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Capital investment âˆ’9.5 âˆ’11.9 âˆ’1.8 âˆ’2.0 âˆ’2.3

Funds flow âˆ’2.4 âˆ’2.7 6.0 7.1 7.1

Remember that the perpetuity formula is value = (funds flow x (1 + growth)) Ã· (CoC â€“ growth).

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136 The five financial building blocks

We can now calculate the economic value of this business. This value will

be equal to the present value of the plan period cash flows plus the present

value of the terminal value. We will calculate the terminal value based on

an assumption that the final-year funds flow will remain constant into the

indefinite future and using a CoC of 9%. The calculation will be as follows:

Valuation of Fence Treatment Inc

2008 2009 2010 2011 2012 Terminal value

Funds flow â€“ $m âˆ’2.4 âˆ’2.7 6.0 7.1 7.1 79.1

Discount factor 0.958 0.879 0.806 0.740 0.679 0.679

PV Funds flow â€“ $m âˆ’2.3 âˆ’2.4 4.8 5.2 4.8 53.7

Cumulative PV â€“ $m âˆ’2.3 âˆ’4.7 0.2 5.4 10.2 63.9

Note first that I have used mid-year discount factors in recognition of the fact

that cash flows occur on average at the middle of each year while I am aim-

ing to calculate value as at the start of 2008. The biggest contributor to value

is the terminal value (TV). This is the final-year funds flow divided by 0.09.

Remember, though, that this is the value as at the end of the plan period and

so this number must then be discounted to the present.

All valuations are only ever as good as the assumptions on which they

are based. One should always test assumptions in order to understand how

important they are. Had I, for example, assumed a 2% pa decline for my TV

calculation the overall value would have fallen to $53.3m.

One words and music test that I always apply is to compare economic

value with accounting value (i.e. capital employed). A business should always

be worth at least its book value.28 As long as the ROCE is close to the CoC this

should be the case. If the return is well above the CoC then the business will

be worth well above book value. We will see in a later part of this book how

we can calculate exactly what relationship to expect between book value and

economic value. For the present, however, we can simply observe that words

and music appear to be in order as the value is above book value but not by

a huge amount. Our 2% decline case would reduce value to a figure that was

still above book value.

Accountants require this or they insist that a so-called asset impairment adjustment be made that

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reduces capital employed to economic value.

137 Building block 4: Planning and control

Present value and value through time

This plan valuation exercise provides a good opportunity to explain one more

important value concept. This concerns the difference between present value

and the value profile of a business or a project over time. Present value is the

value of a business today. The value profile is the value a business will have

at different points in the future. These are two different but related concepts.

The way that they are related is through the combination of annual cash flow

and the CoC.

So far we have explained the value calculation as being the sum of future

cash flows each times the relevant discount rate. This is the same as saying

that the value at the start of a year is equal to the value at the end of the year

discounted by one year plus the cash flow during the year also discounted to

the start of the year.29 This is best illustrated by some numbers.

In the Fence Treatment Inc case study the value of the business as at 1

January 2008 is $63.9m. What is the value as at 1 January 2009? Well, first

we no longer have to allow for the negative funds flow during 2008 because

value is a forward-looking calculation and 2008 is then in the past. Second,

the remaining future funds are all one year nearer. So the value at the start

of 2009 is all of the remaining future cash flows discounted to this new

point.

Actually it is easier to work out value profiles backwards starting with the

terminal value. The terminal value is, by definition, the value of cash flows

beyond the plan period. The value one year earlier than this will equal the

funds flow during that year discounted to the start of the year plus the termi-

nal value discounted for a year.

If we look at the exact numbers, the terminal value of $79.1m which we

calculated was as at mid 2012. So in order to convert this to end 2012 we need

to divide it by the half-year discount factor of 0.958. So the end plan value is

$82.6m. With this as the starting point it is now easy to work out the value

profile over time for Fence Treatment Inc. The calculation is shown below.

This table also shows the calculation of what I term the value return. This is

the sum of value growth plus annual funds flow divided by opening value.30

One has to be very careful to allow for the correct timing of cash flows. If we have been assuming

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mid-year cash flows then the year-end value has to be discounted by one year to get its contribution

to opening year value while the annual cash flow is only discounted for half a year.

Once again, one has to be careful about the exact timing of cash flows. The calculation of value

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return assumes year-end cash flow and the full year value growth. In our case the cash flows are mid-

year and so need to be increased in value by half a yearâ€™s worth of discount factor to get their exact

value effect.

138 The five financial building blocks

Fence Treatment Inc, value profile

Year-end 2007 2008 2009 2010 2011 2012

Value profile 63.9 72.1 81.5 82.5 82.6 82.6

Value growth 8.2 9.3 1.1 0.1 0.0

Funds flow âˆ’2.4 âˆ’2.7 6.0 7.1 7.1

Value return 9.00% 9.00% 9.00% 9.00% 9.00%

What we can now see is that although value grows from $63.9m to $82.6m

over the five year period, the value return is always 9% which is exactly equal

to the CoC.31 So we finish this section about how the numbers work with

what I consider to be a hugely important insight:

In a plan, value growth does not really matter.32 What matters is present value

Value growth in a plan is simply a function of the extent to which the plan

is generating or requiring funds. Value growth is zero when funds flow is

exactly equal to the CoC times value. Value growth is â€“100% when a com-

pany sells its assets and returns all the cash to its owners.

So it is possible to have a plan that shows good value growth but that is

a bad one because the plan is destroying value. A business that is investing

in negative NPV projects will do this. It should stop the projects. The result

will be that its present value will rise by an amount equal to the avoided

NPV loss.33

Value growth matters only after the passage of time. As time passes, new

information becomes available. This information may concern actual cash

flows or the prospects for what remains of the future. If either or both of

these change, then the calculation of value return will become meaningful. If

the return is above the CoC then the investment has been good; if the return

I have shown the value return calculation to two significant decimal places in order to make this

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point.

One cannot say that it does not matter at all because a fast rate of value growth will imply a need for

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future cash injections which particular investors may not wish to see while a big value decline may

imply a greater generation of cash than the investor would have preferred. I experienced this recently

when a property fund that I had invested in sold its buildings at a big profit, passed all its money back

to its investors and ceased to exist. I was pleased with the high return that I earned but in all honesty

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