I can't work something out - Can you?

[Pulse]

So, I am studying, and have the following to work out, but can't for the life of me! Even with the answer in the book! (As it doesn't show how to work it out)

So, I'll give the full text...

You work for Alloy Engines UK Ltd, and you have been supplying engines to Motor Mowers UK Ltd for one year. This was the first year of a four-year supply contract. You are reviewing the selling price of the 9hp petrol engine.

The costs a year ago were quoted as shown in the below table:

Cost Centre	Amount
Direct Labour Costs	£42.0
Direct Materials	£31.0
Direct Overheads	£12.0
Profit	£9.0
Selling Price	£94.0

Your agreement with Motor Mowers UK Ltd is that you can request an increase on direct labour and materials, but your overhead and profit percentages are fixed.

Labour: During the last 12 months the engineering labour index for your industry has moved up by an increase of 2.8%.
Materials: The main items have moved over the same period by an average of 3.6%

Calculate a new selling price for the 9hp petrol engine.

---

The answer given in the book is the following:

Cost Centre	Amount	Percentage
Direct Labour Costs	£43.20	44.5
Direct Materials	£32.10	33.1
Direct Overheads	£12.40	12.8
Profit	£9.30	9.6
Selling Price	£97.0	100

[davepoth]

So the "fixed" costs increase, meaning that a certain percentage of those fixed costs is now bigger than it was.

[Pulse]

That's right, but how on earth, with what they've provided, would I have worked out the new selling price was £97?

[davepoth]

Labour + materials = £73. Overheads are 16.43% of that, which is £12. The profit margin on the whole lot is then 10.58%, which is £9.

So if labour + materials = 75.3, 16.43% of that is £12.4 if you round up. 10.58% profit on the whole lot of that is then £9.3 if you round up, getting you the £97.

Edited by davepoth on Tuesday 3rd May 19:20

[Pulse]

davepoth said:

Labour + materials = £73. Overheads are 16.43% of that, which is £12. The profit margin on the whole lot is then 10.58%, which is £9.

So if labour + materials = 77.6, 16.43% of that is £12.75, or 12.8 if you round up. 10.58% profit on the whole lot of that is then £9.56, or 9.6 if you round up, getting you the £100.

That isn't right, unfortunately. The profit stays at 9.6% from the first figure and the last figure. The answer is at the bottom, which your figures don't match, but I can see where you're coming from. I think some information must be missing to enable me to answer it!

[davepoth]

Pulse said:

That isn't right, unfortunately. The profit stays at 9.6% from the first figure and the last figure. The answer is at the bottom, which your figures don't match, but I can see where you're coming from. I think some information must be missing to enable me to answer it!

I just edited it and corrected it - I read the %age column rather than the actuals, but the method was fine.

[ATTAK Z]

I reckon it's slightly wrong anyway ... here's my answer


Labour up 2.8%
Direct Labour costs = 42.00 x 1.028 = 43.18
Material up 3.6%
Direct Material costs = 31 x 1.036 = 32.12
Overheads remain at 12.8% of selling price
Direct overheads = 12.8% x S (where S is the new selling price)
Profit remains at 9.6% of selling price
Profit = 9.6% x S (where S is the new selling price)

Thus
S = 43.18 + 32.18 + 0.128S + 0.096S
0.776S = 75.36
New selling price = S = 75.36/0.776 = 97.11

[Pulse]

ATTAK Z said:

I reckon it's slightly wrong anyway ... here's my answer


Labour up 2.8%
Direct Labour costs = 42.00 x 1.028 = 43.18
Material up 3.6%
Direct Material costs = 31 x 1.036 = 32.12
Overheads remain at 12.8% of selling price
Direct overheads = 12.8% x S (where S is the new selling price)
Profit remains at 9.6% of selling price
Profit = 9.6% x S (where S is the new selling price)

Thus
S = 43.18 + 32.18 + 0.128S + 0.096S
0.776S = 75.36
New selling price = S = 75.36/0.776 = 97.11

See now I thought it was slightly wrong too in the percentages certainly. For a study book, it's not very good! (An official CIPS one)

Your workings seem to make sense to me, although you've lost me with the 'S' bit!

Does that mean you add the end costs of those that have gone up, to the percentages of the others which stay fixed but in a decimal view, then take the cost of both of those that have increased (75.36) and divide that by the total number arrived at in the former (0.776)?

Sorry I'd love to write that in English!

[Pulse]

Wait, where does the 0.776 come from?

EDIT: Ignore that, the other half just explained. My calculations are as follows, so please tell me if I'm wrong (bear in mind I've kept too long a decimal point really, for a selling price)

Labour goes up to £43.18
Materials goes up to £32.12

So, knowing the percentages, you do this:

43.18+32.12+0.1276+0.0957 = 75.5233

75.5233/0.7765 = £97.26 new selling price

(The 0.7765 arrived at by working out the total percentage of the labour and materials as 77.65% and then decimal pointing the st out of it!)

Is that right?

Edited by Pulse on Tuesday 3rd May 20:11

[ATTAK Z]

Pulse said:

Wait, where does the 0.776 come from?

Selling price = labour + material = overheads + profit

so from the calculations above
S(selling price) = 43.18(labour) + 32.18(material) + 0.128S(overheads) + 0.096S(profit)
so
S = 43.18 + 32.18 + 0.128S + 0.096S
so
S - 0.128S - 0.096S = 43.18 + 32.18
so
0.776S = 75.36
so
S = 75.36/0.776 = 97.11

[ATTAK Z]

Pulse said:

43.18+32.12+0.1276+0.0957 = 75.5233

1st mistake ... you're adding prices to percentages ... not allowed ... it's like adding apples to oranges with the answer coming out in pears

you're looking for the number of apples (Selling price) not the number of pears (costs and percentage price rises) so keep everything in terms of apples

Edited by ATTAK Z on Tuesday 3rd May 20:31

[matsmith]

I would solve this problem by first using the data I have to give me percentages:

Cost Centre	Amount	Percentage
Direct Labour Costs	£42.0	44.68
Direct Materials	£31.0	32.98
Direct Overheads	£12.0	12.77
Profit	£9.0	9.57
Selling Price	£94.0

Then filling in the new table with the data I know (including the inflation increase where appropriate):

Cost Centre	Amount	Percentage
Direct Labour Costs	£43.18
Direct Materials	£32.12
Direct Overheads		12.77
Profit		9.57
Selling Price

So we know that our profit and overheads are a fixed percentage, and the remainder is 77.66% (the component of the selling price made up of labour and materials). Using this percentage you get a new selling price of £96.95. This can then be used to fill in the rest of the table:

Cost Centre	Amount	Percentage
Direct Labour Costs	£43.18	44.53
Direct Materials	£32.12	33.13
Direct Overheads	£12.38	12.77
Profit	£9.28	9.57
Selling Price	£96.95

[Pulse]

ATTAK Z said:

Pulse said:

43.18+32.12+0.1276+0.0957 = 75.5233

1st mistake ... you're adding prices to percentages ... not allowed ... it's like adding apples to oranges with the answer coming out in pears

you're looking for the number of apples (Selling price) not the number of pears (costs and percentage price rises) so keep everything in terms of apples

Edited by ATTAK Z on Tuesday 3rd May 20:31

I see what you mean, you can't do that, but that's how it's calculated, right? It's (effectively) a decimalised percentage, right? Just how you've used it, but I've not put the 'S' after them. In theory, it would work for any figures, right?

[ATTAK Z]

matsmith said:

I would solve this problem by first using the data I have to give me percentages:

Cost Centre	Amount	Percentage
Direct Labour Costs	£42.0	44.68
Direct Materials	£31.0	32.98
Direct Overheads	£12.0	12.77
Profit	£9.0	9.57
Selling Price	£94.0

Then filling in the new table with the data I know (including the inflation increase where appropriate):

Cost Centre	Amount	Percentage
Direct Labour Costs	£43.18
Direct Materials	£32.12
Direct Overheads		12.77
Profit		9.57
Selling Price

So we know that our profit and overheads are a fixed percentage, and the remainder is 77.66% (the component of the selling price made up of labour and materials). Using this percentage you get a new selling price of £96.95. This can then be used to fill in the rest of the table:

Cost Centre	Amount	Percentage
Direct Labour Costs	£43.18	44.53
Direct Materials	£32.12	33.13
Direct Overheads	£12.38	12.77
Profit	£9.28	9.57
Selling Price	£96.95

Agreed on that, in fact if I put in your (more accurate) percentages for overheads and profit my answer comes out as below


Labour up 2.8%
Direct Labour costs = 42.00 x 1.028 = 43.176
Material up 3.6%
Direct Material costs = 31 x 1.036 = 32.116
Overheads remain at 12.77% of selling price
Direct overheads = 12.77% x S (where S is the new selling price)
Profit remains at 9.57% of selling price
Profit = 9.57% x S (where S is the new selling price)

Thus
S = 43.176 + 32.116 + 0.1277S + 0.0957S
0.7766S = 75.292
New selling price = S = 75.292/0.7766 = 96.95

QED

Edited by ATTAK Z on Tuesday 3rd May 20:55

[ATTAK Z]

Pulse said:

ATTAK Z said:

Pulse said:

43.18+32.12+0.1276+0.0957 = 75.5233

1st mistake ... you're adding prices to percentages ... not allowed ... it's like adding apples to oranges with the answer coming out in pears

you're looking for the number of apples (Selling price) not the number of pears (costs and percentage price rises) so keep everything in terms of apples

Edited by ATTAK Z on Tuesday 3rd May 20:31

I see what you mean, you can't do that, but that's how it's calculated, right? It's (effectively) a decimalised percentage, right? Just how you've used it, but I've not put the 'S' after them. In theory, it would work for any figures, right?

yes but you don't know the selling price, it's what you are trying to find so, you can't know a percentage of it either ...that's why you have to substitute S for the thing you are trying to find .... basic algebra IIRC

[Pulse]

I understand (just about ), and I see what you mean - I've not written it correctly as it should have 'S' (or whatever other letter to denote the selling price), but the theory behind it sticks I take it?

[ATTAK Z]

ATTAK Z said:

Pulse said:

ATTAK Z said:

Pulse said:

43.18+32.12+0.1276+0.0957 = 75.5233

1st mistake ... you're adding prices to percentages ... not allowed ... it's like adding apples to oranges with the answer coming out in pears

you're looking for the number of apples (Selling price) not the number of pears (costs and percentage price rises) so keep everything in terms of apples

Edited by ATTAK Z on Tuesday 3rd May 20:31

I see what you mean, you can't do that, but that's how it's calculated, right? It's (effectively) a decimalised percentage, right? Just how you've used it, but I've not put the 'S' after them. In theory, it would work for any figures, right?

yes but you don't know the selling price, it's what you are trying to find so, you can't know a percentage of it either ...that's why you have to substitute S for the thing you are trying to find .... basic algebra IIRC

Pulse said:

I understand (just about ), and I see what you mean - I've not written it correctly as it should have 'S' (or whatever other letter to denote the selling price), but the theory behind it sticks I take it?

yep ... correcting your equation
43.18 + 32.12 + (0.1276 x Selling Price) + (0.0957 x Selling Price) = Selling Price

etc.



Next question

What is the significance of the number 1.6180339887 ?

Edited by ATTAK Z on Tuesday 3rd May 22:22

[Steve UK]

its the golden mean isn't it? something to do with errrrr life?

[davepoth]

Steve UK said:

its the golden mean isn't it? something to do with errrrr life?

The Golden Ratio. Pretty much everything that looks "right" will be in about that ratio somehow.