IF PRICE CHANGES BY X % AND QUANTITY CHNAGES BY Y $ – WHAT WOULD BE THE % CHANGE IN THE REVENUE GIVEN THAT R = P * Q – HOW TO GET THIS BY CALCULUS

R = P * Q

% CHANGE IN R = R ( n) – R ( n-1) / R = d (R) /r

dR = P dQ + Q dP

dR/ R = P ( dQ )/ P*Q) + Q DP/(P*Q)

=> d(R) / R = Change in Revenue / Original revenue = percentage change in R –

= d(Q)/ Q + d (P) /P

= % CHANGE IN Q + % CHANGE IN P

Here P stands for Price,

Q for quantity

and

R for Revenue – ie sales

so,

IF PRICE CHANGE BY 3 % AND QUANTITY CHANGES BY 5 % – THEN THE PERCENTAGE CHANGE IN R – THE REVENUE

= % CHANGE IN ( P + THAT IN Q)

= 3 % + 5 %

= 8 %

NOTE – HERE D or d is the standard operator symbol for the DIFFERENTIAL – as in DIFFERENTIAL CALCULUS

YES U CAN DO THE SAME CALCULUS IS THERE IS A RATIO

AS IN IF SOME NUMBER N = A DIVIDED BY B THEN IF A CHANGES BY X % AND B BY Y % THEN N WILL CHANGE BY X MINUS Y PERCENT

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3 MODELS – TO ACHIEVE THE SAME $1 M OR $10 M TARGET : [A] LINEAR – IE AP -GROWTH MODEL [B] EXPONENTIAL IE GP GROWTH MODEL AND [C] A HYBRID – GROWTH MODEL FOR MRR SPECIALLY

AND YES, WE CAN HIT THE SAME – TARGET – SAY $ 1 MILLION REVENUE OR $100 MILLION REVENUE – BY THESE 3 MODELS : BECAUSE CUMULATIVE YEARLY REVENUE = SUM OF ALL THE 12 MONTH REVENUE –

HOW?

FIRST SEE THE DIFFERENT GROWTH MODELS

[a]

Linear Growth model -means ARITHMETIC progression : as in

{\displaystyle \ a_{n}=a_{1}+(n-1)d},

where

– a 1 = the first term – i.e. – the revenue /sales at the beginning of a month

– a n = the revenue in the nth month

– d = the common difference

S (n) = Sum of all the monthly revenue numbers

S_n=\frac{n}{2}( a_1 + a_n).

In this model a CONSTANT number gets added to the number prior to it – ie. this month revenue = previous month revenue PLUS – a Number called – D

 

 

{\displaystyle \ a_{n}=a_{1}+(n-1)d},

 

 

 

so in this case if we want to arrive at the growth rate formula

then G = growth Rate = a(n) / (a(n-1) – 1

where a ( n-1 ) = a 1 + (n-2) d

substitute and get G = { a (1) + (n-1) /d } / { a 1 + ( n-2) d)

which means and implies that G (n) will not be a constant – and would vary each month

ie – there would be a mean value but since each term { each number} would be different – there would be a variation – and here is the

standard deviation –

 

The standard deviation of any arithmetic progression can be calculated as

\sigma = |d|\sqrt{\frac{(n-1)(n+1)}{12}}

where n is the number of terms in the progression and d is the common difference between terms.

so, there would be a MEAN around the Revenue number and the distribution would have a standard deviation – shown above

[b]

EXPONENTIAL GROWTH MODEL – AKA – THE GEOMETRIC PROGRESSION –

This EXPONENTIAL Model is hard to sustain –

– this model assumes – a constant growth rate –

OBVIOUSLY THIS IS ONE WHICH EVERYONE LIKES

a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots

where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence’s start value.

BECAUSE IT BLOWS UP TO INFINITY – QUICKLY – BUT THIS IS ALSO A HARD ONE TO SUSTAIN WHEN N – APPROACHED LARGE NUMBERS

The n-th term of a geometric sequence with initial value a and common ratio r is given by

a_{n}=a\,r^{n-1}.

Such a geometric sequence also follows the recursive relation

a_{n}=r\,a_{n-1}

for every integer n\geq 1.

OBVIOUSLY BY DEFINITION

– THE GROWTH RATE IMPLIED IN THIS MODEL IS – CONSTANT –

THIS MONTH SALES NUMBER DIVIDED BY LAST MONTH’S SALES NUMBER

=

A(n) DIVIDED BY A(n-1)

WHICH IS EQUAL TO THE SAME

– IE – THE COMMON RATIO R

SO, MONTHLY GROWTH RATE IN THIS MODEL – REMAINS THE SAME.

[C]

THERE IS A 3RD MODEL

 A HYBRID -MODEL

BETWEEN THE AP AND THE GP – MODELS-

I.E BETWEEN THE LINEAR AND THE EXPONENTIAL MODEL :

WHICH IS MORE REALISTIC

AND WHAT WE SHOULD

OR WOULD BE FORCED TO PLAN FOR

– AS N – THE NUMBER OF MONTHS – IN OPERATION – INCREASES LINEARLY WITH T –

THE TIME – FARTHER AWAY

FROM SEPTEMBER 2017 INCREASES

 

in this model – you take the average of the NET – NEW – MRR – numbers –

{ MRR STANDS FOR MONTHLY RECURRING REVENUE }

BY ADDING THE TWO NEW NEW MRR NUMBERS

FROM THE LINEAR AND THE EXPONENTIAL MODELS ABOVE – MENTIONED IN [A] AND [B] – SECTIONS –

AND THEN DIVIDE THAT BY 2 –

AND THEN ADD TO THE PREVIOUS TERM

TO GET THE NTH TERM

BASICALLY

– IN THE LINEAR MODEL U HAD – A COMMON DIFFERENCE – IE D – ADDED TO EACH TERM

– AND IN THE EXPONENTIAL MODEL U HAD THE COMMON RATIO – R MULTIPLIED TO EACH SUBSEQUENT TERM

– IN THE HYBRID MODEL – YOU TAKE THE AVERAGE OF THE TWO END POINTS –

AND ADD TO EACH SUBSEQUENT TERM

 

 

 

YOU CAN DO THE MATHS – IN EQUATION FORMAT

OR – YOU CAN DO ACTUAL NUMBERS AND MACROS AND FORMULAS IN EXCEL

OR GOOGLE SHEETS

 

HERE IS THE LINK FOR GOOGLE SHEETS ->

https://docs.google.com/spreadsheets/d/1k9BW460b8cTRSTFpl61k47Cg28xo4pOBCAx0V5n3FrM/edit?usp=sharing

yes, you can download in CSV format as well..

If you like to see numbers visually

see this graph

– GRAPH OF GROWTH MODELS –

 

IN SAAS growth MATTERS – AND IT MATTERS – A LOT

OR I GUESS SOME WOULD SAY – IT MATTERS THE MOST

The Increasing Growth Rates Of SaaS Companies

SaaS startups are growing faster than ever before. Publicly-traded SaaS companies founded from 2008 through 2014 needed 50% less time to reach $50M than their counterparts founded between 1998 and 2005. I stumbled across this trend when looking at a different chart used in my S-1 analyses that compares the time to $50M for each of the 51 or so publicly traded SaaS companies.

 

WIX IS SHOWN BELOW -in red

MY EYES AREN’T PERFECT -BUT I EYE BALLED IT – AND IT LOOKS LIKE- IT TOOK WIX – 7 YEARS – APPROX – SEVEN YEARS – TO HIT THE $50 M REVENUE COMPANY – WE R US –

 

colored the companies founded in the last ten years in red.

Newer SaaS companies grow faster.

82% of the companies to achieve $50M in revenue in under 8 years have been founded in the last decade.

Meanwhile, all of the companies requiring longer than 8 years were founded before 2004.