two growth rates and the length of the first

post-plan growth stage all set as assumptions. There is a second way of doing

the calculation which becomes essential if the growth rate in the first post-

plan period is greater than the CoC.16 I call this second method the longhand

way. It simply involves calculating the actual funds flows in each year of the

first post-plan period and then using a TV formula at the end of this period.

The above calculation would have looked like this:

Year Plan +1 Plan +2 Plan +3 Plan +4 Plan +5

Funds flow 16.3 17.1 17.9 18.8 19.8

Discount factor 0.917 0.842 0.772 0.708 0.650

Present value 14.9 14.4 13.8 13.3 12.9

Cumulative PV 14.9 29.3 43.1 56.4 69.3

TV factor 11.1

TV 219.8

PV TV 142.9

Total value 212.2

There are a few points to note. First and foremost we get exactly the same

answer! Small rounding errors can creep in if one relies, as I did, on discount

factor tables. The discount factors are all year-end factors because all of the

flows are one year apart. In effect what has been done is prepare a second

plan covering a further five year period. This is slotted on to the end of the

We can observe, by the way, that the 5% additional growth for five years is adding exactly $40m to

15

the TV.

The perpetuity valuation formula only holds for growth rates below the cost of capital. Value is infi-

16

nite if growth rates above this are sustained to perpetuity, which is another way of saying that growth

rates that high simply cannot go on for ever. They are, however, perfectly possible for, say, five years.

363 The third pillar: What sets the share price?

actual plan and a TV is added at the end of the second period. Once again

we have to be thankful for the principle of value additivity which allows us

to break the calculation down into individual parts which together add up to

the number that we want.

This longhand way of doing the sums has the advantage of being easy to

follow and it can cope with growth rates of above the CoC. The drawback is

the difficulty of doing the sums if a decision is taken to change the length of

the first post-plan period.

The next method to explain is the specified company life approach. This

does what the name suggests! Instead of assuming a company life that spans

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