Assuming there are 20 times on a month that a bus with a capacity of 8 drives from A to B and that there are Y subscriptions for the bus service, how does one simulate the events of people wanting to take a bus at a certain day exceeding the capacity of the bus? Knowing that on average a person would take the bus X times per month?
How do you translate the people on average taking the bus X times per month to a distribution of how many people will take the bus on a certain day?
I'll assume that the demand is constant for each customer, independent from trip to trip, and that customers are independent of each other and travel individually (no groups). Under those assumptions, if customer k has an average rate of nk trips per month, and a month contains 20 trips, there is a probability pk = nk / 20 that that customer will want to go on any particular trip. For each of the Y customers generate U, a Uniform(0,1) random number. If U <= pk, add this customer to that day's total demand. Finally, create an indicator variable E: if the total demand exceeds 8, E = 1, otherwise E = 0. Lather, rinse, repeat for as many days as you want to study. The average of the E's is an estimate of the proportion of trips for which demand exceeded capacity.
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A business works on a subscription model basis with a expected churn rate (Cancellations) each month during year 1 at 5% & during the following year a churn rate of 2.5% due to the fact these are now established customers (long term).
A new feature or service is launched with a expect increase of subscriptions each month. I need to calculate how many subscriptions would that be in N years based on a 5% churn rate for the first 12 month & a 2.5% churn rate during year 2.
Below is currently how were are calculating this in excel however this is really in inelegant solution when trying to calculate this for say 5 - 10 year impacts.
https://i.stack.imgur.com/yF5Rx.png
Are there any accounting formulas or something mathamitcally I can produce to calculate this in a single cell? Given I would need to set the given churn rates for each year & length of time.
For ease lets say 95% of the time I would be working on a 3 year model of subscriptions & each year will need its own churn rate.
I thought perhaps something with exp & halving the value might work but have not found anything yet.
Here's one way to build the model. I'll make reference to this image:
First we set up the churn model.
Row 1: Since Churn Rates depend on subscription age, Row 1 has the subscription age (in months). This is for reference only and is not used in the calculations.
Row 2: Churn Rates.
Row 3: Since Churn Rates always enter the calculation as (1-ChurnRate), call that term (Single-month) Retention Rate. As an example, in B3 the formula is =1-B2.
Row 4: Since the effects of churn are cumulative over multiple months, we define another term Multi-month Retention Rate (abbreviated MMRR). In the first month this is set to 1; in subsequent months this is the product of previous single-month retention rates. So in C4 the formula is =B4*B3; in C5, =C4*C3, etc.
Row 5: The model as described in the Question indicated a fixed rate of new subscriptions = 100/month. When the subscription rate is fixed, it is convenient to sum up the MMRRs. So in B5 we have =B4; in C5, =B5+C4; in D5, C5+D4; etc.
At this point we're essentially done. If you multiply the values in Row 5 by any fixed rate of new subscriptions (e.g. 100/month in the original Question) we get the number of subscribers in that month. But what if you want to model where the number of new subscriptions varies month to month? Here's how ...
The basic idea is to multiply the monthly subscription rate by its age-appropriate MMRR. Note that Row 8 has varying numbers of new subscriptions (100, 110, 97) in the first 3 months. To get the total subscriptions in Mar-19 for example, we need to
multiply the 100 (Jan-19) subscriptions (that have a 2 month age) by the MMRR for a 2-month old subscription (0.9025),
multiply the 110 (Feb-19) subscriptions (that have a 1 month age) by the MMRR for a 1-month old subscription (0.95),
multiply the 97 (Mar-19) subscriptions (that have a 0 month age) by the MMRR for a 0-month old subscription (1), and
add those three products together.
This could be calculated on the worksheet by entering in D9 the formula =B8*D4+C8*C4+D8*B4. This type of calculation (sum up the pair-wise products of two arrays) is often done with Excel's SUMPRODUCT function. Here we need to take one of the arrays in reverse order, which is not directly supported by Excel. You could enter new subscriptions in reverse order, but that's an ugly kludge. Fortunately, it is do-able with a combination of the OFFSET(), COLUMN() and N() worksheet functions (see here for details). The required formula for B9 is
=SUMPRODUCT($B4:B4,N(OFFSET(B8,0,-(COLUMN($B8:B8)-COLUMN($B8)),1,1)))
This can then be copy/pasted into the rest of row 9.
This model approach is pretty flexible: the churn rates (row 2) and subscription rates (row 8) can both be varied month to month; the total number of retained monthly subscriptions is calculated automatically.
I was given tens of thousands of bills charged to customers. I am trying to determine if the bills are potentially accurate. The only data I have is the actual bill itself. Here's where things get complicated. There are four scenarios, each with their own nuances:
Scenario 1 Nuances:
Base Fee of $10 * the amount of items bought * the number of deliveries (maximum amount of items bought would be 10 and the maximum number of deliveries would be 7)
If the amount of items bought exceeds 1, the total bill is discounted by 20%
If the boxes are recycled, the total bill is further discounted by 15%
If the good is over 15 pounds, an additional charge of $10 will be assessed per each item over 15 pounds (maximum amount of items would be 10)
If there is no adequate port for delivery, an additional $50 per hour will be charged per delivery (maximum hours would be 3)
Scenario 2 Nuances:
Business that share a port of delivery for the second service will be charged $11 per item
If the business does not share a port of delivery, the fee is $13 per item. Each additionally delivery for a business that does not share a port is $15 per delivery, in addition to each item costing $13 (maximum deliveries would be 7 and maximum amount of items would be 8).
You see where I am going with all of this. The next two scenarios are just as lengthy. Sadly, no information besides the total bill is given. We don't know which scenario the bill belongs to, the number of items, etc., just a single column of the invoice. How would I go about determining all potential costs from each scenario to maybe index the invoice and see if there is a match? Any help on this would be amazing.
I tried creating an index where I wrote out multiple scenarios. For example, a column with the number of items, the number of deliveries, a discount for > 1 item bought, a recycling discount, etc... After attempting this for two hours, I realized this may not be the best method. My first row would be 1 item, 1 delivery, 0% discount for > 1 item bought, and 0% discount for recycling. Next would be 2 items bought, 1 delivery, 20% discount for > 1 item bought, 0% discount for recycling. This is seemingly impossible to do for everything.
My expected output is "Y" if the invoice total matches one of the potential costs from the index, "N" if not.
You can write a macro to calculate every possible scenario. Write a macro with nested loops.
The outside loop is the quantity, such as For ItemQty = 1 to 100 (or to some other likely maximum).
The inside loops are the scenarios and nuances, such as For BoxesRecycled = 0 to 1. Each loop modifies the total, such as Total = Total - (BoxesRecycled * 0.15 * Total).
In the middle of all the loops is code that writes a line with the quantity, nuances, and total.
You will need to match the sequence in which charges and discounts were applied and the way the total was rounded. Probably the sequence was discounted 20%, then discounted 15%, then rounded. But maybe it was discounted 20%, then rounded, then discounted 15%, then rounded. If you don't match the sequence and rounding, then your total might be 1 cent different from an actual invoice.
The case:
Let us say a company is a monopolist in the market, and the supply of products is 100% met by demand every week. All (variable and fixed) costs are set. Based on estimations I have weekly units produced. In addition, the average price throughout the year has to hit approximately X. It is preferrable that the monthly results don't vary too much from break even. How can I quickly set the weekly price for the company’s product so that the company breaks even (Result = approx. 0), and at the same time keep the weekly price at the most stable price possible (as close to average as possible every week).
I have tried to use solver to minimize STD.DEV of prices (also tried skewness), with constraints that the average price is X and estimated result = 0, by changing the weekly prices throughoutthe year. However, this results in a few weeks of extreme price differences, which is the opposite of what I need.
Do somebody have a possible solution to the problem?
You could try the following:
minimize maxp - minp
maxp >= p(w) for all w
minp <= p(w) for all w
This will try to minimize the bandwidth (and additionally is completely linear)
I was hoping someone could help me with this conundrum as l feel like l've been spinning my wheels all day with this one. Here's the scenario and l'll try and keep it simple.
Lets say, l currently have 1.5 million subscribers a month and l get paid on a minimum guarantee (MG) of 2.1 million subscribers a month.
Those 2.1 million subscribers are broken down into 500k increments i.e.
Tier 1 0-500k l get paid £0.20 per subscriber
Tier 2 500k-1,000k l get paid £0.19 per subscriber
Tier 3 1,000k - 1,500k l get paid £0.18 per subscriber
Tier 4 1,500k - 2,000k I get paid £0.17 per subscriber
Anything above 2.1 million subscribers is incremental income (say at £0.16 per subscriber) but l'll always be paid for the MG subs no matter what.
This is my attempted logic at the formula:
IF actual subs are > MG subs then actual subs subtracted from Tier 4 subs (2,000) x cost per subscriber. (I'm subtracting actuals from the Tier 4 subs because l've already factored in the fees l'm being paid on these subscribers). IF that's not true i.e. IF actual subs are < MG subs then MG subs subtracted Tier 4 subs (2,000) x cost per subscriber.
It's tricky to explain and if l could l'd attach a spreadsheet to show you. The complexity is really having something flexible enough to handle changes to Tiers and Tier sizes as well as changes in MG levels. If you have anything better or suggestion to improve that would be a great help.
Thanks for your help,
M.
Do a table like the image
On E5 put
=(E2-VLOOKUP(E2,A:B,1,TRUE)+1)*VLOOKUP(E2,A:B,2,TRUE)+VLOOKUP(E2,A:C,3,TRUE)
The formula may vary because in portuguese they are a bit different, but I think I got it right.
since you are guaranteed the MG, the MG can be computed as
=SUMPRODUCT({500000,500000,500000,500000},{0.2,0.19,0.18,0.17})
which yield 370,000 pound sterling and will be constant.
so if you actually have x subscribers (where value x written in cell A1), you can compute additional return by
=MAX((A1-2000000)*0.16,0)
which will always yield a positive value.
So total return is the sum of the above two results.
= 370 + MAX((A1-2000000)*0.16,0)
BR~
I'm trying to figure out what rate of return I would need on an investment in order to compare to paying down a mortgage.
I have calculated the change in the mortgage - I know how much money I'd save by the end of the loan term and how much money I'd need to put in. I'm trying to compare that to an equivalent investment - treat any lump sum payment as the principal of an investment, treat any monthly overpayment as a monthly contribution to an investment, plug in the final value, and solve for the effective rate of return.
I've looked at the RATE and the IRR commands. IRR seems close to what I want, but it wants a series of values for the input flows, but I have it as a periodic regular investment.
For an example with numbers - if I pay an extra $100 a month on the mortgage for 120 months, I can save $10000 in total cost. What command can I use to calculate this in terms of an investment? If I invest $100 a month for ten years and end up with $10000, what was my annualized rate of return?
If I start with principal PV invested at rate R, I contribute monthly payment M for N months, and I end up with final value FV at the end of those N months, I'd like to solve for R given the other variables.
I know there's another factor regarding the mortgage interesting being tax deductible - I'll look at worrying about that after I figure this part out.
:)
Your monthly return is given by this RATE formula
number of periods = 120 (10*12)
contributions of $100 per period
future value of 10,0000
=RATE(10*12,-100,0,10000)
=-0.32% per month
Note as a check =RATE(10*12,-100,0,12000) = 0
which is equivalent to an annual rate of
=1-(1-0.32%)^12
=-3.73%