#### Print out this page and bring it to class with you.

Learning Objectives – Class 4

After today’s lecture, and after working the homework problems, the student should be able to

- Solve problems where an alternative choice is to be made between projects
- Be able to chose between alternative projects on the basis of net present benefit/value/worth.
- Be able to calculate the net present worth of a project
- Be able to transform alternative projects onto an equivalent time basis
- Be able to compare projects on the basis of net present worth
- Be able to compare projects on the basis of annual cash flow analysis
- Recognize that when a bank says 6% interest, they mean 6% nominal per year, not 6% per month, not 6% per day, not anything else! DOES THIS LOOK FAMILIAR?

#### Topics covered in today’s class

- Review how to move F, P, A, G under non-standard numbering conditions
- The “correct” answer – maximize Net Benefits, either present, future, or annual
- The “incorrect” answer – maximize benefit/cost ratio or internal rate of return
- Example of calculation of Net Present Value (or Worth) of Benefits = present value (or worth) of benefits – present value (or worth) of costs, for a single project
- Example of comparison of two projects using NPV
- Where did the project data in <Table 14.1 page 370 in 1st edition book> {Table 15.1 page 406 in 2nd edition} come from? From the NPV of expanded information found in <Table on page 384 in 1st edition> {Table on page 419 in 2nd edition}, and shown at the bottom of this page.
- How to compare two projects with equal life spans
- How to compare two projects with unequal life spans
- Use multiple lifetimes for the projects until they have the same lifetime
- Use Annual Worth Analysis rather than Net Present Value Analysis
- Why it works

- Commonly used criteria:
- NPV >= 0 (Net Present Value = Present Value (or Worth( of Benefits – Present Value (or Worth) of Costs)
- NFV >= 0 (Net Future Value)
- NAV >= 0 (Net Annual Value)
- B/C Ratio >= 1 (Benefit/Cost Ratio)
- IRR >= MARR (Internal Rate of Return >= Minimum Attractive Rate of Return)
- Payback Period <= some time?

Examples of non-standard cash flows:

EXAMPLE – Incremental Rates of Return Analysis – page 384 (1st edition) – page 419 (2nd edition) Revelle: