ENGR 221 – Class 21 (Incremental IRR Analysis) 10 Oct 2016

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” s look at a couple of announcements and then we need to get into excel excel stuff pretty quickly. Because. Today s exercise is a little bit lengthy please be to bring your computer again on wednesday. Because we re going to be having quiz.

2. And it s an excel question. And so it ll be difficult to do that quiz. Without a computer your next assignment homework.

9. If you look at the schedule. That was supposed to be due on friday. The friday of this week and actually the lectures are still on schedule and i think you probably could complete it by friday.

But i didn t want it to be too much of a rush and so i i added the weekend. So that you could submit that on monday. So just i guess. That s an encouragement not to delay the assignment submission.

Don t delay getting started on that assignment because we ll have everything completed by wednesday that you need to know for that also just another reminder about the project and the project is due on the 18th of november that s before thanksgiving begins. And so get started on one of the two projects that you re doing well you re not doing two projects. You have your choice of doing one project among two alternatives. Okay today.

We re going to be talking about incremental irr analysis. And just to set the stage for that let s review. The spreadsheet that came up in the last class period in the last class period. Where you are comparing two projects.

You re discounting them. According to an interest rate and trying to pick out. Which is better now. The main point of this was just to illustrate that the one that has the best irr is not necessarily the one that has the best present worth.

And what you can see right now is that project a has the higher irr. But project b has the best present worth and so project b is the better alternative. But i ve changed the i ve added what s called conditional formatting. So that whichever of these two is highlighted is the one that s the highest so if i change the interest rate that things are discounted at that s going to change.

Which alternative is best so let me illustrate if these people had borrowed money at 3 interest. Then that makes option b. Even better. But if they had to borrow money at 10 interest suddenly option.

A is better you can see that it s highlighted because the some of the present works here is five thousand three hundred dollars compared to about one thousand dollars. And so the main point here is that depending on how expensive. It is to borrow money and therefore how much we should discount future amounts that changes. Which project is best and so i point that out because there s a figure.

I m going to be showing you in a minute that s actually a graph of this relationship. And it shows that the crossover point the crossover point being when these two projects are equal to each other so. At 10 percent project. A is better at nine percent.

It s still better at eight percent. But then at a certain point project b becomes better all right so that s what this figure is showing. It s showing you re comparing two alternatives and when you re mar is low let s say 010. Then option b has the better present worth of the two alternatives.

But then you in creates. The lar as you can crease the interest rate that all of the future revenues are being discounted at their crossover point at. Which the two alternatives are equal to each other and then as you further increase interest rate. Then how option a is more attractive than option b.

And that s the opposite of what was true prior to that crossover point so. The concept here is you re not supposed to pick the project that has the highest irr. But you re supposed to try and analyze is the additional investment amount between two alternatives is that increment going to earn greater than the mar and so when you re comparing projects. The the revenues that you re supposed to be discounting are at the mar and not at the irr and this is a point of confusion.

Because there are two interest rates in problems like this you re you ve got a marv the minimum attractive rate of return. Which is you can think of as the rate that you re borrowing money at or the firm s minimum acceptable rate. But then you re solving in many cases for another interest rate and so one of the common mistakes. I ve seen in the past is that students think the irr is what you re supposed to do the discounting at but it s not it s it s the given marv that you discount the amounts out and so today in the class.

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What we re going to be doing is looking at the increment and on the backside of the in class exercise from friday. You got the practice and just calculating the incremental amount. But we didn t do the incremental analysis. Yet so here s an illustration of an incremental analysis.

We have two options and like i mentioned last time. You have the cheaper option on the left side and the more expensive on the right so that when you subtract them. And see you have an incremental cost in comparing b. Versus.

A so option b is 13000. More expensive and then the incremental annual revenue is four thousand two hundred and five. So what we want to do is we want to find the irr of each alternative. Just as an initial screening tool.

Remember. It s it s a way for us to say whether or not the project is justified with the criteria being that the initial screening is is the irr better than the mar and so both of these alternatives. A and b passed that test because both of them have an internal rate of return that s been 10. So we can t just immediately reject them yet.

But an incremental analysis is asking the question is the more expensive alternative justified and so when we find the internal rate of return on the increment this. 114 is saying that extra 13000. That it costs to do option b. Instead of option.

A that extra amount is going to yield a return of eleven point four percent. So now this goes back to the question of what if you could go to the bank and borrow money at one rate and then take it somewhere else and invest it at a higher rate. This is one of those cases where what you re doing is you re borrowing money at 10 percent to finance that extra 13 thousand dollar investment and so the criteria is should you do the project yes or no yes. You should choose option.

B because even. Though it s more expensive that extra amount that extra 13000. You re going to earn a higher return on it then it costs you to borrow the money so of course anytime. You can borrow a dollar and make more in return than it costs to borrow you should do as much of that as possible that will maximize your profits.

So here s the concept. The criteria being that if the internal rate of return of the difference is greater than the mahr. Then the additional investment is justified now you ll notice that we ve also calculated the present worth and the present worth says do option b. And that s an ironclad analysis tool.

It s always going to be the case that whatever has the highest present worth is the best alternative. But just knowing that just knowing which alternative is best doesn t actually tell you what the rate of return on the increment is and that s something that you know a superior might want to know that s something that you might want to know before you go to the bank. So calculating the ink that ll internal rate of return tells you what s the spread between mark and the return you re making on the incremental amount. And so there may be intangible things that have to be.

Considered it s not always just about the finances and so. 113. Isn t that much far away from ten percent and so. If option b is somehow less can meet maybe.

The question that the person making the decision would have to ask is you know is it worth making that extra one point four percent above them are or should i just go with option a there might be environmental consequences. That can t quite economically be quantified. There may be social costs or human costs that you can t quite put into dollar terms. And so that s an example of why you shouldn t just always pick the present worth as your means of analysis.

This incremental internal rate of return is is a way of getting a little bit more information when you compare projects and so. It can be used to choose alternatives. And it s more it s a it s a richer source of information than just present worth. Analysis by itself.

So here s the illustration done in a little bit more complex. Way here we have five alternatives and what you ll notice about these five alternatives is number one they re sorted in order of cheapest on the left. Increasing original investment amount a through e is sorted by year zero expenses. How much you have to invest it first now when you have more than one alternative.

This is a tricky thing you have to know what the two comparisons are going to be so the first thing you do is you compare b versus. A and this column h. That s shown here b. Minus.

A that s the comparison of the two alternatives now you can see up in cell b1. That the larr for this is 18. And so. When we re comparing b.

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And a since the a promotion internal rate of return is 22. And that s that tells us yes. We should do option b b. Is better than a and so what we can do now is we can reject a we don t have to consider it anymore.

We don t have to compare any of the all other alternatives to 2a because option b. Our new favorite at this point. So you ll notice that here and call them. I it s saying that the comparison.

Now is c versus b. So c. Minus b. And so all these amounts in this column are simply the amounts from option c minus.

The amounts from osh me option. B so you can see it s an extra. 5000 and then it gives this revenue of 2200 each year and so look at the incremental internal rate of return there you re going to earn a forty three percent return on that extra amount of what c cost versus what b costs and so applying the criteria here it s greater than the mar and so the conclusion is yes we should do c. So now we reject b and c.

Is our new favorite and so now you ll notice in column j. Here. The comparison is d versus c. We calculate the internal rate of return.

It s zero. There s actually no return on investment there because if you add up all of these amounts. It s ten years of five hundred dollars per year. Which is equal to the five thousand so zero percent is less than the mar.

So we reject option d. Now. This is the place where students always make mistakes. Often they don t always make the mistake.

But often is knowing what the next comparison should be like which two alternatives do you compare. When you ve rejected one of them. So here. We ve just rejected alternative d.

And so. The question is what should be our last. Comparison. We still haven t analyzed e.

But should we analyze option e. To something. We ve just. Rejected.

No of course. Not we already said. We re throwing d in the garbage. We don t want to do option.

D. No. Good. So.

What you have to compare. Alternative e. To is the last option. That was attractive and so that s why this.

Final column here column k. Is e. Versus c. What i m.

Doing is i m. Comparing alternative e. To alternative c. Because c.

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Was. The yet was the last s. That we had it was the the final thumbs up before we got to this option d. That had to be rejected.

And so when you calculate the internal rate of return this time it s 14 which you know at least that s better than 0. But it s not as good as the mar. So we have to reject alternative e. As well.

Therefore our final conclusion is that option c. Is the one that we should pick because it was the it was the most expensive option that was justified and remember we want to do the most expensive option. That s justified because we re going to earn a bigger rate of return on that original investment amount so all of the incremental costs are more than balanced out by the incremental revenues. So any questions about the sequence of comparisons like how do you know which one to reject and which one to use is the next comparison compare.

A and eat no once you reject an alternative. You never have to come back to it i ll let me put it this way. I ll never ask you to calculate the second best option. You know maybe you know there is a scenario where maybe your boss would want to know well how does you know dell compared to lenovo i maybe you know it s conceivable that that somebody might ask you to do that but i want it s good question are there any other questions before we move on ok so again the principle here is spend every extra dollar that will bring a return greater than the mark so pick the most expensive alternative.

That s justified by analyzing the increment today s in class exercise. Now the table. That s on the screen. There is showing let s see 1 2.

3. 4. 5. 6.

Alternatives that you re comparing each of them lasts for 10 years. Just to keep things a little bit more simple. They have the same useful life. And you re going to have to first of all figure out through internal rate of return analysis.

If any of them should be rejected right off the bat. Because remember that might cut down how many options you have to analyze if you can just reject some of them straight away now today i m going to ask you to submit your file on submit your file on mu online. And for every student who does that who uploads theirs their excel file to mu online. I m going to give you five bonus points in the homework category so let me show you where you can get at that if you go to just our website.

You know the mu online login it ll come up on the course web page as an assignment. Now there s no penalty. If you don t do it. It s just you don t earn those five bonus points for doing it and it s just going to be all or nothing.

So you go to 221 and it s in the course content folder. If that s not the one that comes up immediately. It s here on the left side course content you scroll down. And it s the 10 october incremental internal rate of return analysis click there and then you can upload a file you just browse my computer and get at the excel file location of where you save your work.

Ok. So everyone has a copy of today s in class exercise. Right yeah. It s open until.

I think the end of class. So you know i d like you to submit what you ve got at the end of class. I think it s one o clock. That it s going to close ok.

So you re comparing these options. These six options. The first thing you should do is just calculate the irr of each and then the the next thing that you do after that just following the steps you got to list them in order of what s the cheapest on the left and increasing cost so right now. It s not in order right now.

It s sort of randomly distributed so you put it most expensive on the cheapest on the left. Most expensive on the right and then go through that incremental irr analysis and let me show you the the way it looked on the previous slide. This is sort of how you re going to have to set it up you ll have one series of problems. That s the amount like this.

So. That you ll have the amounts in order. And then skip a cell as skip a column and then in the subsequent columns is where you re doing the comparison. You know one the other one to calculate the increments.

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So i ll leave this slide up just. So you have an idea of what the formatting should look like as you go through and do your work let me step you through a description of why you do one comparison versus. Another. Okay.

So here is the data to begin with and i ve ordered it in terms of the cheapest on the left. And gradually increasing to the most expensive and the first approach is the initial screening. So you calculate the internal rate of return for every alternative and of these you ll notice that only one has the internal rate of return less than the lahr. The komatsu equipment.

And so right now we can immediately reject the komatsu equipment. None of our additional comparisons have to include that alternative. So then here in column. I i m comparing the caterpillar and deer and so i m comparing the caterpillar cat deer.

And so the incremental cost is twenty five thousand seven hundred and then the incremental revenue is an additional four thousand four hundred each year. So then i calculate the internal rate of return on that and it s only eleven point two percent. So that tells me since that eleven point two percent is less than the mar. Which is twelve that tells me i should reject the more expensive alternative.

So cat is not better than deer. Because the additional expense of the cat is not justified. So deer remains my favorite so i go on up the chain now i m looking at hitachi versus deer. So hitachi versus deer that s what s in column j.

Calculating the irr of it eighteen. Percent is higher than the mar. So that tells me now that the additional amount that the hitachi costs is justified. So now hatake is my current champion.

It s my favorite. So all be a comparisons you we reject one option keep a favorite for the next one so volvo versus hitachi. Now by the way. I don t know whether i m going to accept.

Volvo or whether i m going to keep itachi and so i can t necessarily label all of the columns at the beginning. Because you can only label the next column. Until you know the result of the one that before it and so volvo hitachi. The volvo fails since the internal rate of return actually is negative here.

You ve only got seven thousand dollars in revenue over the ten years offsetting. The fifteen thousand dollar cost. And so that s a bad investment and so then my last comparison. The atlas versus hitachi.

The internal rate of return this time at least. It s positive. But still it s below the marr and so i have to reject the atlas and it s the hitachi that comes out on top and so. The hitachi is the best option.

The second best option was the last one that i said okay before i decided on the hitachi instead and so it looks like the last one. I said okay was the was the cat no let s see hitachi versus deere. So it was the deer. Yeah.

So my best alternative is to talk and then here. I m calculating the net present value to just sort of verify in the back of my mind. I want to be absolutely sure that hitachi is the correct one to choose and the finding the present worth of all the alternatives proves that hitachi is best because it s got the hottest npv do you have a question specific about yours alright. I ll be right there so as a reminder about the npv function.

It should only include years that are in the future. So when you do npv. You re discounting everything at damar and you include 1 through 10 inside the npv function. And then you close the parentheses.

And add what s at year 0. Separately and then that ll give you the overall present value of each alternative. ” ..

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