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)
Related
I'm wondering if there is a way to automatically select the amount of past data when calculating features.
For example, I might want to predict when a customer is going to make their next purchase, so it would be good to know a count of purchases or average purchase price by different date cutoffs. e.g. Purchases in the last 12 months, last 3 months, 7 days etc.
What is the best way to approach this with featuretools?
You can create a feature matrix thats uses only a certain amount of historical data using the training window parameter in featuretools.dfs. When training window is set, Featuretools will use the historical data between the cutoff time and cutoff_time - training_window. Here's the example from the documentation:
window_fm, window_features = ft.dfs(entityset=es,
target_entity="customers",
cutoff_time=cutoff_times,
cutoff_time_in_index=True,
training_window="1 hour")
When determining which data is valid for use, the training window will check if the time in the time_index column is within the training window.
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?
I am trying to figure out what the optimal number of products I should make per day are, displaying the values in a chart and then using the chart to find the optimal number of products to make per day.
Cost of production: $4
Sold for: $12
Leftovers sold for $1
So the ideal profit for a product is $8, but it could be -$3 if it's left over at the end of the day.
The daily demand of sales has a mean of 150 and a standard deviation of 30.
I have been able to generate a list of random numbers using to generate a list of how many products: NORMINV(RAND(),mean,std_dev)
but I don't know where to go from here to figure out the amount sold from the amount of products made that day.
The number sold on a given day is min(# produced, daily demand).
ADDENDUM
The decision variable is a choice you make: "I will produce 150 each day", or "I will produce 145 each day". You told us in the problem statement that daily demand is a random outcome with a mean of 150 and a SD of 30. Let's say you go with producing 150, the mean of demand. Since it's the mean of a symmetric distribution, half the time you will sell everything you made and have no losses, but in most of those cases you actually could have sold more and made more money. You can't sell products you didn't make, so your profit is capped at selling 150 on those days. The other half of the time, you won't sell all 150 and will take a loss on the unsold items, reducing your profit a bit. The actual profit on any given day is a random variable, because it is determined by random demand.
Since profit is random, you can calculate your average earnings across many days based on the assumption that you produce 150. You can also average earnings based on the assumption that you produce 140 per day, or 160 per day, or any other number. It sounds like you've been asked to plot those average earnings versus how many you decided to produce, and choose a production level that results in the highest long-term average earnings.
I'm looking to compute and show individual row totals and a Grand Total. I just need the formulae to put in the boxes so the calculation is automatic but the problem is the calculations are a little complicated...
I'm using data validation to select the day type. This is what I think I need:
Assign a price to the day type (either Standard day = £23 or Extended day = £26).
Apply a volume discount where appropriate. If Jack is attending all week (5 days) and the day type is the same for all (all Standard or all Extended), the total cost is £100 (or £120)
Else the total number of days needs to be added up for Jack. (Number of days for each ‘day type’) and priced up.
For his siblings after the first, as above but apply an additional discount of 15%.
The grand total then needs to show at the bottom.
Well, it is not the best of data layouts but this may serve, in L6 and copied down to L13:
=IF(OR(A6="Brother",A6="Sister"),0.85* IF(COUNTIF(B6:F6,"Standard day")=5,100,IF(COUNTIF(B6:F6,"Extended day")=5,120,COUNTIF(B6:F6,"Standard day")*23+COUNTIF(B6:F6,"Extended day")*26)), IF(COUNTIF(B6:F6,"Standard day")=5,100,IF(COUNTIF(B6:F6,"Extended day")=5,120,COUNTIF(B6:F6,"Standard day")*23+COUNTIF(B6:F6,"Extended day")*26)))
and =SUM(L1:L16) in D16.
It would be better practice not to hard code the daily rates/discount, but extracting these from C1:D2 would have increased the length of the formula further.
Note also the result is not £429.95 (you may have changed your example after doing your calculations).
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%