1. Options

2. Exam prep item  An firm has a project with NPV>0 that costs a lot of money.  It pays off after the owner dies.  Should she invest? In the project? In financial assets? How?

3. Time zero cash flow Time one cash flow An investment opportunity that increases value. NPV Invest to here Finance to here

4. Exam prep item  What is the interest rate?

5. Don’t write  The interest rate is the time value of money.

6. Do write:  The interest rate is the premium for current delivery of money.  P 0 is the price of current money in current money, namely 1.  P 1 is the price of time-one money in terms of current money, something <1.  P

7. Teaching evaluations  Now

8. Definition of a call option  A call option is the right but not the obligation to buy 100 shares of the stock at a stated exercise price on or before a stated expiration date.  The price of the option is not the exercise price.

9. Example  A share of IBM sells for 100.  The call has an exercise price of 95.  The price of the call should be at least 5.  Actually, it will be more.

10. Options of Microsoft Calls-Last Puts-Last Option andStrike NY ClosePriceJulyOct.JulyOct. Microsoft 90 3/8859 3/4-3 1/2- 90 3/8954 3/4-8-

11. Why are options valuable?  Options are insurance policies.  In case a stock I don’t hold goes up, I get part of the gain.  Options are more valuable as the share price is more risky.  Opposite of the share price, which is lower as the share is more risky.

12. Compare  Stock is at 50. In six weeks either 60 or 40, with equal probability.  1. Borrow 5000, buy 100 shares. In six weeks have either +1000 or -1000.  2. Buy 100 calls with exercise price = 50. Cost about $200. In six weeks have either +800 or -200.  Risk reduction, an insurance contract.

13. Payoff from an option  Forget the price of the option. That’s sunk cost.  Look at the value at expiration.

14. Payoff of a Call Option on the Expiration Date Value of common stock (S T ) at expiration ($) Value of call (C) at expiration ($) 0 50 Exercise price

15. Seldom exercise an option before expiration  Sell it to someone else, instead.  You no longer want the insurance.  Someone else does.

16. Application: firm near bankruptcy  Viewpoint of equity.  Exercise price = pay off the bond holders.  If the firm is worth less than the bonds, equity gets zero.  If the firm is worth more than the bonds, equity gets the difference.  Just like a call option.

17. Value of a Call Option before the Expiration Date Value of the physical firm ($) Value to Equity 0 50 Bonds owed Higher risk implies higher value This is about the value of equity of a nearly bankrupt firm. Higher risk

18. Risk  Raises the value of the near bankrupt firm.  Raises the value of a call option.

19. The option to expand  Project: A restaurant with two locations.  Probability.5 of modest success. NPV calculation holds.  Probability.5 of huge success, expand to 100 locations, capture value, become rich.  Project is a call option in addition to having NPV.  Option value can overcome conventional NPV < 0.

20. Definition of a put option  A call option is the right but not the obligation to sell 100 shares of the stock at a stated exercise price on or before a stated expiration date.  The premium (market price) of the option is not the exercise price.

21. The option to abandon is a put.  Project: build and market a new surf board line. NPV over a long horizon.  Probability.5 of success.  Probability.5 of failure, which will be evident at once. Sell the machinery, cease operations.  Value of put is in addition to usual NPV.

22. Exam review  AOL is considering building a cafeteria for its employees.  At a high discount rate appropriate to AOL’s risk, the NPV of the cafeteria is negative.  At a low discount rate appropriate to a Wendy’s, the NPV of the cafeteria is positive.  Should AOL build the cafeteria?  Explain briefly.

23. Answer  Build the cafeteria.  The project is safe like a Wendy’s, not risky like an internet service.  NPV is market value.  The market is not deceived but sees the project for the safe investment that it is.

24. Sets of Information relevant to a stock Past prices Publicly available information All information

25. Exam prep item  What are the flaws of payback period as a measure of a project’s worth?

26. Answer  In mutually exclusive choices, it ignores the effect of scale. It can incorrectly favor melons over malls.  It doesn’t adjust to changes in market interest rates.  It ignores timing of cash flows inside the payback period.  It ignores all cash flows after payback is complete.

27. Exam review question  When a firm creates value through a financial transaction, who gets the increase?

28. Answer  Old equity means the shareholders at the time the decision is made.  Old equity gets the gains.  Why? Old equity has no competitors. Everyone else is competitive and must accept a market return.  Recall the first problem set.

29. Exam prep item  Two assets have the same expected return.  Each has a standard deviation of 2%.  The correlation coefficient is.5.  What is the standard deviation of an equally weighted portfolio?

30. Answer  Var P =.5x.5x4+.5x.5x4+2x.5x.5x.5x2x2  = 3  Standard deviation = sq. root of 3  =1.732

31. Exam prep  A firm has a project with positive NPV.  The project costs 100M to start.  The firm has only 50M.  What should it do?

32. Answer  Raise the money in the capital market.  It can because NPV is market valuation.

33. Exam prep item  What is the weighted average cost of capital?

34. Answer  Don’t tell us a story.  Give the definitions and the formula.  r B = bond rate  r S = expected return on shares  B = market value of bonds  S = market value of shares  T C = corporate tax rate

35. Pay-off pitch  r WACC = (S/(S+B))r S + (B/(S+B))(1-T C )r B  Now say that it applies when  (1) the physical project has the same risk as the firm  (2) it is financed like the firm.

36. Exam review  Does a good project have IRR greater than the hurdle rate, or less?

37. Answer  IRR is the discount rate that makes NPV(IRR) = 0.  The hurdle rate is the market rate for the risk-class.  Investing means cash flows are first negative, then positive.  Financing (in this context) means cash flows are first positive, then negative.

38. More answer  Other sign patterns, IRR is not useful.  Investing, a good project has IRR > hurdle rate.  Financing, a good project has hurdle rate > IRR.