1. UGBA 103-2 Section 2

2. UGBA 103-2 Section 2 Ziemowit Bednarek 2 NPV rule recap NPV or net present value of the project tells us whether we should undertake the project or not Proper discount rate should be selected for the calculation of NPV Whenever NPV>0 – undertake the project, however…

3. UGBA 103-2 Section 2 Ziemowit Bednarek 3 NPV rule recap cont. When there is more than one project available you have to calculate several NPVs and undertake the project with the highest NPV Sometimes you are presented with the following problem:

4. UGBA 103-2 Section 2 Ziemowit Bednarek 4 You have to choose out of a number of projects assuming you have a budget constraint – cash available or the amount of loan you can take from the bank There are usually different states of the economy (different future scenarios) For each scenario there are different cash flows Projects differ in risk – some are riskier than others

5. UGBA 103-2 Section 2 Ziemowit Bednarek 5 This implies use of different discount rates for the calculation of NPV

6. UGBA 103-2 Section 2 Ziemowit Bednarek 6 Potential investors by calculating NPVs of available projects want to achieve a particular pattern of consumption For instance: a) you may want to consume everything now b) you may want to consume everything next period

7. UGBA 103-2 Section 2 Ziemowit Bednarek 7 c) you may want to consume everything in period n d) you may want to consume n% of your wealth in period n Simple example: You have $1000 in cash now and want to maximize your account balance next period given that you eat $500 now. What you may do:

8. UGBA 103-2 Section 2 Ziemowit Bednarek 8 a) simply eat $500 now out of your cash pile and invest the rest in the project with the highest NPV b) this project may be a savings account or a purchase of an ergonomic chair which you think will improve your work efficiency, etc. c) you may also invest all your money in the project with the highest NPV and take a bank loan for $500

9. UGBA 103-2 Section 2 Ziemowit Bednarek 9 Another possibility would be for instance consuming $500 out of your cash reserve and investing the other $500 plus some loan in a profitable project What is best for you to do depends on a particular market scenario which includes perspectives for your projects, anticipated rates of return on them, interest rate spread (difference between borrowing and lending interest rates), etc.

10. UGBA 103-2 Section 2 Ziemowit Bednarek 10 How do we find a desired pattern of consumption? We maximize the utility function given existing budget constraints This gives a ‘guide’ how to make a particular investor happy However certain assumptions are required to choose the right utility function form

11. UGBA 103-2 Section 2 Ziemowit Bednarek 11 Utility functions reveal information on investor’s risk preferences The more risk averse an investor is, the more of uncertain future income is he willing to give up for a sure bet This is clearly visible in the curvature of utility functions

12. UGBA 103-2 Section 2 Ziemowit Bednarek 12 Some utility functions Y=1-Exp(-5x) Negative exponential utility function Constant Absolute Risk Aversion

13. UGBA 103-2 Section 2 Ziemowit Bednarek 13 Y=x^.25/.25 power utility, constant relative risk aversion

14. UGBA 103-2 Section 2 Ziemowit Bednarek 14 In a well functioning capital market every investor is able to achieve preferred pattern of consumption Risk preference is best captured by the amount of money invested in risk-free vs. risky assets The more is invested in risk-free assets (for instance T-bills) the more risk averse an investor is (this is however not true when risk-free investment gives better

15. UGBA 103-2 Section 2 Ziemowit Bednarek 15 investment opportunities than other risky projects).

16. UGBA 103-2 Section 2 Ziemowit Bednarek 16 Preferences are convex sets, indifference curves are convex When considering available investment projects it is possible to draw a production possibilities curve which you have seen in lecture

17. UGBA 103-2 Section 2 Ziemowit Bednarek 17 IRR Another measure of the project profitability – Internal Rate of Return (IRR) IRR is the discount rate at which NPV=0

18. UGBA 103-2 Section 2 Ziemowit Bednarek 18 IRR cont. Whenever IRR is greater then the opportunity cost of capital – invest! IRR is not a good measure for mutually exclusive projects