© Dr. B. C. Paul 2002 revisions 2008, 2011
Note – The subject covered in these slides is considered to be “common knowledge” to those familiar with the subject and books or articles covering the concepts are widespread.

 A classic investment requires money into a project
 Project then produces earnings of value throughout some life
 Figure out whether those earnings justify the cost to get the project
 Some projects may have negative cash flows at other than the beginning

 Example
 Mining project
 Costs money to build the mine
 Makes nice money while it runs
 At the end you have to clean-up your mess and reclaim
 Environmental requirements are often leaving used stuff with negative value at the end
 Cash flows that change sign multiple times are called unconventional
 Subtraction derived cash flows in all cost alternatives problems may reverse sign many times

 This case challenges what people mean by a project rate of return because the project obligates money that will never be used in the profitable part of the project
 Raises havoc with the IRR because part of the investment will never be invested in the project to obtain a return from within the project
 How can a rate be internal?

 Cash flows times magic numbers have the form of a polynomial
 we know from math that polynomials have as many roots as axis crossings
 that means there is more than 1 interest rate that makes the NPV zero!
 From a physical standpoint because some of the negative cash flow money grows inside the project, and some of it grows outside its just telling you about rates of growth inside and outside of the project that make
NPV zero
 Of course that means the whole concept of internal growth is crap

 If you have unconventional cash flows in any of the scenarios being compared you may not be able to get a good clean IRR
 Multiple roots are telling you about different interest rates for money brought in at different points
 Books contain examples to help you see they can mean something – trouble is it’s a major exercise to figure out what
 So much for IRR contests to pick winning investment portfolios
 Well I still have PVR so I’ll do a PVR contest

 PVR was designed for comparing invest and earn cash flows of unequal duration and magnitude
 It tells you how many dollars of positive NPV you get for every dollar invested
 This is how it gets around the largest investment wins problem
 Investments with highest PVR are stronger

 PVR values cash at your required rate of return
 Interest rates (especially high ones) shift emphasis to short range returns
 A highest IRR contest will put emphasis on quick money - not necessarily most
 PVR values all money at required rate - will maximize the cash you get at your required rate
 Answers are not equal

Even when Money Rules
Comparative Decisions Don’t have
Just One Right Answer
 An IRR contest
(if you can pull it off unconventional cash flow problems) tends to give answers that maximize wealth if you can jump in and out of investments
 Some of the Wall Street raiders of the 80s and 90s
 Good for Slash and Burn strategy

 IRR = Slash and Burn
 PVR chooses investments that maximize your wealth at your required rate within investments
 Because interest rate is fixed for the type of investment it is optimized for someone who is going to stay with the investment.
 Some businesses are designed around the idea that this is what we do – we win because we do it better than everyone else.

 Biggest NPV
 Almost never used
 Tends to pick the biggest projects
 If minimizing number of investments while making required rate is goal may be right way
 IRR (if it can be made to work) Slash and Burn
 Work well if you are very fluid
 PVR maximize growth of wealth at required rate of return