7 Homogeneous Measures
Lindon Robison
Learning goals. At the end of this chapter, you should be able to: (1) properly construct a present value (PV) model; (2) understand the need for homogeneous measures when building PV models; and (3) describe PV model dimensions that require homogeneous measures.
Learning objectives. To achieve your learning goals, you should complete the following objectives:
- Define PV models and describe their uses.
- Learn how to compare challenging and defending investments.
- Learn how to convert a challenging investment’s future earnings and costs to their value in the present.
- Learn how to represent the cost of sacrificing a defending investment by using its internal rate of return (IRR).
- Learn about PV model dimensions that require homogeneous measures to accurately and to consistently compare investments.
Introduction
Firm managers either continue their commitment to an existing investment called a defender or disinvest in the defender and commit to a new investment called a challenger. The financial manager’s assignment is to analyze and to rank defenders and challengers. What adds complexity to the ranking process is that defenders and challengers are sometimes measured in different units. These differences in measures between challenging and defending investments may result in unstable and inconsistent rankings when more than one ranking method is used. This chapter intends to describe present value (PV) models that consistently and accurately rank defending and challenging investments using homogeneous (same) measures.
What is a Present Value (PV) Model?
A PV model is a mathematical expression that represents the value of future cash flow in present dollars. The present value of future cash flow earned by a challenging investment exchanged at the discount rate equal to the defender’s IRR is called net present value (NPV). The NPV of the future cash flow of an investment discounted by its own IRR is zero.
To rank uniquely a defending and challenging investment requires that we reduce their current and future earning to a single number in the same period. To make this point, that ranking investments uniquely requires a one-dimensional measure, assume that we determine the winner and loser of a sporting event by several different measures. For example, suppose that the winner of the Super Bowl football game depended on the following measures: points earned, yards gained, yards earned on the ground divided by the yards earned passing, yards penalized, injuries sustained, and the number of persons viewing the contest. Most football sports fans would agree that the success measures just described matter—but we will never determine who wins and who loses with such multidimensional measures unless in some rare event one team dominated in all dimensions. So, we must decide which measure matters most and in the case of football—the measure that matters most is points earned.
To avoid the indecisiveness of a multi-dim