1. FIN 614: Financial Management Larry Schrenk, Instructor

2. 1.What is the Internal Rate of Return ? 2.Calculating the Internal Rate of Return 3.Analysis of the Internal Rate of Return 4.Technical Issues 1.Comparing Projects 2.Multiple Sign Changes

3. IRR is the discount rate that makes present value of all cash flows (including any required investments) equal to zero.

4. Rule: Do project if IRR > required rate of return (r). If the return on the project (IRR) is greater than the return expected on projects with this level of risk (r), then do the project

5. -C0-C0 C1C1 C2C2 C3C3 C4C4

6. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 1 ) C 1/ (1+IRR)

7. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 2 ) PV(C 1 ) + C 1/ (1+IRR) C 2/ (1+IRR) 2

8. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 2 ) PV(C 1 ) PV(C 3 ) + + C 1/ (1+IRR) C 2/ (1+IRR) 2 C 3 /(1+IRR) 3

9. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 2 ) PV(C 1 ) PV(C 3 ) PV(C 4 ) + + + C 1/ (1+IRR) C 2/ (1+IRR) 2 C 3 /(1+IRR) 3 C 4 /(1+IRR) 4

10. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 2 ) PV(C 1 ) PV(C 3 ) PV(C 4 ) + + + C 1/ (1+IRR) C 2/ (1+IRR) 2 C 3 /(1+IRR) 3 C 4 /(1+IRR) 4 Total PV =

11. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 2 ) PV(C 1 ) PV(C 3 ) PV(C 4 ) |-C 0 | + + + C 1/ (1+IRR) C 2/ (1+IRR) 2 C 3 /(1+IRR) 3 C 4 /(1+IRR) 4 Total PV =

12. -C0-C0 C1C1 C2C2 C3C3 C4C4 PV(C 2 ) PV(C 1 ) PV(C 3 ) PV(C 4 ) |-C 0 | + + + = C 1/ (1+IRR) C 2/ (1+IRR) 2 C 3 /(1+IRR) 3 IRR is the discount rate that makes Total PV = |C 0 | C 4 /(1+IRR) 4 Total PV =

13. EXAMPLE (r = 10%): IRR Calculation: Result: 18.10% > 10% Good Project 01234 -1,000300200400700

14. Finance Apps #8 Screen will show irr( Function Syntax irr(CF 0, {CF 1, CF 2,…}, {Freq 1, Freq 2,…}) CF t = Cash Flow at Time t Freq t = Frequency of Cash Flow at Time t CF 0 = -Initial Investment When doing uneven cash flows, CF 0 = 0

15. Consider again these cash flows: irr(CF 0, {CF 1, CF 2,…}, {Freq 1, Freq 2,…}) irr(-1000, {300, 200, 400, 700} and ENTER Answer: 18.10% Notes: Cash Flows 1+ are not entered as negative (Unless they are negative numbers). Enter investment (CF 0 ) as negative.

16. Assuming no technical problems occur, NPV and IRR always give the same and the correct answer about whether or not to do one specific project. NPV > 0 iff IRR > r

17. The IRR and MIRR rules cannot be used to compare projects or select among projects since they do not meaningfully compare the absolute advantage of one project over another. Instead, the NPV rule must be used to compare or select among projects.

18. EXAMPLE (r = 10%): Period12345 A-1,000300200400700 B-10040305080

19. IRR A IRR B

20. NPV A NPV B

21. Results IRR A = 18.1% < IRR B = 29.6% NPV A = $216.65 > NPV B = $53.36 Question: Would you rather have a higher rate of return or a higher dollar return? In the end it is the dollar return that counts Project A increases firm value by $216.65. Project B increases firm value by $53.36. Project A is worth $163.29 more than B!

22. What is the IRR of the following cash flow? 01234 -320-16-3232

23. There are multiple correct answers! This is possible whenever there is more than one sign change in the cash flows!

24. The line crosses the x-axis at each IRR.

25. Advantages Properly adjusts for time value of money Uses cash flows rather than earnings Accounts for all cash flows Project IRR is a number with intuitive appeal Key Problems: Cannot compare projects Multiple IRR’s

26. FIN 614: Financial Management Larry Schrenk, Instructor