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.” Basic Principle #6

/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.

/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.

/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.

onacci.htm In this series of numbers each term is the sum of the previous two terms as follows: etc. The division of any two adjacent numbers gives the amazing Golden number e.g. 34 / 55 = or inversely 55 /34 =

R.Knott/Fibonacci/fibnat2.html If there are Phi (1·618...) leaves per turn (or, equivalently, phi=0· 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.

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

Equity & Total Invested Capital (expressed as a percentages)

Ratio of Price to Sales 1.618