1. Qinglei Dai for FEUNL, 2006 Finance I October 10

2. Qinglei Dai for FEUNL, 2006  Capital budgeting: decision-making process for accepting or rejecting projects  Various methods NPV Internal rate of return Topics covered

3. Qinglei Dai for FEUNL, 2006 Net Present Value Opportunity Cost of Capital

4. Qinglei Dai for FEUNL, 2006 Net Present Value Example Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value?

5. Qinglei Dai for FEUNL, 2006 Net Present Value Example Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return?

6. Qinglei Dai for FEUNL, 2006 NPV method  The NPV rule:  Value-additivity:

7. Qinglei Dai for FEUNL, 2006 Net Present Value Example You have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building?

8. Qinglei Dai for FEUNL, 2006 Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?

9. Qinglei Dai for FEUNL, 2006 IRR method  Internal Rate of Return (IRR):  Basic IRR rule:

10. Qinglei Dai for FEUNL, 2006 IRR method  Example: suppose a certain project brings a cash flow series of t=0, c=-200 t=1, c=100 t=2, c=100 t=3, c=100 What is the IRR for the project? Should we accept the project when the discount rate is 20% (30%)?

11. Qinglei Dai for FEUNL, 2006 IRR method  When r=20%,  When r=30%

12. Qinglei Dai for FEUNL, 2006 Problems with IRR  Independent project:  Mutually exclusive projects:  2 general problems of IRR for both of independent projects and mutually exclusive projects  2 specific problems of IRR for mutually exclusive projects

13. Qinglei Dai for FEUNL, 2006 Problems with IRR  1st general problem with IRR: when the cash inflows occur before the cash outflows Example:  t=0, c=100; t=1, c=-130

14. Qinglei Dai for FEUNL, 2006 Problems with IRR  investing-type project:  Financing-type project:

15. Qinglei Dai for FEUNL, 2006 Problems with IRR  2nd general problem with IRR: multiple rates of return with “flip-flop” cash flows Example: a project with cashflows of (-100, 230, -132)

16. Qinglei Dai for FEUNL, 2006 Problems with IRR  How to solve the above problem?  NPV rule:  Modified IRR (MIRR)

17. Qinglei Dai for FEUNL, 2006 MIRR  Example: cash flow stream (-100, 230, -132), r=14%

18. Qinglei Dai for FEUNL, 2006 Problems with IRR  1st specific problem with mutually exclusive projects: the scale problem  Example: r=25% C0C1NPVIRR 1-1040 2-2565

19. Qinglei Dai for FEUNL, 2006 Problems with IRR  How to adjust for this deficiency? Incremental IRR:

20. Qinglei Dai for FEUNL, 2006 Incremental IRR C0C1NPVIRR 1-1040 2-2565 Incremental cash flow from choosing large budget instead of small budget

21. Qinglei Dai for FEUNL, 2006 Problems with IRR  2nd specific problem with mutually exclusive projects: timing problem NPV 0123IRR0%10%15% A-101011 B-101112 B-A