Not sure if this is the best place for this question but here it goes.

I am taking a class in engineering economics and he question that I am working on for homework is:

Firewood can be purchased during July for $55 a cord. If the purchaser waits until November, the cost of the same wood is $70 a cord.
Calculate the annual rate of return that the purchaser would receive by buying the wood in July instead of November.

I worked this as:

70-55/55= 27.27%

Anybody know if this is correct?

Please forgive me if I am wrong....
In order for you to show a rate of return on your investment of a $55 cord of wood, dont you have to show a profit (or a loss). Otherwise it is only a savings.
Unless you are working for a goverment, then you did earn a profit of $15 :cool:

Please forgive me if I am wrong....
In order for you to show a rate of return on your investment of a $55 cord of wood, dont you have to show a profit (or a loss). Otherwise it is only a savings.
Unless you are working for a goverment, then you did earn a profit of $15 :cool:

That is why I subtracted the 70 from the 55 save 15 or I guess you could look at it as a profit of 15. Not sure if this is right?

That is why I subtracted the 70 from the 55 save 15 or I guess you could look at it as a profit of 15. Not sure if this is right?When I was taking economics in graduate school 45 years ago, my professor would have willingly killed me if he thought he could get away with it, because I asked questions like these to muddy the water during his lectures:

What is the value of the interest I could earn on the money if I wait until later to purchase?
Is there a way to option the firewood today to lock in the price in the future?
Can I do like the Big Three and order ten million cords to get the ten million cord price, but only accept delivery on one cord?
Should I buy TWICE as much as my projected need and sell the excess in competition with my supplier when the price rises later in the year?
What will my cost of storage and maintenance be during the interim period?
Can I finagle the seller into storing the stuff for a small downpayment now and selling at today's price when I take delivery?
Can I unwind the deal if I decide not to use the fireplace?I'm kinda tired or I could go on and on. Even though I'm tired, a pitcher of margaritas would induce me to go on and on:lmao: :lmao: :lmao:

Not sure if this is the best place for this question but here it goes.

I am taking a class in engineering economics and he question that I am working on for homework is:

Firewood can be purchased during July for $55 a cord. If the purchaser waits until November, the cost of the same wood is $70 a cord.
Calculate the annual rate of return that the purchaser would receive by buying the wood in July instead of November.

I worked this as:

70-55/55= 27.27%

Anybody know if this is correct?


Actually, ignoring all of the other stuff presented here (after all, accountants assume complete information as the basis for all calculations, unless other info becomes available), you are incorrect, as the question asks for the ANNUAL rate of return, not just for the months July - November. Divide your answer by 5 (months) and multiply by 12 (for simple interest).

Adding a present value factor will more than double your enjoyment.

Actually, ignoring all of the other stuff presented here (after all, accountants assume complete information as the basis for all calculations, unless other info becomes available), you are incorrect, as the question asks for the ANNUAL rate of return, not just for the months July - November. Divide your answer by 5 (months) and multiply by 12 (for simple interest).

Adding a present value factor will more than double your enjoyment.


Craig, I can tell you took the CQE exam too!:rolleyes:

Actually, ignoring all of the other stuff presented here (after all, accountants assume complete information as the basis for all calculations, unless other info becomes available), you are incorrect, as the question asks for the ANNUAL rate of return, not just for the months July - November. Divide your answer by 5 (months) and multiply by 12 (for simple interest).

Adding a present value factor will more than double your enjoyment.


Huh? You lost me?

After some ethought this is what I came up with:

0= -55+ 70(P/F I*, 4) so you have to solve by trial and error and then interpolate then I multiplied the results by 3 for an annual return. . * *

Huh? You lost me?

After some ethought this is what I came up with:

0= -55+ 70(P/F I*, 4) so you have to solve by trial and error and then interpolate then I multiplied the results by 3 for an annual return. . * *


Ok, assuming the time period is July through November, inclusive, that is where I came up with the 5 months, instead of the 4 you use here. Your basic calculation in your first post looked OK to me, it just did not go far enough (it didn't annualize, a common and costly error for this type of problem on an exam).

My comment about present value was a tongue-in-cheek reference to a more complicated solution to the problem.

If my mumbo jumbo added to the problem, sorry.

Ok, assuming the time period is July through November, inclusive, that is where I came up with the 5 months, instead of the 4 you use here. Your basic calculation in your first post looked OK to me, it just did not go far enough (it didn't annualize, a common and costly error for this type of problem on an exam).

My comment about present value was a tongue-in-cheek reference to a more complicated solution to the problem.

If my mumbo jumbo added to the problem, sorry.

I see what you are saying and after talking myself thru the problem I think my second attempt is more accurate.

I have a fifteen year old gadget called 'HP12c' business calculator. Solves your problem and most of what Wes put forward in a breeze. Good toy to carry around.

OK guys, if you buy one cord of wood in July instead of in November, you have made only one purchase in the year. The number of months has nothing to do with the calculation. If there were a sliding scale between July and November and multiple cords were purchased throughout that period then the months would mean something. In this case, you made one purchase in the year and saved "X".

The question is did you save as Aaron calculated 70 - 55 = 15 / 55 = 27% or did you save 70 - 55 = 15 / 70 = 21%

Aaron's calculation shows the percentage of increase in the price of the wood. The second calculation shows the percentage saved on the price of the wood. Now we need to determine which calculation applies to the question.

The term 'rate of return", as pointed out correctly by errhine, indicates an investment was made and a return will be realized. Therefore you could conclude the wood is to be purchased and a profit will be realized. The question can then be re-phrased as "what percentage of profit will be realized by buying the wood in July and selling it in November?" Aaron's answer would then be correct.

The alternate question would be "What percent savings could be realized by buying the wood in July rather than in November?". The second calculation would apply here.

As usual, this is just my opinion.

Dave

I have a fifteen year old gadget called 'HP12c' business calculator. Solves your problem and most of what Wes put forward in a breeze. Good toy to carry around.

Unfortunately, those are rarely allowed into exams.

I don't think you get what I mean, Rachel. If you know the mechanics, manual calculation is good enough to solve most problems.

What I like you to know is the manual that comes with HP12c. It is well written and comes with many everyday life examples such as those put forward by Aaron or examples mentioned by Wes.

Regards.

I don't think you get what I mean, Rachel. If you know the mechanics, manual calculation is good enough to solve most problems.

What I like you to know is the manual that comes with HP12c. It is well written and comes with many everyday life examples such as those put forward by Aaron or examples mentioned by Wes.

Regards.


Harry-

I have a TI BAII which is pretty much the same thing. I did consult the manual but was unable to find what I was looking for.

Rachel-

Yes, these are actually allowed in exams now.

Not sure if this is the best place for this question but here it goes.

I am taking a class in engineering economics and he question that I am working on for homework is:

Firewood can be purchased during July for $55 a cord. If the purchaser waits until November, the cost of the same wood is $70 a cord.
Calculate the annual rate of return that the purchaser would receive by buying the wood in July instead of November.

I worked this as:

70-55/55= 27.27%

Anybody know if this is correct?

I just taught a financing class last quarter to business majors. The use of the HP12C calculator was required for the course. There were also tables in the book that could be used during homework and the exams.

There are two issues with the problem:

1. You do need to convert to an annual rate of return. In the context of Engineering Economics and Finance, all rate of returns are calculated on an annual basis.

2. You do need to take into account "compounding" of the interest. If we assume we went from July 15 to November 15, that is a four month interval. Thus this is one interval out of 3 for the year. The calculator or the net present value tables can be used to get that answer.

Actually, ignoring all of the other stuff presented here (after all, accountants assume complete information as the basis for all calculations, unless other info becomes available), you are incorrect, as the question asks for the ANNUAL rate of return, not just for the months July - November. Divide your answer by 5 (months) and multiply by 12 (for simple interest).

Adding a present value factor will more than double your enjoyment.

Craig H. came the closest to the correct answer. The only change is that the divide is by 4 months.

The Annual Rate of Return = (70 - 55)(12)/(55*4) = 81.8 %

The problem did not state monthly compounding, nor did it give a discounted rate of return in order to determine a present value. The annual rate of return is simply the rate of return for the four months, multiplied by three.

As previously noted, it would have been more accurate to state purchase in July for $55 and sell in November for $70.

Since there are no dates given for the July and November months, one must assume the same date with each month, so the time is just four months.

Wes R.

Those who are interested may like to look at some hp12c tutorials at this site:
http://www.educalc.net/137015.page

I just taught a financing class last quarter to business majors. The use of the HP12C calculator was required for the course. There were also tables in the book that could be used during homework and the exams.

Wow - I stand corrected. Seems things have changed in the last three years - all I ever got for *any* exam were the tables and a simple, non-programmable calculator with no real functions (sine and cosine being pretty much all that was allowed).

Craig H. came the closest to the correct answer. The only change is that the divide is by 4 months.

The Annual Rate of Return = (70 - 55)(12)/(55*4) = 81.8 %

The problem did not state monthly compounding, nor did it give a discounted rate of return in order to determine a present value. The annual rate of return is simply the rate of return for the four months, multiplied by three.

As previously noted, it would have been more accurate to state purchase in July for $55 and sell in November for $70.

Since there are no dates given for the July and November months, one must assume the same date with each month, so the time is just four months.

Wes R.

OK, same date each month is acceptable to me, but it should be stated in the problem (ahem). Anyhow, the mechanics are the same.

FWIW, I think some folks "freeze up" when they see phrases like "annual rate of return" or "return on investment" (aka ROI), much like other folks "freeze up" when we say mean instead of average. The concepts are not really that hard, but the mental block goes up.

Its often as though statisticians and accountants (finance folks too) are seen as some kind of black artists. The professional equivalents of the dreaded boogie man.

:magic:


Of course, JMHO

Thanks for all your input. I will let you know what happens when I find out what the right solution is.

I am leaning towards 0= -55 + 70 (P/F i*,4) and end up interpolating, based on what the Professor said.

Craig H. came the closest to the correct answer. The only change is that the divide is by 4 months.

The Annual Rate of Return = (70 - 55)(12)/(55*4) = 81.8 %



Wouldn't it be more appropriate to compound the return, rather than simply multiply by three.
After 4 months you would have
$55*1.2727 = $70
After 8 months you would have (assuming you reinvest the whole amount at the current rate of return)
$70*1.2727 = $89.09
After 12 months, you would have
$89.09*1.2727 = $113.39

That is a return of (113.89-55) = $58.39,
or 58.39/55 = 106%

Tim F

Wouldn't it be more appropriate to compound the return, rather than simply multiply by three.
After 4 months you would have
$55*1.2727 = $70
After 8 months you would have (assuming you reinvest the whole amount at the current rate of return)
$70*1.2727 = $89.09
After 12 months, you would have
$89.09*1.2727 = $113.39

That is a return of (113.89-55) = $58.39,
or 58.39/55 = 106%

Tim F


Tim,

Depending on the situation, you certainly could. However, many times there is an interest rate that is given that should be used. For instance a company may have a threshold of a 15% per annum payback on capitol expenditures.

In this case, where the question comes from a basic engineering economics class, where it appears that the basic concepts are being explored, the simple (interest) approach is likely best for now.

BTW, when present/future value is used to pitch a project, six sigma or otherwise, it is always a good idea to discern what interest rate was used to calculate the payback. It is quite easy to inflate (or decrease) the perceived value of a project by simply playing around with the rate. As with statistics, it is a good idea to take a look at where the figures (and data) come from.

I am glad to see that we are having this discussion at the Cove. One of the problems with our profession is a general lack of ability to speak this language, IMHO. Sell quality - quality sells.

To bring closure to this thread, could you let us know what your professor says is the answer to this question?

Hi Aaron,

If you choose to compound interest monthly, then the annual interest rate is 74.5719%

Here are the calculations for that rate:
July 1 $55.00
August 1 $58.41788
September 1 $62.04815
October 1 $65.90402
November 1 $69.99951

Note that I have carried the fractional portions of the dollar earned each month, which banks would not do, if they compounded monthly. Since we are only dealing with the 55 and 70 values.

I too, am interested to see what the "official" answer is.

Wes R.

To bring closure to this thread, could you let us know what your professor says is the answer to this question?


I will do that. My class is next week, so I will pst after I find out.

It is really interesting, I never know or ever paid attention to the compound interest if it is compounded daily or monthly, until I looked into this question,

if it is daily compounded, then the rate of return is

55*(1+X/365)^120=70, X=.734272, or 73.4%

if it is monthly, the the annual return is .745741, or 74.6%.

How does it work with banks?

Funny thing is I tried to look into MS Excel for information, and found out, they use 360 days for one year, will anybody tell me why, given that with computers so widely used in these days, why not use 365 or 366?

Thanks

It is really interesting, I never know or ever paid attention to the compound interest if it is compounded daily or monthly, until I looked into this question,

if it is daily compounded, then the rate of return is

55*(1+X/365)^120=70, X=.734272, or 73.4%

if it is monthly, the the annual return is .745741, or 74.6%.

How does it work with banks?

Funny thing is I tried to look into MS Excel for information, and found out, they use 360 days for one year, will anybody tell me why, given that with computers so widely used in these days, why not use 365 or 366?

Thanks

Hi Roland,

Interest can also be compounded instantaneously or continuously. Do a search on the internet for "instantaneous compounding interest."

Note that the resulting amounts are still finite.

Wes R.

Well here is the answer, the formula I was using 0= -55 + 70 (P/F i*,4) and end up interpolating,was correct, however, you need to multiply the answer by 12 months to get 74.6% as the nominal rate of return, but the effective rate is i* =(1+.746/12)^12 -1= 106.2%.

Once again thanks for your input on this problem, there were a couple of people that were pretty close to the correct answer.

Well here is the answer, the formula I was using 0= -55 + 70 (P/F i*,4) and end up interpolating,was correct, however, you need to multiply the answer by 12 months to get 74.6% as the nominal rate of return, but the effective rate is i* =(1+.746/12)^12 -1= 106.2%.

Hi Aaron,

Thank you for posting the instructor's answer. Can I make an investment in this business?

Wes R.

... The use of the HP12C calculator was required for the course.

I was wondering how long the HP12C has been around (I know it's been a while). Actually, this year is it's 25th anniversary! HP introduced it in 1981, priced at $US 150. It's still being sold -- I recently saw them at an office supply store for $US 82. A couple of years ago HP introduced the 12C Platinumn Edition, which for a few dollars more adds faster speed, much more program memory, several new functions, and algebraic entry mode :biglaugh:.

http://tinyurl.com/ksxo5

How many other business or consumer products (a) have been in continuous production for 25 years, and (b) cost 1/4 their original price after adjusting for inflation?

How many other business or consumer products (a) have been in continuous production for 25 years, and (b) cost 1/4 their original price after adjusting for inflation?How about personal computers? Back in 1982, I paid $1,500 for an 8086 powered PC with TWO 360K floppy drives, 15 inch amber monochrome screen, 10 meg hard drive. Today, I see Dell has a special (newspaper ad) for $299 with an 80 gig hard drive,
Intel® Celeron® D Processor 325 (2.53 GHz, 533 FSB),
CD-RW/DVD ROM drive, 17-inch color monitor.

I was wondering how long the HP12C has been around (I know it's been a while). Actually, this year is it's 25th anniversary! HP introduced it in 1981, priced at $US 150. It's still being sold -- I recently saw them at an office supply store for $US 82. A couple of years ago HP introduced the 12C Platinumn Edition, which for a few dollars more adds faster speed, much more program memory, several new functions, and algebraic entry mode :biglaugh:.

[/B]How many other business or consumer products (a) have been in continuous production for 25 years, and (b) cost 1/4 their original price after adjusting for inflation?

Hi Graeme,

Remember the HP-35, HP-45 and HP-65 calculators?

I bought an HP-41C, then started buying wand, modules, etc. for it. I put a lot of dollars into it, it is an excellent calculator, and still have it. I also have two HP-11C that I won back in the early 1980's. They both work and very seldom do I need to replace batteries.

Wes R.

I was wondering how long the HP12C has been around (I know it's been a while). Actually, this year is it's 25th anniversary! HP introduced it in 1981, priced at $US 150. It's still being sold -- I recently saw them at an office supply store for $US 82. A couple of years ago HP introduced the 12C Platinumn Edition, which for a few dollars more adds faster speed, much more program memory, several new functions, and algebraic entry mode :biglaugh:.

[/B]How many other business or consumer products (a) have been in continuous production for 25 years, and (b) cost 1/4 their original price after adjusting for inflation?

I have seen the HP12C for ~$30.

How about personal computers? Back in 1982, I paid $1,500 for an 8086 powered PC with TWO 360K floppy drives, 15 inch amber monochrome screen, 10 meg hard drive. Today, I see Dell has a special (newspaper ad) for $299 with an 80 gig hard drive,
Intel® Celeron® D Processor 325 (2.53 GHz, 533 FSB),
CD-RW/DVD ROM drive, 17-inch color monitor.

Wes,

I agree that personal computers as a class are a vastly better value now that they were 25 years ago. On the other hand, there is no specific computer model that was manufctured then that is still commercially available, unchanged, today. Most of the companies don't even exist. The big names then were Radio Shack, Apple, Commodore, Kaypro, Amiga, Osborne, Atari, Texas Instruments and a handful of others. Of those companies, only Apple is still selling computers under their own name. The leading OS was CP/M, and Microsoft was still in Albequerque. Note that the IBM PC is also 25 years old this month, but at that time it was a latecomer in a crowded field.

Any other candidates for a specific product that is still being sold, unchanged, after 25 years?

Graeme

--

Hi Graeme,
Remember the HP-35, HP-45 and HP-65 calculators?

I remember them, although I did not use them much. a co-worker at my previous job has a HP 45 that he uses every day. Personally, I favored the Texas Instruments calculators, with my favorite being the TI-59 programmable. Cost was one factor (where I worked at the time helped) and another was laziness - it was too much brain strain to remember the RPN I had learned in college computing classes and apply it to a calculator every day.

BTW, the TI-59 calculator probably still works but battery packs are no longer available so it's buried in a box in the storage room.

Graeme

I remember them, although I did not use them much. a co-worker at my previous job has a HP 45 that he uses every day. Personally, I favored the Texas Instruments calculators, with my favorite being the TI-59 programmable. Cost was one factor (where I worked at the time helped) and another was laziness - it was too much brain strain to remember the RPN I had learned in college computing classes and apply it to a calculator every day.

BTW, the TI-59 calculator probably still works but battery packs are no longer available so it's buried in a box in the storage room.

Graeme
It takes some time to get used to Reverse Polish Notation (RPN), but I use it, and think it has fewer keystrokes for calculations with more involved terms. I have the HP-41C rechargeable battery pack, but it has not held a charge for years. Now I just use the N batteries, although they are sometimes hard to find.

The TI-59 was quite a powerful calculator. One girl that worked for me had the printer with it. I was impressed with the matrix function capabilities.

Wes R.