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2. If you require a 12% annual return, what would you pay for… …\$90 to be delivered in 1 year? (\$80.3571) …\$95 to be delivered in 2 years? (\$75.7334) …\$99 to be delivered in 3 years? (\$70.4662) …all of the above? By adding together the present values, you find the value of allthe cash flows in the stream. Discounting unequal cash flows i = 12% ? 99 90 95 0 1 2 3 90 ÷ (1+0.12)1 80.3571 75.7334 + 70.4662 226.5567 There’s an easier way… kind of. 95 ÷ (1+0.12)2 99 ÷ (1+0.12)3

3. Using the calculator (NPV function) • NPV(12,0,{100,200,300,400,500})

4. Using the calculator (NPV function) • NPV(9,0,{100,90,80,25},{1,1,1,6})

5. Using TVM to Make Business Decisions

6. Project Valuation & Decision Making • How do you properly answer the fundamental question? • Applications • Operating expenditures • Capital budgeting • Marketing campaigns • Considerations • Mutually exclusive projects (vs independent projects) • Capital rationing (vs unlimited funds) • Timing • Approval process • Ranking projects • Criteria • Key Criteria: NPV, IRR, PBP • Other criteria (PI, MIRR, etc.)

7. Pay Back Period (PBP) • How long will it take to recoup the cash outlay? • For example, a machine which costs \$1,000k and saves \$250k per year would pay for itself in 4 years (1,000 ÷ 250). • Therefore, the payback period would be 4 years. • What would the PBP be for this project? • What labels might be put on the cost? • Initial Investment, I0, CF0 • Why is PBP a valid criterion? • What are the weaknesses of judging projects on PBP? 0 1 2 3 4 100 100 100 100 Cost: \$380

8. Internal Rate of Return (IRR) • IRR = the “interest” implied by a stream of cash flows • If IRR > hurdle rate, project should be approved • If IRR < hurdle rate, project should be rejected • Why is IRR a valid criterion? • What are the weaknesses of judging projects on IRR?

9. Using the calculator (IRR function) • IRR(-1100,{100,200,300,400,500})

10. Using the calculator (IRR function) • IRR(-250,{10090,80,25},{1,1,1,6})

11. Net Present Value (NPV) • Present value of a stream of cash flows, minus the cost • If NPV > 0, project should be approved • If NPV < 0, project should be rejected • What does NPV = 0 imply about the IRR for a project? • Why is NPV a valid criterion? • What are the weaknesses of judging projects on NPV?

12. Using the calculator (NPV function) • Once you know the present value, how would you find NPV? • To find NPV easily, put the cost where CF0 goes in your calculator. • What if the initial investment were \$1,100?

13. Using the calculator (NPV function) • Once you know the present value, how would you find NPV? • To find NPV easily, put the cost where CF0 goes in your calculator. • What if the initial investment were \$250k?

14. Profitability Index (PI) • Puts projects into the same scale & provides a single, easy to read number • ΣPV ÷ Cost • If PI > 1, what does this imply about NPV? • If PI < 1, what does this imply about NPV? • Remember: • PI = ΣPV ÷ Cost • NPV = ΣPV – Cost

15. Exam #2 • Tuesday, 2/19/13