How to create exponential growth in excel over a year - excel

So I am trying to build an excel model where every month the numbers will increase exponentially to a point at the end of the year which is driven by annual expectations. Currently I have it divided by 12 and each year there are huge jumps over the previous making the chart/growth very jumpy. For illustration purposes, lets say for 2020 the desired number for the year is 12. In the current state, I would get 1 per month (12/12), however, what I want is for it to be growing gradually/exponentially, so for example 0.2, 0.5, 0.9 etc with December being the largest, and the sum for the entire year equaling 12. Then the next year (2021), starting in January, it would take into account the December 2020 number and grow from there again to the desired number (lets say total 24 for 2021) and so on. I'd love for it to have a more exponential / hockey stick-like growth.
What would be a good way to do this?

The function RRI can be used to find an interest rate which will give you a given target value. This can be used to find terms in a geometric series which have a given sum (which is what you seem to be asking for).
For example, say you want 12 exponentially increasing numbers which, when added to 100, gets you to 2000. Starting with 100, repeatedly multiply by (1 + RRI(12,100,2000)). To get the numbers that you want (which will be 12 numbers which sum to 1900) just calculate the difference each month:

I think the simplest way to solve this is by using Goal Seek. First you need to build a sheet like this:
You choose the starting value in January (B1) and every month is a constant growth rate (D1) bigger than the previous month. You also calculate the total sum at the bottom in B13.
Now you use goal seek to find the growth rate which makes the sum equal to 12:
The answer I get for a starting value of 0.1 is a growth rate of 1.376:

Related

How can I predict the Monthly Recurring Revenue (MRR) for a product when I have transactions for only 4 days?

I assume I want to extrapolate to find the sum of the MRR at month's end (for January), however, I only have transactions (each has it's own MRR value of course) for January 3rd,4th,5th, and 6th.
I tried to use =forecast but I keep getting a large negative number which does not seem right at all. If A2:A5 contain the values of 8234.72, 2374.9, 2231.054, and 5386.3505 and then B2 is 1/3 or perhaps just 3 is better and it goes all the way down to 31 for the amount of days in January, I am unsure of how to predict the total MMR at the end of the month, I keep getting errors.

Formula to Adjust for Rounding Issues

I am trying to create a formula in Excel that solves for the base number of units needed on a monthly interval with an annual growth escalator that matches in whole units the total I'm starting with. I can't from a practical standpoint have fractions.
This is an example of the formula x is number of monthly units, y is the total number of units and the desired annual growth rate is 20%. Here is the algebra butin practice only one variable will need to be solved for (x): y= 12x + (1.2x)*12+(1.2^2)*x*12+(1.2^3)*x*12. I get close using the round function but always end up a few short of the total desired due. Is there a way to add on the difference at the end formulaically?
ROUND(20000/(12+(12*(1+20%))+12*(1+20%)^2+12*(1+20%)^3),0)
I'm extremely close but I need to make sure the total by month matches the total desired.

How to calculate a... median? of hour/day/month of occurence?

My problem concerns day of month however, I can see that the same logic would apply to month number or hour number or any other variable that ends on some value and then starts from 0 again.
It is defined as follows: I'm trying to calculate a day of month when a payment is made to use it for a forecast. So I have for example for one case:
1 May 2016
2 June 2016
30 June 2016
29 July 2016
6 September 2016
A simple average would give me 14th, and the median would give me 6th. But the result I'm looking for is more like the 1st.
I see I could do it somehow by calculating geometric median, or euclidean distances after placing the points on a circle etc, but I believe it can be approached in a much simpler way. I also see that solving this problem with standard means and averages would cause a situation where it gives more than one result.
But if we add an assumption that it should occur once in 30 days/a month? Wouldn't this assumption make the problem easier?
Please let me know if you solved a similar problem before or if you have any ideas
If the result you are "looking for is more like the 1st", then I would hazard a guess that you are really looking at a series of monthly payments (perhaps falling due on the first of each month or the first working day of each month) and you want some measure of the deviation between the due date and the actual date of payment.
If that is the case then simply calculate the difference in days between the due date and the actual date of payment for each monthly payment (following a consistent convention such as positive values denote late payment and negative values are early) and then apply your chosen measure (median, mean, etc) to the series of differences.

FV and PV formula's in Excel

I'm trying to calculate a lifetime value of a customer. Let's assume a new customer pays $100K per year and stays for 5 years. Let's discount any future years' payments with 10% rate.
This is manual calculation:
Year 1 $100,000.00
Year 2 $90,000.00
Year 3 $81,000.00
Year 4 $72,900.00
Year 5 $65,610.00
---------------------
Total $409,510.00
I can get the same value by using FV with negative rate.
FV(-0.1,5,-100000,0,0) = $409,510.00
What I'm trying to do is to get the same value using PV. And it's not exactly the same:
PV(0.1,5,-100000,0,1) = $416,986.54
I'm not sure what am I missing here. Does MS Office Excel 2010 PV understand discounting differently?
If you calculate out what PV is doing manually, the formula is actually this, for each individual year:
=Base Amount / (1 + Discount Rate) ^ Periods
Vs what FV is doing manually, the formula is this (which you seem to know based on coming to the same answer in your data):
=Base Amount * (1 - Discount Rate) ^ Periods
The reason for the difference in calculation is the mathematical difference between the two items - for background see here: http://www.investopedia.com/walkthrough/corporate-finance/3/time-value-money/future-value.aspx and here: http://www.investopedia.com/walkthrough/corporate-finance/3/time-value-money/present-value-discounting.aspx.
In short, if you have $100k today, and invest it in something which gives you 10% each year, then each year you add 10% of the current balance to get the new balance. ie: in year 1 you add 100k * 10% = 10k, giving a new total of 110k; in year 2 you add 110k * 10% = 11k, giving a new total of 121k, etc. - Mathematically, each year's amount is given by the formula listed above for the FV calculation.
Where this gets tricky is that you are giving yourself a negative interest rate - meaning every year, the value is decreasing each year by 10%. You have attempted to use the FV calculation with a negative interest rate, but that's not quite correct. What you should be using is the PV formula.
For the PV formula, if you know that you will receive 100k each year, you need to determine how much cash you would have needed originally, in order to earn the same amount - that is the present value of the cash flow stream. Now, you need to 'gross-up' the value of each year's income stream. The formula for this gross-up is derived mathematically and results in what I have above there for PV. Think about it like this - if there's a shirt that normally costs $100 and is now 30% off, you can see that you simply multiply it by 30%, to get $70. But if you see of shirt on sale for $70, and it's 30% off, then to determine the original base price you need to take $70 & divide by .3 - which gives us $100.
To prove to yourself that the PV formula is appropriate, take the income stream of, say, year 4 [3 periods of interest later, assuming first payment is received in day 0]: 100k / (1 + 10%)^3 = $75,131. Now, work backwards - if you want to know the future value of a $75k investment held for 3 periods of interest compounded annually with a 10% annual rate, you go: 75,131 * (1 + 10%) ^ 3 = 100k.
This is an important financial distinction, and you should read over the sources I've linked to ensure you understand it.
There is a difference in the calculation. FV takes 100,000 and discounts it by 10% to the number X so that X is 90% of the original value (i.e. X=90,000). PV by contrast discounts it to the number X such that 100,000 is 10% more than X. Quick math says X will be 10/11 of 100,000, i.e. 90909.09.
Indeed, if we apply this calculation 5 times:
Year 1 $100,000.00
Year 2 $90,909.09
Year 3 $82,644.63
Year 4 $75,131.48
Year 5 $68,301.35
---------------------
Total $416,986.5
I don't know if there is a way to make them behave the same way (I don't think there is, as they're calculating different things), but since FV solves your problem why not just use that?

Subtracting viralnes

i have a yearly unit that i divide by a percentage to give me the monthly equivalent. I have a growth formula that increases the monthly unit to a yearly one month by month, how can i create a formula that give me the actual unit per month not the growth. Example
4
5
7
8 this is the growth but i what 5-4=1....
7-5=2...
=ROUND(Q59*$B$49,0) is how i get 4..5..6..7..8 how do i get to 1..2..1 in one formula . Thanks
If I'm understanding you correctly you are looking for the incremental increase rather than the total increase. Without more information it is difficult to understand exactly what your looking for, but your formula sounds like it is multiplying over 100%. You want to multiply by the percentage of increase. so essentially what your doing is adding the beginning balance back in. Change your percentage in the cell to the increase and not the increase plus beginning.

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