I agree with your WACC comment. I would need to add further discussion around equity to use this term correctly. I think I will revert back to using “hurdle rate”. But the new value add taken from Dr. Jeffery’s reference related to assignment of a higher rate for more risky projects still seems both valid and useful.

Yes to your second point too. What follows are notes to incorporate into an updated blog post. I think I could rephrase the relationship between NPV and IRR as follows…

NPV and IRR are related to each other:

(1) If NPV(CF,R) = 0
     Then R = IRR

(2) For any set of cash flows estimated for a prospective project
     There is only one value for NPV
     But, the same project model can result in several IRR values,
     where NPV = 0

(3) If IRR > Cost of Capital
     Then a prospective project may make
     an acceptable investment

(4) If IRR >> Cost of Capital i.e. significantly greater than
     Then a prospective project may carry too much risk

(5) The Cost of Capital can be replaced with a hurdle rate
     Where Hurdle Rate includes both a
     minimum desired rate of return for a project and
     a threshold representing risk
     (5-a) A typical Hurdle Rate for an E-Business project
             might be 15%
     (5-b) A typical Hurdle Rate for an embedded systems project
             might be 18%
     (5-c) Embedded Components, Inc. is focused on lowering risk
             for its members by promoting the re-use of pre-existing
             components through its online marketplace training centers
             for embedded device manufacturers and their communities

(6) In general seek to maximize NPV, not IRR

(7) Yet, if two projects have NPV curves that cross over each other
     Then the interest R where the curves cross is called
     the Crossover Point
     (6-a) If the Crossover Point > IRR
             Then accept the project with higher NPV
     (6-b) If the Crossover Point < IRR
             Then accept the project with higher IRR

Best regards,

Ron

another issue is with this statement:

“NPV and IRR are related to each other:
(1) If NPV = 0
(2) Then IRR = Cost of Capital”

IRR is not CC. IRR concept is a bit involved, I wont get into details. In capital budgeting one of the project acceptance criteria is IRR > CC.

I don’t think that you need WACC at this level of discussion. It’s for debt vs equity financing.

I also saw some people looking at IT projects as real options.

argyn

Some corrections are in order…
Wow! I think I see the light. You have had to be patient in your comments above to get me to this point. I do now see a flaw in my use of PV for calculating ROI. I also agree with you that my ROI equation can be corrected using your improved equation:

ROI = NPV[CF(k), R] / (- IV)

If I were to add more reality to my MathCad template, I should consider changing my Cash Flow terms, CF(k), to periodic incomes and expenses, then a new ROI equation may be used:

ROI = NPV[(income(k) - expense(k)), R] / [ (- IV) + PV[(expense(k)), R] ]

By including PV (present value) in the ROI equation, we can measure time’s effect on expenses more effectively. Expenses deferred to a later time in the life of a project, where possible, could yield a more effective use of capital. So the deferred expense should also reflect an improved ROI value.

IV is still the initial investment at period 0.

k is the cash flow count from 1 to N, where N is the total number of periods.

R does not have to be only defined as the annual interest rate. It could also be repurposed as the weighted average cost of capital (WACC). A value of 15% seems typical for a Web or network information technology project. A value should be chosen that includes enough risk for projects undertaken in specific market sectors. A web site IT project may have lower risk (WACC of 15% for R) than an embedded system development project (WACC of 20% for R), for example. See my reference below to Dr. Jeffery’s “Return on Investment Analysis for E-Business Projects” article below.

Note the difference in the type of cash flow used for NPV and PV: income - expense vs. just expense. This was a significant part of the error I now see in my first draft.

I plan to update my MathCad template to reflect these corrections in PV, ROI, along with a project example with periodic incomes and expenses. I need to add an IRR equation, and a PI equation too, as these make good alternative ROI calculations.

ROI is uniquely qualified to level a group into a team
Meanwhile, after reading your great Colorado MBA preso in your previous comment, I realize that finance people don’t actually use the term ROI at all. My finance book does not have a single equation that uses the term ROI. I think it is considered too vague an expression. I found an out of print book with some sample pages online that captured the problem in using the term ROI for finance nicely:

The Internet Encyclopedia
3 volume set
Edited By Hossein Bidgoli
Published 2004
John Wiley and Sons
ISBN 0471222046

Specifically, volume 3 pp 211 to 227
“Return on Investment Analysis for E-Business Projects”
By Mark Jeffery, Northwestern University

Where Dr. Jeffery offers a few options for ROI calculation. Now this 3 volume set sells for as much as $900+ on Amazon.com and is unavailable most other places. But Dr. Jeffery’s full article is online here:

Return on Investment Analysis for E-Business Projects

Dr. Jeffery suggests three separate methods for predicting ROI:

IRR, equation 7, page 6:
NPV[(income(k) - expense(k)), IRR] = 0

Profitability Index (as you have already suggested), equation 5, page 5:
Profitability Index = NPV / Investment

An ROI equation similar to the one I present above, equation 6, page 6:
ROI = 100% x (Project Outputs - Project Inputs) / (Project Inputs)

In summary, I really appreciate your patience following along with me to identify these problems and in participating within this new ROI framework with me as a way to stay focused on improving the framework itself. There is an additional lesson I learned as a result of our discussion, argyn. ROI is a term less used by financial experts but often used to make business decisions. Yet ROI requires effective use of financial equations. And, the team discussion to decide whether to invest in one of two or more technology projects requires careful engineering consideration too. All combined, ROI indeed can make a good framework for ethical discussion because no one expert likely can dominate an ROI investigation - all three professional classes of experts have an equal but separate place within this ROI Framework for effective communications.

To be clear, I believe the: (a) engineer, (b) finance professional, and (c) business executive, can work effectively together using ROI as an ethical framework for conversations that lead to high quality decisions as a team of equals.

What I have learned…
Each participant in an ROI-based project review naturally wants the best decision to be made. Yet, each of the members on the team may feel a little embarrassed at one point or another, as I too have during this blog conversation thread, when I realized how patiently argyn has been in getting me to realize my PV usage mistake. Why embarrassed? Well know that I understand argyn’s point, I read over my original references used to craft this blog post in the first place, and the correct PV usage was there all along. I just didn’t understand it. In my case: a reference to PV (Costs), for example, is not the same thing as just PV (Anything). Yet I am here to tell my readers now that the potential for a small embarrassment leads to an even greater feeling of reward in finding answers only a team conversation can yield. What kind of reward? To understand a point being missed, allows me know to apply this new gained knowledge in many related areas. A reward well earned by putting forth new ideas for discussion in the first place. So I say to you, try to make your best effort in a team participation, don’t be defensive, don’t give in to every “nattering nabob of negativity” either. Be patient and expect patience from others. But in the end, learn to more quickly accept other points of view that can be demonstrated to be correct. Just another positive result from ethical team conversation, I suppose.

Thanks again and best regards,

Ron

“ROI using Rich Schlesinger’s ppt slide 21″
http://www.embeddedcomponents.com/blogs/wp-content/uploads/2007/12/mathcad-npv2_slide21.pdf

This slide again uses a wrong formula. NPV of proj A is computed correcly, it’s 4.8139e+005. However its ROI is not good. It divides NPV by present value of future cash flows from investment. It doesnt make any sense. It has to divide it by -IV, i.e. $1180083.
You invested IV, you are trying to compute a return on your investment, then divide by -IV.
You’d get “ROI”=40.79%.

check out this presentation: http://leeds-faculty.colorado.edu/zender/MBAC6060-Eve/L-Notes/Rules-Nt.ppt
It gives a brief overview of capital budgeting techniques.
What you call “ROI” is there under Profitability Index method description.

Your proj A IRR is 23.39%. I dont prefer IRR over other methods, it’s just one of the methods of comparison.

cheers
argyn

I really appreciate your taking the time to add value to this discussion. Reading through the slide set I picked at the top of a google search is time well spent for my readers. It has a high rank on google because it may be a popular reference.

You are absolutely correct. Rich’s slide 17 does have a potential “typo” in using Present Value (PV) instead of Future Value (FV). I say “typo” in quotes because he only uses the equation in slides 27 and 28 with words that very well could be considered future value (“total cost” and “total benefit”) - as such slide 17 may simply be a typing error. Let’s ask him and see? At UC Berkeley I was required to buy my professor’s notes in a binder while he/she used our class participation to correct the notes we had to buy. These notes would often have many errors and typo’s. To Rich’s credit, he posts his notes for public use and for his students to use at no cost. So having some typos, like PV instead of FV, does not take away from his over all concepts.

Your summary of my project A example using the PV set to $100,000 is fine. Using PV at year zero vs. NPV at year 4 all seem consistent - no news here. But I am glad that you restated it here using some different language for my readers.

Meanwhile, I used my MathCad template on Rich’s detailed ROI example data on slide 21, just as I did in my example:

ROI Example: Simple Project Comparisons Using NPV
http://www.embeddedcomponents.com/blogs/2007/09/roi-as-an-effective-communications-tool-for-engineers/#NPV

I added an annual interest rate, R, of 7% and come out with an ROI number of 29% - just as Rich did using his alternate ROI method. So I think my ROI equation for these simple periodic cash flows works just fine - the same ROI equation Rich uses on slide 28. See my attached PDF report of the MathCad exercise here:

ROI using Rich Schlesinger’s ppt slide 21

The finance book I studied for my MBA program is the same resource I used to extract my equations for this blog post in the first place:
Financial Management, Principles and Practice
By Timothy J. Gallagher and Joseph D. Andrew, Jr.
Copyright 1997, Prentice-Hall, Inc.
ISBN 0-02-340271-7

I can tell from your own blog posts that IRR is a favored technique. I agree that IRR is useful too. In fact, I use the IRR method in my blog post too. See “figure 2 - sample financial spreadsheet” in section “ROI Example: Evaluating an Infrastructure Project” above.

Lastly, you bring out a very important point for engineers to consider when using my proposed ROI methods (NPV and IRR) to make ethical project decisions. The dichotomy between engineers, business professionals, and executives alike will not be solved just because an engineer tries to bridge the conversation gap by adopting a financial ROI approach. All team members must actually want to find the best solution between them. The tools you and I presented here - around time’s effect on a project’s cash flows - may still be one very promising ethical approach.

Best regards,

Ron

I’m trying to help you sort out issues with financial computations.

You mentioned this ppt:

Role of a Systems Analyst
by Rich Schlesinger
http://science.kennesaw.edu/~rschlesi/3600fa07/Session%203_project%20initiation.ppt

it’s screwed up

Look at slide 17. It says
NPV = PV / (1+rate)^n

This is plainly misleading. It should be:
PV = FV / (1+rate)^n

You discount the future value and get the present value. This is a fundamental equation of finance, time value of money.

NPV concept is different. It’s “Net”, meaning that you add all cash inflows and outflows. In the example on slide 17 $100,000 is a future value, it’s 5 years from now. Today it’s worth 95,242.63 at a given discount rate of 5% annual with annual compunding. That’s the PV. IF this was the only cash exchange, then this is also NPV. If there were other cash exchanges, then you add them up.

On the other hand, look at slide 27 and 28. It says that you compute “cumulative” NPV, i.e. “costs and benefits”; then divide it by PV of COSTS.

In you case A, if you’d follow the slides, then PV of costs is equal the face value, i.e. $100,000. why? because you invest NOW, this means period ZERO, there’s no discounting. NPV remains the same, then you divide it by $100,000, your costs.

Actually, I dont like this approach too. The issue is that NPV in numerator is already accounting for interest rate. Now when you compute ROI it’s going to be already discounted. So you get a rate which has another rate inside. In this particular case I would simply get IRR or compare NPVs but in a different way.

This is all standard financial stuff, look for “project financing”, dont read anything written for “engineers by engineers” on this subject. Grab any book written for finance professionals.

cheers
argyn

I agree that my sample test case comparing two projects is too mundane. It was meant to be simple so others can follow. What may be needed as a follow on post is a real-life example on how to effectively move NPV and IRR out of the financial domain and into engineering due diligence. This might include market attractiveness, time to market, and cash flows that bundle a mix of income and expense.

Many text books and financial preso’s conclude that ROI does equal cumulative NPV/PV.

Here is one such preso (see slide 28):
Role of a Systems Analyst
by Rich Schlesinger
http://science.kennesaw.edu/~rschlesi/3600fa07/Session%203_project%20initiation.ppt

From a purely MathCad style perspective, I am interested in taking the NPV equation (figure #1 in this blog post) to its natural limit of N := infinity. Move the equation into the domain of a calculus boundary value problem. This may lend itself to some automation with less of a need for special case consideration for a more uniform ethics discussion between engineers and business stake holders.

Thanks for the positive interest in bridging the conversation gap between naturally self-interested engineers and equally naturally self-interested business managers. I have seen the problem time and again where it can be hard to weigh the advice of several engineering options with the nagging thunder of “just get it done as soon as possible” by the business team. Using a financial equation seems like a neat solution to me because it covers both the time issues and the money issues in an ethical or fair way that helps even the playing field between those that understand the technology and those that understand the financial risks. I will ping you before crafting such a post and if you have future ideas please let me know.

Best regards,

Ron