Formula to Calculate Subscriber Churn Revenue - excel

I'm trying to sum up 12 months of subscriber revenue factoring a 6% monthly churn (assuming no signups) to come up with the one-year value of a subscriber. A simple future value gives me the start and end values, but I'm looking to get the sum of the monthly declining revenues in a single Excel / Google Sheets formula. I can make 11 entries (plus the starting month full value), but is there a better one-liner or formula for this?
This gives me the 12th-month revenue:
=FV(-6%,11,0,100)
I'd like to get the sum without this:
=100 + FV(-6%,1,0,100) + FV(-6%,2,0,100) ... FV(-6%,11,0,100)

You are looking for the sum of a finite geometric series:
1 + r + r^2 + r^3 .... + r^11
And the sum of this series is
(1 - r^12) / (1 - r)
where r = 1 - 6%
So the formula would be
= (1 - (1-6%)^12 ) / (1 - (1-6%) ) * 100
This is assuming the OP meant
=100 + FV(-6%,1,0,-100) + FV(-6%,2,0,-100) ... FV(-6%,11,0,-100)
as FV(-6%,1,0,100) would output a negative number

I don't know much about such math but would the following formula give you the result?
=100+SUMPRODUCT(FV(-6%,ROW(1:11),0,-100))
The formula works in both Excel and Google Spreadsheets

Related

Simple(r) Excel formula to calculate forward stock (inventory) cover

This is a perennial question for retailers, for which there are a number of solutions in existence:
How can you calculate the "forward cover" of a product knowing its current inventory and armed with forward sales estimates.
eg.
current inventory 100 units (cell A1)
weekly forward sales estimates: 25, 30, 10, 40, 90... (in range
A2:AX)
Here the answer would be 3.875 weeks (3 full weeks plus 0.875 of week 4)
I have a UDF to do this already.
I also have some slightly complicated array functions to do this, eg.
=MATCH(TRUE,SUBTOTAL(9,OFFSET(A2:A13,,,ROW(A2:A13)-ROW(A2)+1))>A1,0)-1+(A1-SUM(A2:INDEX(A2:A13,MATCH(TRUE,SUBTOTAL(9,OFFSET(A2:A13,,,ROW(A2:A13)-ROW(A2)+1))>A1,0)-1)))/INDEX(A2:A13,MATCH(TRUE,SUBTOTAL(9,OFFSET(A2:A13,,,ROW(A2:A13)-ROW(A2)+1))>A1,0)-1+1)
I was wondering if there is a neater way with these 'new-fangled' array functions which have been available for the last few years in later versions of Excel?
Here is another possible solution, although it requires the LET() function which is only available to newer version of excel (2021, 365 and later I believe).
The solution would be the following formula:
=LET(
sales,A2:A50,
inventory,A1,
cum_sum,MMULT(SEQUENCE(1,ROWS(sales),1,0),(ROW(sales)<=TRANSPOSE(ROW(sales)))*sales),
week_full,MATCH(TRUE,inventory<cum_sum,0) - 1,
week_frac,(inventory - INDEX(cum_sum,week_full)) / INDEX(sales,week_full + 1),
week_full + week_frac
)
Explanation
Given inventory and the forward looking sales estimates, the formula calculates the running total (i.e. cumulated sum) of the sales estimates as shown in the table here below
Inv and Sales
Cumulated Sum
Inv > Cum_Sum
Week
100
25
25
0
1
30
55
0
2
10
65
0
3
40
105
1
4
90
195
1
5
...
...
1
6
The formula goes on to get the number of full weeks of 'forward cover' by finding the the value for the cumulated sum that exceeds the inventory minus one (here 4 - 1 = 3).
Lastly, for the value of the week fraction covered in the last week, the formula calculates inventory minus sum of sales estimates of all previous weeks divided by sales estimate of final week of cover (i.e. (100 - 65) / 40 = 0.875).
Edit
After simplifying the formula you used with the LET() function, I noticed it's doing exactly the same calculation with the only difference of how the cumulated sum is being calculated. Here's your formula using LET():
=LET(
sales,A2:A50,
inventory,A1,
cum_sum,SUBTOTAL(9,OFFSET(sales,,,SEQUENCE(ROWS(sales)))),
week_full,MATCH(TRUE,cum_sum>inventory,0)-1,
week_frac,(inventory - INDEX(cum_sum,week_full)) / INDEX(sales,week_full+1),
week_full + week_frac
)
=LET(inv,A1,
sales,A2:A6,
cs,SCAN(0,sales,LAMBDA(x,y,x+y)),
m,XMATCH(A1,cs,1)-1,
m+(inv-
IF(m=0,
0,
INDEX(cs,m)))
/INDEX(sales,m+1))
SCAN() is perfect for creating a cumulative sum.
It can be referenced inside XMATCH because of the use of LET.
Here m returns the number of full weeks and the final calculation is the number of full weeks + (inv- cumulative sum up to the full week)/sales of the following week.

Trying to show a full years amount based on a smaller fraction of the year's total

this is my first post.
Right now, I have a limited set of data ranging from the beginning of this financial year until now. I'm trying to show what a full year's worth of that data would look like.
For example, if the number is at 10, and the data range is from 1/07/2021 - 30/12/2021 (half the year), then the end output should be 20. Or for example, turn a 12 with 3/4 of the year date range to 16 for a full years' worth.
However, my current formula would end up with 15 (10 + "half") rather than (10 + 10)
Right now this is what I have, but I know there's something off on my logic, as the output is smaller than it should be:
D1+((364-(F1-E1))/365)*D1
where E1 is the start date and F1 is the end date, and d1 is the number for that date range
Thanks in advance
endDate - startDate will give you the number of days the data covers.
(endDate - startDate) / 365 will give you what fraction of a year the sample represents.
Let’s say this works out to be 30%, or 0.30.
annualValue * 0.30 = periodValue and therefore we know that periodValue / 0.30 = annualValue.
So there it is, the cell you want the Annual Value in should be:
= periodValue / ( ( endDate - startDate) / 365 )
I will leave it to you to replace each of the three named values in my example to be the correct cell references. I suspect that’s probably:
=D1/((F1-E1)/365) which is the same as (D1*365)/(F1-E1).
The easy way to remember this is that it’s just cross-multiplication.
periodValue / days is proportionate to annualValue / 365. Thus periodValue / days = annualValue / 365. Cross-multiply and you get periodValue * 365 = annualValue * days. Divide both sides by days and you get `annualValue = (periodValue * 365)/days.

Get Sum of Products in same column

I have the below data set:
Let's assume it starts in A1. I would like to calculate the Total Costfor January by taking each Count and multiplying by the Rate below it.
I currently have the following, nonsensical formula:
Total Cost = (B1 * B2) + (B3 * B4) + (B5 * B6) + ... + (Bn + Bn+1) for n > 0
Is there a whizzy way to do this using an Excel formula? Perhaps something with SUMPRODUCT()? But I can't seem to get that to work the way I need it...
Simplified example:
=SUMPRODUCT(--(A1:A5="Count"),B1:B5*B2:B6)

Formula for weighted averages

This is a bit of a hybrid between a mathematical and an Excel issue. I currently have an Excel sheet with a list of yearly observations. To simplify, lets say that for five years I'm looking at:
2015=5
2014=3
2013=4
2012=1
2011=6
What I would like to do is write a formula that counts the number of values in question (5 in this case), divides 100% of the weight and and makes each preceding value be worth 10% less than the last.
So in this case
2015 would be worth (roughly rounded) 24%
2014=22%
2013=20%
2012=18%
2011=16%
if you add the weight for each they add up to 100%.
As an example the numbers to be presented for weighting are:
1.225 for 2015 (5*.24)
.6615 for 2014 (3*.22)
.7938 for 2013 (4*.20)
.1786 for 2012 (1*.18)
.9645 for 2011 (6*.16)
I have calculated all of these numbers manually but would need a formula that can adapt to the number of periods being used as I will be adding more over time.
Sum of n terms (Sn) of an geometric series starting with a and having ratio r is:
Sn = a(1 − r^n)
___________
1 − r
All you need to do is rearrange and solve for a given Sn=100, r=0.9 and n=number of terms....
a(1 − r^n) = Sn(1-r)
a = Sn(1-r)
_______
(1-r^n)
For 5 terms:
a = 100 * (1 - 0.9) / (1 - 0.9^5) = 24.419
for 10 terms:
a = 100 * (1 - 0.9) / (1 - 0.9^10) = 15.353

Formula to calculate salary after x year?

Knowing that i am getting paid $10 000 a year, and that each year my salary increase by 5%.
What is the formula for Excel to know how much i will get in 5 year?
Thank you for any advise
The formula in Excel is:
=VF(5%;5;0;-10000)
Which results in: $12,762.82
If your Office is english version you can use:
=FV(5%;5;0;-10000)
=(10000*((1 + 0.05)^5))
The Compound Interest Equation
P = C (1 + r/n)^nt
Where...
P = Future Value
C = Initial Deposit/Salary
r = Interest Rate/Pay Increase (Expressed as a Fraction: EX = 0.05)
n = Number of Times per Year the Interest/Pay Raise Is Compounded (0 in Your Example)
t = Number of Years to Calculate
The Formula is POWER(B1,C1)*10000, and the cell B1 is (1+5% ), the cell C1 is the number of years
current = 10 000
for each year -1
current = current * 1.05
end for
current now has current salary for the given number of years

Resources