12 Homogeneous Rates of Return
Lindon Robison
Learning goals. After completing this chapter, you should be able to (1) construct present value (PV) models using multi-period equivalents of accrual income statements (AIS); (2) find multi-period before and after-tax internal rates of return (IRR) on assets and equity and relate these to before and after-tax return on assets (ROA) and equity (ROE) derived from AIS; (3) understand the importance of measuring rates of return on defending and challenging investments using homogeneous measures: equity or assets; and (4) solve practical investment problems using PV model templates are consistent with generalized AIS construction principles.
Learning objectives. To achieve your learning goals, you should complete the following objectives:
- Describe the similarities and differences between an AIS and IRR PV models.
- Construct multi-period IRR models by generalizing AIS earning measures.
- Demonstrate that before and after-tax return on assets (ROA) and return on equity (ROE) measures derived from an AIS are equivalent (equal) to rate of return measures derived from multi-period (one-period) IRR models.
- Construct net present value (NPV) models by discounting a challenger’s cash flow using a defender’s IRR.
- Show how NPV models that discount a challenger’s cash flow and changes in operating and capital accounts with a defender’s IRR can be used to rank defenders and challengers.
- Learn how to construct PV models that measure returns on assets versus returns on equity and use homogeneous rates of return when comparing the profitability of investments.
- Develop PV construction skills by using Excel templates.
Introduction
This chapter demonstrates that present value (PV) models are multi-period generalizations of an accrual income statement (AIS). While the AIS and PV approaches each focus on changes in wealth, a major distinction involves the time value of money that is explicitly considered through discount rates in the multi-period PV analysis. We find it important for investment evaluations to identify the connections between these financial perspectives and their effects on alternative rates of return. In addition, we compare ROA and ROE derived in AIS to internal rates of return on assets, IRRA, and equity, IRRE. We note that returns on assets and equity may provide inconsistent rankings, making it all the more important that we use homogeneous rates of return when ranking investments.
We often describe PV models as a beginning investment and the discounted present value of cash flow and the liquidated value of the investment at the end of the analysis. In fact, most investments are much more complicated. For one thing, we need to determine if we are investigating returns on equity or assets. We need to account for changes in accounts receivable, inventories, accounts payable, and accrued liabilities. In sum, we need to be prepared to construct PV models with the same level of detail that is inclu