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Phi Finance
Finance based on growth relationships
Where Organic Chemistry is the chemistry of carbon compounds
By
Gaylen Bunker & Collin Bunker
“The valuation of a privately
owned company is both
science and art.”
http://www.vrbusinessbrokers.com/pages/mergers/valuation_services.jsp
Basic Principle #6
http://www.mathacademy.com/pr/prime
/articles/fibonac/index.asp
The growth of a nautilus shell, like the growth of
populations and many other kinds of natural
“growing,” are somehow governed by
mathematical properties exhibited in the
Fibonacci sequence. And not just the rate of
growth, but the pattern of growth. Examine the
crisscrossing spiral seed pattern in the head of a
sunflower, for instance, and you will discover
that the number of spirals in each direction are
invariably two consecutive Fibonacci numbers.
http://www.mathacademy.com/pr/prime
/articles/fibonac/index.asp
• This number was known to the ancient
Greeks and was called by them the
Golden Mean. It is usually denoted by the
Greek letter f (phi), and sometimes by m
(mu). They believed that the proportion f:1
was the most most pleasing, indeed the
aesthetically perfect proportion, and all of
their artwork, sculpture, and especially
architecture made use of this proportion.
http://www.mathacademy.com/pr/prime
/articles/fibonac/index.asp
• Thus 1 and 1 are 2, 1 and 2 are 3, 2 and 3
are 5, and so on. This simple, seemingly
unremarkable recursive sequence has
fascinated mathematicians for centuries.
Its properties illuminate an array of
surprising topics, from the aesthetic
doctrines of the ancient Greeks to the
growth patterns of plants.
http://www.goldenmeangauge.co.uk/fib
onacci.htm
In this series of numbers each term is the
sum of the previous two terms as follows:
0 1 1 2 3 5 8 13 21 34 55 89 etc.
The division of any two adjacent numbers
gives the amazing Golden number e.g.
34 / 55 = 0.618
or inversely 55 /34 = 1.618.
http://www.mcs.surrey.ac.uk/Personal/
R.Knott/Fibonacci/fibnat2.html
• If there are Phi (1·618...) leaves per turn (or,
equivalently, phi=0·618... turns per leaf ), then
we have the best packing so that each leaf gets
the maximum exposure to light, casting the least
shadow on the others. This also gives the best
possible area exposed to falling rain so the rain
is directed back along the leaf and down the
stem to the roots. For flowers or petals, it gives
the best possible exposure to insects to attract
them for pollination. The whole of the plant
seems to produce its leaves, flowerhead petals
and then seeds based upon the golden number.
http://kjmaclean.com/Geometry/Fibona
cci.html
• The success of life itself must be based
upon harmonious growth. Ø represents the
perfect division, so life itself must be related to
Ø. Otherwise we would not see this ratio so
prevalent in the design of life forms. Biological
life is based on Ø. The pentagonally shaped
deoxyribose sugar is the central component of
the nucleotide, the basic building block of DNA.
The Fibonacci sequence quickly approximates
to Ø. And so life can grow and be healthy. The
more growth, the closer to perfection life comes
to Ø.
Golden Mean for BCR
Total Benefits (annunity) = 1.618 x Cost
45.0%
2
internal rate of return
40.0%
35.0%
-0.9088
y = 0.7797x
30.0%
4
25.0%
20.0%
6
8
15.0%
10
10.0%
12 14
16 18 20
22 24 26 28
5.0%
0.0%
0
5
10
15
Project Life
20
25
30
Equity & Total Invested Capital
(expressed as a percentages)
Equity Percentage
Percentage of Equity
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1997
1.618
0.618
1998
1999
2000
2001
Year
2002
2003
2004
2005
Ratio of Price to Sales
Historic Price to Sales Ratios
Price to Sales
4
3.5
3
2.5
2
1.5
1.618
1
0.5
0
1997
1998
1999
2000
2001
Year
2002
2003
2004