1. Finanças October 24

2. Topics covered  Decision trees  Sensitivity analysis  Breakeven analysis

3. Decision Trees

4. Example of Decision Tree

5. Decision trees  Example: The test marketing for a new project will take one year and will cost $100 million. There is a 75% chance that the test will be successful. If successful, the project will be taken and the NPV is estimated to be $1,517 million at year=1. If not successful, the project will have an NPV of $-3,611 million at year=1. The discount rate is 15% for the firm.

6. Decision trees Year 1Year 2-6 revenues6000 Variable costs3000 Fixed costs1791 depreciation300 Pretax profit909 Tax (t=0.34)309 Net profit600 investment-1500 Net cash flow-1500900

7. Decision trees Now Test marketing -$100 million Year 1 Investment

8. Decision trees  Sequence of decisions  How to solve the problem

9. Sensitivity Analysis

10. Sensitivity analysis  Example: In the previous example, the NPV depends on revenues, costs and investment of the project.

11. Sensitivity analysis Revenue = Cost = Example: market size  Pessimistic: 5000  Expected: 10000  Optimistic: 20000  Given that market share is 30%, P=2 mil per item, variable cost = 1 mil per item, fixed cost = 1791 mil

12. Sensitivity analysis Year 1Year 2-6 Pessimisticexpectedoptimistic revenues6000 Variable costs3000 Fixed costs1791 depreciation300 Pretax profit909 Tax (t=0.34)309 Net profit600 investment-1500 Net cash flow-1500900 NPV1517

13. Sensitivity analysis pessimisticexpectedoptimistic Market size10000 Market share30% Price per item2 mil Variable cost per item1 mil Fixed cost1791 mil investment1500 mil

14. Break-Even Lease Payment Joe Machens is contemplating leasing the University of Missouri a fleet of 10 minivans. The cost of the vehicles will be $20,000 each. Joe is in the 34% tax bracket; the University is tax-exempt. Machens will depreciate the vehicles over 5 years straight-line to zero. There will be no salvage value. The discount rate is 7.92% per year APR. They pay their taxes on April 15 of each year. Calculate the smallest MONTHLY lease payment that Machens can accept. Assume that today is January 1, 2003 and the first payment is due on January 31, 2003

15. Break-Even Lease Payment: Depreciation  Let’s cash flow this out from Joe’s perspective.  The operating cash flow at time zero is  The depreciation tax shields are worth

16. Present Value of Depreciation Tax Shield The PV of the depreciation tax shields on April 15, 2003 is PMT I/Y FV PV N

17. Present Value of Depreciation Tax Shield The PV of the depreciation tax shields on January 1 2003 is $53,176.99 PMT I/Y FV PV N

18. Where we’re at so far:

19. Step Two: Taxes Recall that taxes are paid each April 15.

20. Present Value of Tax Liability The PV of the tax liability is PMT I/Y FV PV N

21. Present Value of Tax Liability The PV of the tax liability PMT I/Y FV PV N

22. Solution: Payments  In addition to the depreciation tax shields and income taxes

23. Present Value of Gross Revenue The PV of 60 months of gross revenue on January 1 2003 is PMT I/Y FV PV N

24. Solution (continued)  So the least Joe can charge is:

25. Summary Joe Machens