Pricing Efficiency and Increacing profit margins

[geirskogul]

ShellCO sells shells at $2.71 per shell with a tiered discount based on order purchase price:

Order Amount (pre-discount)	Discount%
$0-31.99	0%
$32-39.99	1%
$40-53.99	2%
$54-66.99	3%
$67-80.99	4%
$81-107.99	5%
$108-134.99	6%
$135-270.99	7%
$271-541.99	8%
$542+	9%

It costs ShellCO 0.12% + $0.50 for processing each order (after the discount%).
It costs ShellCO a flat $3.33 per delivery for each order.
Assume the remainder of each order is profit

What is currently the most cost effective discount tier for ShellCO? Is it possible to increase ShellCO's profit by altering its current discount table? If so, how?
How could you increase the overall profitability of ShellCO's bulk discounts without altering it's price per shell?

____________________________________________

I don't even know where to start... :| please help!

 

[Ishuda]

ShellCO sells shells at $2.71 per shell with a tiered discount based on order purchase price:

Order Amount (pre-discount)	Discount%
$0-31.99	0%
$32-39.99	1%
$40-53.99	2%
$54-66.99	3%
$67-80.99	4%
$81-107.99	5%
$108-134.99	6%
$135-270.99	7%
$271-541.99	8%
$542+	9%

It costs ShellCO 0.12% + $0.50 for processing each order (after the discount%).
It costs ShellCO a flat $3.33 per delivery for each order.
Assume the remainder of each order is profit

What is currently the most cost effective discount tier for ShellCO? Is it possible to increase ShellCO's profit by altering its current discount table? If so, how?
How could you increase the overall profitability of ShellCO's bulk discounts without altering it's price per shell?

____________________________________________

I don't even know where to start... :| please help!

You might make a table and see what your 'profit' is per shell at each level. Because of the flat rate cost per order (the $3.83 processing and delivery cost) you profit per shell will tend to increase as you sell more shells. Because you get less (discount increases and the 0.12% processing cost) your profit will tend to decrease as you sell more shells. Somewhere in there your profit per shell will be a maximum. You will want to structure your discount to encourage people to order that amount of shells.

As an example, say someone buys 2 shells. Income is $5.42. Costs are $0.51 processing and $3.33 delivery for a gross profit of $1.58 or $0.79 per shell. Do the math for selling 12 shells to get a gross profit of $2.36 per shell.

BTW: You would really need to know (estimate) what you would sell with a particular discount structure to know what your real profit would be. Also, 'twer me, I would state the discount in number of shells. That is buy 10 shells and get a 1% discount type of statement.

 

[geirskogul]

Denis:
Why were you given the problem then ?

I'm going to assume you intended for this question to be taken literally, rather than as a means to belittle.
I believe the purpose of this question was to allow students to self-assess their knowledge on this subject, prior to learning about it. Considering I didn't know where to begin, I figured that would've been the obvious conclusion. I'll specify next time, if you think this information is necessary to help me understand and solve this problem.

Ishuda:
You might make a table and see what your 'profit' is per shell at each level. Because of the flat rate cost per order (the $3.83 processing and delivery cost) you profit per shell will tend to increase as you sell more shells. Because you get less (discount increases and the 0.12% processing cost) your profit will tend to decrease as you sell more shells. Somewhere in there your profit per shell will be a maximum. You will want to structure your discount to encourage people to order that amount of shells.

Thank you very much for your response, Ishuda! I appreciate your help with this Shelling efficiency question

Okay, I believe I'm tracking. I've added the information you suggested to this table:

Order Amount (pre-discount)	Discount%	Shells Sold	Profit Per Shell (with the Discount)	Profit Per Shell (after processing cost)	Profit Per Shell (After delivery cost)	Final Profits Divided by amount of shells sold
$0-31.99	0%	0-11	$0-29.81	$0-29.48	$0-26.15	2.37
$32-39.99	1%	12	$32.19	$27.83	$24.50	2.04
$40-53.99	2%	15	$39.84	$34.56	$31.23	2.08
$54-66.99	3%	20	$52.57	$45.77	$42.44	2.12
$67-80.99	4%	25	$65.04	$56.74	$53.41	2.14
$81-107.99	5%	30	$77.24	$67.47	$64.14	2.14
$108-134.99	6%	40	$101.90	$89.17	$85.84	2.15
$135-270.99	7%	50	$126.02	$110.39	$107.06	2.14
$271-541.99	8%	100	$249.32	$218.90	$215.57	2.16
$542+	9%	200	$493.22	$433.53	$430.20	2.15

So, when selling shells in smaller quantities, to sell out of their stock they would have to make more deliveries (driving their profits down), which should impact profit margins at said quantities, correct? How do I calculate the best shell-quantity-per-delivery ratio? I'm not really sure if I'm explaining that question correctly—hopefully you understand what I'm attempting to ask. I tried dividing the profit per shell (after delivery cost) by the amount of shells sold, but I'm not sure if those numbers turned out correctly. I would've thought the bulk quantities generated more profit.

Do I need to redo the table with every single shell quantity?

 

[Ishuda]

...Okay, I believe I'm tracking. I've added the information you suggested to this table: ...
Do I need to redo the table with every single shell quantity?

First, no you don't need to redo the table. However, the columns are labeled wrong and it appears you have used a 12% rather than a 0.12% for your (partial) processing costs. As for the column labels, columns 4, 5, and 6 should be Profit (...) not Profit Per Shell (...) .

I get slightly different numbers possibly due to rounding errors but get essentially the same as you do except for the first row (0% discount) where apparently you used 11 sold and I used 2 sold. Note that, if you only sell 1 you actually lose money.

Looking at the table, your most cost effective discount tier is at the 8% level (ignoring the 0% tier which is an anomaly) which is the same thing I get. As far as affecting the overall profitability, one would have to have (or estimate) the buying structure and how it would change in order to do this.

 

[geirskogul]

First, no you don't need to redo the table. However, the columns are labeled wrong and it appears you have used a 12% rather than a 0.12% for your (partial) processing costs. As for the column labels, columns 4, 5, and 6 should be Profit (...) not Profit Per Shell (...) .

I get slightly different numbers possibly due to rounding errors but get essentially the same as you do except for the first row (0% discount) where apparently you used 11 sold and I used 2 sold. Note that, if you only sell 1 you actually lose money.

Looking at the table, your most cost effective discount tier is at the 8% level (ignoring the 0% tier which is an anomaly) which is the same thing I get. As far as affecting the overall profitability, one would have to have (or estimate) the buying structure and how it would change in order to do this.

I'm not sure what I was thinking when labeling those columns, I see what you're saying. Funnily, I mistakenly typed in 0.12% in when making this post—it was actually supposed to be 12%.

Out of curiosity, how would I go about estimating the buying structure so I could do that? Or is that not possible with the given information?

Thanks again

 

[Ishuda]

I'm not sure what I was thinking when labeling those columns, I see what you're saying. Funnily, I mistakenly typed in 0.12% in when making this post—it was actually supposed to be 12%.

Out of curiosity, how would I go about estimating the buying structure so I could do that? Or is that not possible with the given information?

Thanks again

With the given information it is not possible. But would the instructor want you to make any particular assumptions?

 

[geirskogul]

Well, we also needed to know where to start with solution;
it's quite a common question from a help site.

Well, luckily for me, "I don't know where to start...", was all that was necessary for Ishuda to establish a starting point and help me fully understand those questions. As I previously stated, in the future I'll include more background story for helpers like you, Dennis—college, teacher, course number, etc.

With the given information it is not possible. But would the instructor want you to make any particular assumptions?

Understood. As it turns out, the table was all the information that was required, and the response, "It is not possible to answer this with the given information because...", was adequate for a number of those questions.
Thank you again!