im a bit of a rookie to Excel and I cant find an exact answer to my question.
Basically I want to get picture 1(https://i.stack.imgur.com/8E5zv.png) to do what picture 2 (https://i.stack.imgur.com/LXJhq.png
) is showing. Its probably a really easy question.
So any value total over 10,000 will be charged at the 25p rate and any value below 10,000 will be charged a the 40p rate.
so cumulatively, one person may have claimed 9999 miles since starting and they put in a new expense claim for 10 miles, I would like the 1 mile to go to the 40p rate and the other 9 to the 25p rate.
What sort of formula would I need?
Thanks for any help in advance!
If the previous cumulative mileage is denoted by Old, the additional mileages by Miles and the threshold at which the lower rate is payable by Thold then consider the following. There are 3 cases:
Old+Miles<=Thold: All Miles paid at the higher rate
Old<Thold<=Old+Miles: Miles split so that Thold-Old paid at higher rate and Miles-(Thold-Old) at lower rate
Thold<=Old: All Miles paid at lower rate.
Miles are paid at the higher rate whenever Old is less than Thold and the number of miles paid at the higher rate is the lesser of Miles (Case 1.) and Thold-Old (Case 2.). This could be expressed in Excel-like way as
`=IF(Thold-Old>0,IF(Miles<Thold-Old,Miles, Thold-Old),0)`
but a much more succinct expression is
`=MIN(Miles,MAX(Thold-Old,0))`
Both formulae, deliver a correct result in all 3 cases (including a value of zero for case 3.) and so each represents a generally applicable formula for the number of miles to be paid at the higher rate.
Similarly, miles are paid at the lower rate whenever Old+Miles exceeds Thold and the number paid at this rate is the lesser of Miles (Case 3.) and Miles-(Thold-Old) (Case 2.). In this case the IF expression is:
`=IF(Old+Miles>Thold,IF(Miles<Miles-(Thold-Old),Miles,Miles-(Thold-Old)),0)
but this can be equivalently written as
`=IF(Old+Miles-Thold>0,IF(Miles<Miles+Old-Thold,Miles, Miles+Old-Thold),0)`
and I will leave it for you as an exercise to work out the succinct version. The formula(e) deliver a result of 0 for case 1. and so are generally applicable for calculating the miles to be paid at the lower rate.
Related
The Doobie Brothers garage band is planning a concert. Tickets are set at $20. Based on what other bands have done, they figure they should sell 350 tickets, but that could fluctuate. They figure the standard deviation of sales at 50 tickets. No shows are uniformly distributed between 1 and 10. Fixed costs are 5000.
How profitable is the concert likely to be?
So I am able to enter the excel formula for revenue 50*20 and subtract 5000 for FC, but I am having trouble deciphering how to account for the no show costs. I know that I have to use RANDBETWEEN(1,10) formula, but I am not sure if it gets multiplied or divided by something. Again, I am looking for what to do with the formula in the context of a profit equation.
If it helps, the mean for the number of tickets sold is 350 and stdev is 50, so I used that to get the number of attendees in a simulated sense...That is, NORM.INV(RAND(),350,50)
Of course, this problem may not be realistic in real life because promoters keep the money, but for the purposes of the problem...just assume that no promoters exist here.
So for example: You want to receive $X in today's dollars at the beginning of each year for Z# of years. Assuming a 3% constant inflation rate and a 7% compounded annual rate of return.
I know the formula to calculate the inflation adjusted returns; for the rate of return you have to use this formula:
[[(1+investment return)/(1+inflation rate)]-1]*100 OR in this instance
[(1.07/1.03)-1]*100
then you need to use the Present Value formula to calculate the rest PV(rate,nper,pmt,[fv],[type]) to find out how much $ is needed to sustain $X adjusted for inflation for Z# years. So here's my formula that I'm using:
=PV((((((1+E16)/(1+B15))-1)*100)),H14,-O7,,1)
Where E16 is my Annual Return (7%), B15 is my Inflation Rate (3), H14 is the number of years I need the payment (30), -O7 is my payment amount (made negative to give a positive #)($127,621.98), future value [fv] is left blank as is unnecessary, and Type is 1 so I calculate for receiving the payment at the beginning of the year.
What all this "should" return is $2,325,327.2044 according to my financial calculator, however Excel is giving me $160,484.6347.
What am I doing wrong here?
The syntax for PV includes:
Rate Required. The interest rate per period. For example, if you obtain an automobile loan at a 10 percent annual interest rate and make monthly payments, your interest rate per month is 10%/12, or 0.83%. You would enter 10%/12, or 0.83%, or 0.0083, into the formula as the rate.
So don't factor by *100.
Many parentheses serve no purpose as the formula below is sufficient:
=PV((1+E16)/(1+B15)-1,H14,-O7,,1)
The Excel (2013) result to four DP is: $2,325,327.2045.
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 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%