# 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 ### ᐧ # Google Alert – international cricket stadium lucknow international cricket stadium lucknow Daily update ⋅ January 29, 2018 NEWS With on going inspections, Lucknow’s cricket stadium a hot favourite to host IPL 2018 matches! Knocksense Lucknow, which has never hosted an international cricket match in last 2 decades will definitely witness a high footfall. Also, the facilities provided in Ekana stadium is far superior than many stadiums in India. In comparison to Delhi’s Feroz Shah Kotla Ground, Lucknow’s stadium has 9000 more chairs, … See more results | Edit this alert  You have received this email because you have subscribed to Google Alerts. Unsubscribe | View all your alerts Receive this alert as RSS feed Send Feedback # 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 ### , 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 ### ### 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 ### , ### 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 ### ### where is the number of terms in the progression and 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 ###  ### 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 ### ### Such a geometric sequence also follows the recursive relation ### ### for every integer ### 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 – ### ᐧ ### 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 – 