9 Homogeneous Sizes
Lindon Robison
Learning goals. At the end of this chapter, you should be able to: (1) understand how internal rate of return (IRR) and net present value (NPV) models can produce inconsistent rankings; (2) produce consistent IRR and NPV rankings by adjusting for investment size differences and by adopting common reinvestment rate assumptions; (3) understand why some NPV and IRR rankings are unstable; (4) recognize how different initial size adjustment methods (addition, scaling, or some combination) produce consistent but sometimes different investment rankings; and (5) recognize how investment type differences can be used to identify the proper size adjustment method.
Learning objectives. To achieve your learning goals, you should complete the following objectives:
- Recognize that IRR and NPV rankings may be inconsistent and that NPV rankings may be unstable.
- Understand the difference between periodic investment sizes and initial investment sizes.
- Describe how different reinvestment rate assumptions can produce inconsistent IRR and NPV rankings.
- Show how resolving periodic and initial size differences and a common reinvestment rate produce consistent challenging investment rankings.
- Illustrate the different methods available for resolving periodic size investment differences.
- Demonstrate how scaling and addition can be used to resolve initial size differences in investments.
- Demonstrate that while different methods for resolving periodic and initial size differences can each produce consistent rankings, the consistent rankings may not be the same.
- Understand the conditions under which IRR and NPV provide the same rankings as the size adjusted IRR and NPV models.
- Recognize the four basic investment models
- Recommend the appropriate investment model based on challenger characteristics.
Introduction[1]
In the single equation NPV model, we assumed that cash flow was exchanged between time periods at the defender’s IRR. In the single equation IRR model, we assumed that cash flow was exchanged between time periods at the challenger’s IRR. In the NPV model, the challenger (defender) was preferred to the defender (challenger) if the NPV were positive (negative). Furthermore, the NPV ranking of the defender and challenger was the same ranking obtained by comparing their respective IRRs. As a result, both IRR and NPV criteria produce the same ranking.
This chapter recognizes that when we rank multiple challengers funded by one defender, their IRR and NPV rankings may be different. Furthermore, we observe that changes in the defender’s IRR may produce unstable NPV rankings. We demonstrate these results in Table 9.1 that ranks three challengers.
Table 9.1. Inconsistent IRR and NPV rankings and unstable NPV rankings among three mutually exclusive investments of different initial and periodic cash flows.
| initial investments where i = 1,2,3 | period one cash flows where t = 1 generated by initial investments where i = 1,2