Відео

Thank you!

In this example, for the "Lawn Guy" mower, we do have 2 annuities. One goes from yr 1 to yr 10, the other goes from yr 11 to yr 20. We then find the 'PW' of each of these annuities, and their PW values are placed at yr 0 and yr 10. The value at yr 10 must then be 'moved' to yr 0 using the P/F factor. Watch the video again to better understand these details. From your comment, I suspect you might not be aware that the value of an annuity can also be positioned at it's 'beginning'...? Perhaps you should also explore some of my other videos in my Cash Flows playlist.

Good observation. I'm writing the normal way and I'm using software to horizontally flip the image.

Happy to help! Good luck in your course!

Glad you think so! Good luck in your course!

Ha! Thanks for the nice comment!

You're welcome!

Assuming your company is profitable, the best method for converting expenses(such as the ones you describe) into 'after-tax' expenses is to simply multiply them by (1 - t), where t is the company's tax rate. Multiply any revenues by the same (1 - t) factor. Or, if you like, you can gather the expenses and the revenues into a net monthly cash-flow and just multiply this 'net' amount by (1 - t). I hope this helps!

Yes. As long as you follow the rules for drawing the flow lines and potential lines, the 'ratio' of the number of flow channels to number of potential drops should be approximately the same.

This example is focused on depreciation for taxes and accounting purposes. If you are concerned about market-value of an asset, then you cannot use a simple mathematical method such as the method described in this video.

Glad you think so!

Good question. Google "compound interest factor tables". There should be lots to choose from. These tables can also be found in an Appendix to most Finance or Engineering Economics textbooks.

Happy to help! Good luck.

Yes! However, 0.5% is the same as 0.005, but I can see the potential for confusion! Thanks for the comment.

You make a good point. I could have given the formula for the (A/G, i, N) factor! It probably comes up somewhere else in one of my other videos - BUT, for the benefit of anyone looking for it...it's a complicated one: [ 1 / i ] - [ N / (( 1 + i )^N - 1)] There are other forms, but this is the most compact. I will "pin" this comment to the top of the list so anyone looking for the formula can hopefully find it. Thanks for the comment. Good luck on your Board Exams!

Thank you for the encouragement! I'm working on it! I hope you've had a chance to explore all of my playlists for Engineering Economics. I should have videos coving all of the main topics. www.youtube.com/@EngineeringEconomicsGuy/playlists

Thanks for the comment!

Good observations. Just to clarify a bit; declining balance has a depreciation 'rate', but straight line depreciation is a constant dollar amount. I'm sorry but I don't have a video for unit of production or other depreciation methods... I should make one!

@@EngineeringEconomicsGuy makes sense thanks! Just had my midterm, the existing videos made a huge difference already! Look forward to the other ones hahah

Glad my videos have been helpful! Good luck in the rest of your course!!

Great question. 6% is what we call the NOMINAL rate. Since the Nominal rate is quoted as "compounded monthly", that tells use we need to divide by 12 to get a monthly rate which is the true mathematical rate we use in the time value of money calculations...this is just how the financial world quotes interest rates. You just need to learn how to interpret the words. Please note, when we use a rate of 0.5% interest (i), we must use a value of N measured in months! Please search for my video explaining "Nominal and Effective Interest Rates".

The key is the amount of money invested. Lathe 1 only uses $100k, and lathe 3 uses $300k. If you buy lathe 1, what are you going to invest the unused $200k in?? We assume you will invest it in a project that earns the MARR. So, its better to invest all $300k in lathe 3...this gives a better return than $100k in lathe 1 and $200k in 'something else' that just earns the MARR. Watch the video again starting at around time 10:00... hopefully, that helps!

You are so welcome!

Thank you very much for the nice comment!

Very reasonable to not understand that! The explanation has its own video! Watch my video on Nominal and Effective interest rates. How interest rates are quoted follow rules that you just need to learn!

@@EngineeringEconomicsGuy Where can I get those videos please

Start with this video: ua-cam.com/video/aT1n_bbQQbM/v-deo.html Then I invite you to explore my video playlist titled: "Interest". ua-cam.com/play/PLcfz9wmNxKqjTG5dsXDnIyUT8mCtA44Wu.html You will need to understand how to manipulate nominal and effective interest rates before you can move on with more time-value-of-money calculations. Good luck!

You are 100% correct!

Glad it was helpful!

You're welcome 😊

It is a good idea to clarify this point - thanks. Always use the effective interest rate that matches the frequency of the payments in calculations. ..meaning, if your problem has monthly payments you must use the effective monthly interest rate. The nominal rate is usually the information you are given in the problem, but this needs to be converted to the effective rate before doing the calculations. I hope this helps! Please explore some of my other videos to familiarize yourself with the procedure.

I'm glad you're thinking about the method!

Ha! No, I'm using software to horizontally flip the video.

This would be a different type of problem. If the "shape" of the cash flow diagram is the same as this example but with an unknown 'G', then you can still create a 'time-value-of-money' equation that is of the same form as this example. To solve for the unknown G you would need to be given the value of P.

You're so welcome! Good luck in your course.

i got it sir . please don't waste your time explaining this . thank you

OK - thanks! Good luck in your course!

I think what you are asking is better described as the "net" cashflow for a given time period. For year 4 the net cash flow is a down arrow of -$7500 (-5000-2500). For year 7, the net cash flow is a down arrow of $500 (+2000-2500). For year 1, the net cash flow is just a down arrow of -$2500. The purchase that occurs at time t=0 is NOT a year 1 cash flow. For time value of money calculations (i.e. when you start calculating compound interest), you will treat all down arrows as negative cash flows and up arrows as positive cash flows. I hope this helps!

So nice of you! Thanks!

Excellent question, and excellent observations! It does given the appearance of lying when interest rates are quoted using the nominal rate. I had the same feeling when I first discovered this. There are 2 answers to your question; a simple answer, and a much deeper math-based answer. Simple answer: Quoting a nominal rate is the convention the financial world uses - you just need to learn it. Better answer: The practice of quoting a nominal rate reveals it's "correctness" when the number of compounding periods approaches infinity! (?!?) Have a look at my video on Continuous Compounding. Jacob Bernoulli actually discovered the value of 'e' (Euler's Number), through an exploration of nominal and effective interest. The Wikipedia entry for Euler's Number also has some good info. Hope this is what you were looking for!

@@EngineeringEconomicsGuy excellent! Thanks for responding so quickly too. Because this video is several years old, I hadn't held out much hope that you'd respond at all, but I checked and saw that you had recently posted others so I took a chance you might still be around. Im glad I did! Your range of topics looks fascinating to me. I'm a Physics & CompSci guy now running an engineering consulting firm, and while my background gives me the ability to handle the mathematics of business, I often bump into the fact that there is often more *to* the quantitative side of business than just the math. It often occurs to me that if I was going to do it all again, I might choose a technical financial education route, rather than a so-called STEM one. I love finding where deeper math influences real-world finance and accounting just as much as it does the world of physics and computation. Good stuff; I'll definitely follow the pointers you gave; and you have a new subscriber. Cheers!

Good question! Incremental IRR can still be used for the situation you describe. You need to evaluate the the option with increasing annual savings using other time-value of-money techniques. There is a formula for patterns of cash flows that increase by a constant amount (an arithmetic gradient), or a constant rate (a geometric gradient). I have videos on these methods if you want to explore my channel, HOWEVER, I will warn you that solving for the "rate" is never easy in these types of problems. I would recommend using the built-in IRR function in excel - I also have a video on that! Good luck!

Good question - the answer is 'basically' NO. Present Worth and Annual Worth don't really provide a fair comparison when the investment options are mutually exclusive AND, most importantly, they have different initial investment amounts. For instance, if one option has an initial investment of $100 and another option has an initial investment amount of $1000, the Present Worth or Annual Worth methods will give you a dollar-value-answer for the PW or AW of the investment but you can't make a decision based on these dollar amounts. You CAN calculate the rate-of-return on these investments and compare them to the MARR (+ an assumed rate-of-return equal to the MARR on the 'difference' between the dollar amounts of the investments (!) - whew!). This logic is challenging but I think you can get there - watch the video again and pause during my explanations of the logic! Good luck!

Well... yes and no. Yes, you are doing a good job thinking about how to best manage your money (!), but you've actually changed the problem's parameters by buying two of the same things. The key assumptions underlying the Incremental IRR method are: 1) the options are "mutually exclusive" (you choose one -only), and 2) the difference in the dollar amount of the investments is assumed to earn a return equal to the MARR (i.e.- if you don't use all of your 'budget', the left-over money is assumed to be invested somewhere else and it is assumed to earn the MARR). I have other videos on Incremental-IRR that might be helpful. It might seem like a strange way to evaluate investments but there is some good logic behind it! Perhaps it would be useful to think of this method as something used by large companies making lots of investment decisions. Good luck.

You would compare lathe 3 and 4 since lathe 3 is the current best-option. If the Incremental IRR for lathe 4 (compared to lathe 3) was less than the MARR, then lathe 3 would remain the leading choice. If there was a lathe 5, you would then calculate the Incremental IRR for lathe 5 (compared to lathe 3)... then repeat this process, always comparing the current leading choice to the next option. I hope this makes sense.

@@michaeljustason1144 Thank you good sir, phenomenal explanation.

Indeed - an excellent explanation!

Happy to hear this! Good luck in your course!

Or inflow = outflow?

Yes and no. Yes, for these types of problems we are equating inflow and outflow, BUT, we do it using the principles of the time value of money... fancy way of saying we account for the effects of compound interest associated with the timing of each cash flow.

@@EngineeringEconomicsGuy Thank you for clarification!

You are most welcome!

You are absolutely correct! I will pin this comment to the top for others. Thank you.

This question is extremely important. For Incremental IRR you must start the comparisons with the alternative with the lowest initial investment. The Incremental IRR for each subsequent alternative then becomes an implied comparison between the Incremental Return on the next highest investment and the MARR. The question being answered is "is it better to choose the higher investment alternative, or is it better to invest that "incremental amount" in some other unknown project that earns a return equal to the MARR. This is sometimes tricky logic for students. Please watch the video again and listen closely to the dialogue; I do explain it. Hopefully, the idea clicks for you. Good question.

Sorry, I didn't see you comment for some reason. You definitely need to know the depreciation rate! Maybe your question uses another clue such as the "Asset Class"; this would be an indirect way of specifying the depreciation rate...

Great to hear! Thanks for the comment.

You are so welcome!

Good question and a common error. Draw a cash flow diagram. Remember to start counting years at the number zero! The A/F for 100 should have n=1, and the A/F for 200 should have n=2. I hope this helps!

@@EngineeringEconomicsGuy, yes, it does. Thank you. I think it is safer to move them all to PW, like you did, or some FW prior to applying either A/p or A/F. Sir, I owe everything to you as far as engineering economics is concerned. Thank you so much...

Thanks a lot!

This problem is illustrating how to deal with cash flows that occur MORE frequently than the compounding period. The point of the example is to show at you MUST simple add the dollar amounts of the payments together since there are no interest calculations occuring at the time of the payments...so it is correct to simply add the numbers. Watch the video again and listen to the explanation very carefully. The video is correct. Perhaps the purpose of the video is what is unclear?

I get you, because the video is using a lump sum approach (assuming the bank does nothing with the first 2 installments of each quarter), but some other models, like yours probably, require you to convert the less frequent compounding period interest rate to what is called an "effective monthly interest rate", which the bank applies to every monthly payment despite say a quarterly or semi-annually compounding period. They are two distinct calculations; which one applies to your course really depends on the lecturer.