MadManMike Posted June 11, 2015 Report Share Posted June 11, 2015 So, working on price curves, I normally start at the low end. For example, if I want to sell a product for £140 for 1 unit, I can apply the following curve to get the rest of the prices: 10-24 units: x 0.45 of £140 25-49 units: x 0.28 of £140 50-99 units: x 0.23 of £140 100-299 units: x 0.21 of £140 300 units: x 0.20 of £140 That's simple. However, I'm having a dumb moment. Starting at 300 units, with my base price of £70, I want to basically do that curve in reverse. I'm sure it's dead simple, but I just can't figure it out. Can anyone help? Quote Link to comment Share on other sites More sharing options...
Luke Rainbird Posted June 11, 2015 Report Share Posted June 11, 2015 I'm probably just not thinking straight after a morning of turbine work, but couldn't quite make out what you're asking, Mike. Can you clarify a little please? Happy to help once I understand the problem Quote Link to comment Share on other sites More sharing options...
Mark W Posted June 11, 2015 Report Share Posted June 11, 2015 If you mean it like I think you mean it, it just means your price for one unit would be £350? Assuming you mean that it'd be £70 per unit for 300 units (making the £70 0.20 of the overall single unit price)? Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 11, 2015 Author Report Share Posted June 11, 2015 I'll try, lol. So normally when I'm pricing things up, I will get a costing - you add together machining time, machine set up time, material, plating etc. This gives you a base price. For arguments sake, this base price is £140 for 1 unit. From there, we can add a price curve, that gives you a discount based on multiple units, so the example in my original post means that if you order 10 units, the price goes to 0.45 of £140 (So £63). If however your base price is £70 for 300 units and I need to work backwards down to 1 unit, I can't figure out the actual sum to do. Normally I do this: 1 unit: £140 10-24 units: x 0.45 of £140 25-49 units: x 0.28 of £140 50-99 units: x 0.23 of £140 100-299 units: x 0.21 of £140 300 units: x 0.20 of £140 What I need to do is this: 1 unit: £70 x ??? 10-24 units: £70 x ??? 25-49 units: £70 x ??? 50-99 units: £70 x ??? 100-299 units: £70 x ??? 300 units: £70 Ignore actual costs and what the price should be, I just need to know how to basically reverse the original sum. Sorry for the crap explanation!Yes Mark you got the right end of the stick. I need to know the actual sum, as I need to apply this curve to several hundred lines in Excel. I'm 99% sure it's dead easy, I just can't figure it out. Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted June 11, 2015 Report Share Posted June 11, 2015 1 unit: £350 10-24 units: £157.50 25-49 units: £98 50-99 units: £80.50 100-299 units: £73.50 300 units: £70 Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 11, 2015 Author Report Share Posted June 11, 2015 So how did you achieve that? That's what I need to do, but for several hundred different products. Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted June 11, 2015 Report Share Posted June 11, 2015 1 unit: £70 x 5 10-24 units: £70 x 2.25 25-49 units: £70 x 1.4 50-99 units: £70 x 1.15 100-299 units: £70 x 1.05 300 units: £70 Truth is I don't even know. I used your example in the first post to reverse engineer multipliers to go back up from the 300 @ £70 mark. I'm sure someone can describe it properly but I think it's to do with 1/your ratio shown above... Quote Link to comment Share on other sites More sharing options...
Mark W Posted June 11, 2015 Report Share Posted June 11, 2015 Dave - unless I got the first bit wrong, I'd make it the single unit price was £350, so the 10-24 price would be £157.50 and so on? EDIT: You sneaky editing so-and-so Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted June 11, 2015 Report Share Posted June 11, 2015 Dave - unless I got the first bit wrong, I'd make it the single unit price was £350, so the 10-24 price would be £157.50 and so on? EDIT: You sneaky editing so-and-so I somehow missed the 50-99 line so everything got shuffled a line. Fixed now Is that (post 7) what you need Mike? Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 11, 2015 Author Report Share Posted June 11, 2015 Yup that's what I need, I still can't get my head around how you reached that conclusion though. I'm fine with normal percentages, but reverse engineering them just baffles me. Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted June 11, 2015 Report Share Posted June 11, 2015 Does that help/make sense? (Click on it to make it big enough to actually see!) Basically from the example you give you can work out what multiplier can get from £28 for 300 to £29.40 for 100 (1.05 in that case) and so on and you can then just use those same multipliers starting at £70 for 300 (or whatever price you want). Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 11, 2015 Author Report Share Posted June 11, 2015 Yeah that makes sense - I'd never have figured that out myself. Tried all sorts of stupid ideas, none of which got close to the solution. Cheers guys, massive help, appreciate your time Quote Link to comment Share on other sites More sharing options...
Mark W Posted June 11, 2015 Report Share Posted June 11, 2015 "I don't get why you're so obsessed with riding bikes." "Well, it means I can get prompt answers to strange maths questions." 4 Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 11, 2015 Author Report Share Posted June 11, 2015 It's fair to say a good portion of my brain power has come from this forum. I've asked all sorts of weird things and always had speedy answers! I've managed to buy and sell quite a lot of non bike related stuff on here too. #TF4LIFE Quote Link to comment Share on other sites More sharing options...
HippY Posted June 11, 2015 Report Share Posted June 11, 2015 (edited) It's fair to say a good portion of my brain power has come from this forum. I've asked all sorts of weird things and always had speedy answers! I've managed to buy and sell quite a lot of non bike related stuff on here too. #Dannsbum4LIFE so bascially I have a product for £100 (because it is easy to use) If you buy 1 product, it should be £100/unit If you buy 100 product, it should be £50/unit if you want to multiply 10-24 units: x 0.55 of £140=£77 25-49 units: x 0.72 of £140=100.8 and the price is raising, the opposite you want there are 50% difference between 1 and 300, that means 0.167% discount of each item so the equation = 1-((Item number * 0.16)/100) at 10-24 item the % would be: 1.6%-4% 25-49 units:%4.16- %8.16 50-99 units: %8.3-%16.5 100-299 units: %16.6-%49.83 300 units: 50% So more item you sell, the cheaper they get Edited June 11, 2015 by HippY 1 Quote Link to comment Share on other sites More sharing options...
waybe2014 Posted June 11, 2015 Report Share Posted June 11, 2015 (edited) All seems a complicated way of doing things. Wouldn't dividing by the number instead of multiplying give the answer? Although that is just to give you your initial figure to put back into your formula Edited June 11, 2015 by waybe2014 Quote Link to comment Share on other sites More sharing options...
stirlingpowers Posted June 11, 2015 Report Share Posted June 11, 2015 (edited) Your discount factors define a relative discount function. Relative means it needs to be multiplied with an absolute base price for a certain quantity to get the real selling price. For brevity, let's call the discount function d. It gives back a value d[q] for a certain quantity q. The base price shall be called b, the real selling price r: d[q] * b = r At quantity 1, d has the value 1: d[1] = 1 At quantity 300, d has the value d[300] = 0.2 You know the following equation is true: d[300] * b = £70 When you divide this equation by d[300]: b = £70 / d[300] = £70 / 0.2 = £350 The rest of the prices is found by just multiplying the basePrice with the discount function at the desired quantity: d[q]*£350 = r Edited June 11, 2015 by stirlingpowers 1 Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 15, 2015 Author Report Share Posted June 15, 2015 maths.jpg Does that help/make sense? (Click on it to make it big enough to actually see!) Basically from the example you give you can work out what multiplier can get from £28 for 300 to £29.40 for 100 (1.05 in that case) and so on and you can then just use those same multipliers starting at £70 for 300 (or whatever price you want). I've tried to get my head around Hippy and stirlingpowers above, but it's not making much sense to me. I'm really not good with this kind of maths! Your image makes sense, but that seems to be including my original example as the base calculation - (1pc @ £140). Is that correct? Where I put: 10-24 units: x 0.45 of £140 25-49 units: x 0.28 of £140 50-99 units: x 0.23 of £140 100-299 units: x 0.21 of £140 300 units: x 0.20 of £140 That was just an example, because for that product, the base price was £140 for 1pc. All I want to use from that is the curve, the £140 is not relevant. Is there a way to use that price curve in reverse? I'm starting at 300pcs @ £70 each, the lower quantity prices have not been defined. I thought it would be a simple case of starting at £70 and making that 0.20 of the 1pc price. If I change the curve to: 1 unit: x 1.00 of ??? 10-24 units: x 0.60 of ??? 25-49 units: x 0.40 of ??? 50-99 units: x 0.30 of ??? 100-299 units: x 0.25 of ??? 300 units: £70 Surely there's a simple way of calculating this?? I appreciate all your efforts guys, I'm eager to learn but this part of my brain just doesn't seem to work. Quote Link to comment Share on other sites More sharing options...
stirlingpowers Posted June 15, 2015 Report Share Posted June 15, 2015 In your last post: Is the discount factor at 300 units known? If not, does the discount at 300 apply to 300 and more units? Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted June 15, 2015 Report Share Posted June 15, 2015 Sorry, only just found this. I feel I've let the speed of the prompt answers to strange maths questions side down . In the image I used the example with £140 to work out the relative ratios you wanted (i.e. the discount curve) based on the ratios given. The £140 is irrelevant so long as you're happy with the respective discounts (in fraction/percentage terms) for each jump in quantity. If the example had been based on an item selling for £345.32 for one item it would still work out the same assuming you were happy with the 0.45, 0.28, 0.23, ... As mentioned above, the other way of doing it is by starting with the 300 @ £x and multiplying x by 1/(whatever your max discount is). For the case of 0.2 as your max discount that would be 1/0.2 = 5. From that point you've got what you started with and you can then make whatever discount ratio/curve you want. I was lost by stirlingpowers reply too! Edit: For any discount amounts the above way is probably the way to go and use something like the following: So all you need is how much you want for 300+ (or whatever) items and a discount 'curve' for the various quantities (including the maximum allowable discount for the 300+) and you'll be able to work out the respective values from there. Quote Link to comment Share on other sites More sharing options...
stirlingpowers Posted June 15, 2015 Report Share Posted June 15, 2015 (edited) I'll restate what I think might be the solution in more common terms: You always apply this equation to calculate your selling prices: discount factor x base price = selling price Now you know that at 300 units, where you have defined a discount factor of 0.2, you have a selling price of £70. Then you can calculate your base price with the above equation: 0.2 x base price = £70 If you divide by 0.2 on both sides of the equal sign, you get: base price = £70 / 0.2 This is where the £350 base price comes from. With this base price and your discount factors, you can get a selling price at any amount of units: discount factor x £350 = selling price That is the straightforward way for me. Pasting this into your original problem statement gives you: 1 unit: £140 10-24 units: x 0.45 of £140 25-49 units: x 0.28 of £140 50-99 units: x 0.23 of £140 100-299 units: x 0.21 of £140 300 units: x 0.20 of £140 What I need to do is this: 1 unit: £70 / 0.2 x 1 = £350 10-24 units: £70 / 0.2 x 0.45 = £157.5 25-49 units: £70 / 0.2 x 0.28 = £98 50-99 units: £70 / 0.2 x 0.23 = £80.5 100-299 units: £70 / 0.2 x 0.21 = £73.5 300 units: £70 In your second answer, you said: 1 unit: x 1.00 of ??? 10-24 units: x 0.60 of ??? 25-49 units: x 0.40 of ??? 50-99 units: x 0.30 of ??? 100-299 units: x 0.25 of ??? 300 units: £70 If you don't have the discount factor at 300 units, you will have to extrapolate that curve to 300 units. I can post a simple technique of extrapolation, based on just the numbers given above, or based on fixed and running costs if necessary. But I don't assume that this is the problem you want to have solved here. I think it is more like this: If you choose a discount factor of 0.14 for 300 units, my solution pasted in your statement would be: 1 unit: x 1.00 of £70/0.14 = £500 10-24 units: x 0.60 of £70/0.14 = £300 25-49 units: x 0.40 of £70/0.14 = £200 50-99 units: x 0.30 of £70/0.14 = £150 100-299 units: x 0.25 of £70/0.14 = £125 300 units: x 0.14 of £70/0.14 = £70 But I am not quite sure about this being the solution, since I did neither consider how the discount factors came to be nor the total amount of cost at a certain amount of units. Edited June 15, 2015 by stirlingpowers 1 Quote Link to comment Share on other sites More sharing options...
monkeyseemonkeydo Posted June 15, 2015 Report Share Posted June 15, 2015 300 units: x 0.14 of £70/0.14 = £70 Take it that's what you meant there. I think you're pretty much doing what I'm doing but more proper . My answer is for kids who don't read good and want to do other stuff good too... Quote Link to comment Share on other sites More sharing options...
stirlingpowers Posted June 15, 2015 Report Share Posted June 15, 2015 Take it that's what you meant there. I think you're pretty much doing what I'm doing but more proper . My answer is for kids who don't read good and want to do other stuff good too... Jup, the little pedantic teacher in me is really triggered by math forum questions. Anyway, that 0.15 instead of 0.14 typo is crucial for understanding, good you found that one. Quote Link to comment Share on other sites More sharing options...
bikeperson45 Posted June 15, 2015 Report Share Posted June 15, 2015 I'm still working on whether the damn plane takes off. Quote Link to comment Share on other sites More sharing options...
MadManMike Posted June 16, 2015 Author Report Share Posted June 16, 2015 Edit: For any discount amounts the above way is probably the way to go and use something like the following: maths_mk2.jpg So all you need is how much you want for 300+ (or whatever) items and a discount 'curve' for the various quantities (including the maximum allowable discount for the 300+) and you'll be able to work out the respective values from there. Awesome, thanks to you and stirling! Just one question / comment on your screen shot though - the formula in there looks wrong and should create a circular reference?? So, here's what I've come up with, based on the suggestions you guys posted. Using my first example: 10-24 units: (x 0.45) £157.50 25-49 units: (x 0.28) £98.00 50-99 units: (x 0.23) £80.50 100-299 units: (x 0.21) £73.50 300 units: £70 And my second example: 10-24 units: (x 0.60) £210 25-49 units: (x 0.40) £140 50-99 units: (x 0.30) £105 100-299 units: (x 0.25) £87.50 300 units: £70 Those numbers seem to concur with the examples you guys posted, so I think we're there I owe you both a large, cold beer! Thanks chaps Quote Link to comment Share on other sites More sharing options...
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