### Tip of the Week #65                     Tip Index

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# Choice of Denominator in Investment Ranking Criterion

Dear John,

I have a question about the correct definition of the Profit-to-Investment ratio.1

It is clear that in numerator we put the Net Present Value of our cash flow.   For the denominator, we use the Present Value of investments.

My question is this.  Should we use PV of the negative initial part of cash flow?  Or the PV the capital investments?

 `Year` `1` `2` `3` `4` `5` `Revenues - Operating Expense` ` 0` ` 0` ` 100` ` 100` ` 100` `Capital Expenditures` ` 100` ` 100` ` 50` ` 0` ` 0` `Net Cash Flow` `-100` `-100` ` 50` ` 100` ` 100`

In this example, should the 50 units of capital expenditure in year 3 be considered in computing the PV of of investments?

Thanks.

 1The Profit-to-Investment Ratio (PI or P/I) is a popular decision criterion for ranking investments when capital is constrained.  This criterion goes by other names, and people disagree as to the best calculation.  In recent years, the name Discounted Return On Investment (DROI) has emerged, and I think this label is most descriptive.  Such criteria are popular despite problems when applying risk-weighting for uncertainty.

I wish that I had an easy answer to your question.  If you asked 10 companies how they do it, you would likely get 10 different answers. Economic evaluation is not rocket science, yet there is so much confusion about what decision policies work best.

In computing PI, some possibilities for the denominator include:
a)  Sum the investments (usually excluding abandonment and salvage).
b)  Use PV investments  (very popular, especially for mult-year investments).
c)  Use investment in the budget year (If you're trying to maximize PV or EMV per unit of constraint).

I think (c) is the most correct.  As a ranking tool, for optimizing the investment portfolio, the denominator should be units of the constraint.  No company I know discounts budget amounts: The spending allowance is the same whether the money is invested in January or December.  Because of this, I suggest NOT discounting the denominator in most situations.  However, if you expect capital rationing to continue after the budget year this gives added weight to using a  PV investment calculation.

Here's another possibility for the denominator:

d) Use the Maximum Negative Cashflow (MNC) for the "investment."

This avoids any problems with classifying disbursements as investments vs. expenses.  Also, this recognizes that some projects are earning money while drilling or other investment continues.  I like this as a supplemental criterion, even if it isn't used in the ranking calculation.  For accuracy, I suggest doing the MNC calculation in 1-month time periods.

The other issue is, is there really a capital constraint?  There is lots of money in this world seeking investment opportunities.  I think the capital constraint idea is a useful fiction to help manage a company.  Typically, the real constrain is not having enough people to do all the worthy projects.  For widely-held, for-profit companies, I recommend that the overall process attempt to maximize Expected Monetary Value (EMV) of the company.

PI (or DROI) is an excellent investment ranking tool.  The main drawback is that you must be watchful for significant correlations among projects.  E.g., if there is a synergy between two projects, they might together be attractive yet neither one alone.   Examining the possibilities, especially in the context of constraints and risk aversion is the subject of portfolio theory and a much longer discussion.

—John Schuyler, February 2000