Practice of Capital Budgeting

1. Practice of Capital Budgeting Finding the cash flows for use in the NPV calculations

2. Reading note • Chapters are being covered out of order. • I talk about chapter 6 first, then chapter 5.

3. Topics: • Incremental cash flows • Real discount rates • Equivalent annual cost

4. Incremental cash flows • Cash flows that occur because of undertaking the project • Revenues and costs.

5. Focus on the decision • Incremental costs are consequences of it • Time zero is the decision point -- not before

6. Application to a salvage project • A barge worth 100K is lost in searching for sunken treasure • Sunken treasure is found in deep water. • The investment project is to raise the treasure • Is the cost of the barge an incremental cost?

7. The barge is a sunk cost (sorry) • It is a cost of the earlier decision to explore. • It is not an incremental cost of the decision to raise the treasure.

8. Sunk cost fallacy is • to attribute to a project some cost that is • already incurred before the decision is made to undertake the project.

9. Product development sunk costs • Research to design a better hard drive is sunk cost when … • the decision is made to invest in production facilities and marketing.

10. Market research sunk costs • Costs of test marketing plastic dishes in Bakersfield is sunk cost when … • the decision to invest in nation-wide advertising and marketing is made.

11. Opportunity cost is • revenue that is lost when assets are used in the project instead of elsewhere.

12. Example: • The project uses the services of managers already in the firm. • Opportunity cost is the hours spent times a manager’s wage rate.

13. Example: • The project is housed in an “unused” building. • Opportunity cost is the lost rent.

14. Side effects: • Halo • A successful drug boosts demands for the company’s other drugs. • Erosion • The successful drug replaces the company’s previous drug for the same illness.

15. Net working capital • = cash + inventories + receivables - payables • a cost at the start of the project (in dollars of time 0,1,2 …) • a revenue at the end in dollars of time T-2, T-1, T.

16. Real and nominal interest rates: • Money interest rate is the nominal rate. • It gives the price of time 1 money in dollars of time 0. • A time-1 dollar costs 1/(1+r) time-0 dollars.

17. Roughly: • real rate = nominal rate - inflation rate • 4% real rate when bank interest is 6% and inflation is 2%. • That’s roughly, not exactly true.

18. Real interest rate • How many units of time-0 goods must be traded … • for one unit of time-1 goods? • Premium for current delivery of goods • instead of money.

19. Inflation rate is i • Price of one unit of time-0 goods is one dollar • Price of one unit of time-1 goods in time-1 dollars is 1 + i. • One unit of time-0 goods yields one dollar • which trades for 1+r time-1 dollars • which buys (1+r)/(1+i) units of time-1 goods

20. Real rate is R • One unit of time-0 goods is worth (1+R) units of time-1 goods • 1+R = (1+r)/(1+i) • R = (1+r)/(1+i) - 1 • Equivalently, R = (r-i)/(1+i)

21. Real and nominal interest Time zero Time one Money Food =

22. Upshot

23. Discount • nominal flows at nominal rates • for instance, 1M time-t dollars in each year t. • real flows at real rates. • 1M time-0 dollars in each year t. • (real generally means in time-0 dollars)

24. Why use real rates? • Convenience. • Simplify calculations if real flows are steady. • Examples pages 171-174.

25. Valuing “machines” • Long-lived, high quality expensive versus … • short-lived, low quality, cheap.

26. Equivalent annual cost • EAC = annualized cost • Choose the machine with lowest EAC.

27. Costs of a machine

28. Equivalent annuity at r = .1

29. Overlap is correct

30. Compare two machines • Select the one with the lowest EAC

31. No arbitrage theory • Assets and firms are valued by their cash flows. • Value of cash flows is additive.

32. 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.

33. Example • A share of IBM sells for 75. • The call has an exercise price of 76. • The value of the call seems to be zero. • In fact, it is positive and in one example equal to 2.

34. S = 80, call = 4 Pr. = .5 S = 70, call = 0 Pr. = .5 t = 1 t = 0 S = 75 Value of call = .5 x 4 = 2

35. Definition of a put option • A put 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 price of the option is not the exercise price.

36. Example • A share of IBM sells for 75. • The put has an exercise price of 76. • The value of the put seems to be 1. • In fact, it is more than 1 and in our example equal to 3.

37. S = 80, put = 0 Pr. = .5 S = 70, put = 6 Pr. = .5 t = 1 t = 0 S = 75 Value of put = .5 x 6 = 3

38. Put-call parity • S + P = X*exp(-r(T-t)) + C at any time t. • s + p = x + c at expiration • In the previous examples, interest was zero or T-t was negligible. • Thus S + P=X+C • 75+3=76+2 • If not true, there is a money pump.

39. Options are financial investments • In our example, the guy who owns a share of IBM can “fully insure” by buying 1.666… puts. • Cost is 1.666… x 3 = 5. Net in the good state is 80 – 5 = 75. • Payoff in the bad state is 1.666… x 6 = 10 • Net in the bad state is 75 = 70 – 5 + 10. • The position is riskless. • P.S. This works because there are only two outcomes. In general, more is needed for a perfect hedge.

40. Puts and calls as random variables • The exercise price is always X. • s, p, c, are cash values of stock, put, and call, all at expiration. • p = max(X-s,0) • c = max(s-X,0) • They are random variables as viewed from a time t before expiration T. • X is a trivial random variable.

41. Puts and calls before expiration • S, P, and C are the market values at time t before expiration T. • Xe-r(T-t) is the market value at time t of the exercise money to be paid at T • Traders tend to ignore r(T-t) because it is small relative to the bid-ask spreads.

42. Put call parity at expiration • Equivalence at expiration (time T) s + p = X + c • Values at time t in caps: S + P = Xe-r(T-t) + C • Write S - Xe-r(T-t) = C - P

43. No arbitrage pricing impliesput call parity in market prices • Put call parity already holds by definition in expiration values. • If the relation does not hold, a risk-free arbitrage is available.

44. Money pump • If S - Xe-r(T-t) = C – P + e, then S is overpriced. • Sell short the stock and sell the put. Buy the call. • You now have Xe-r(T-t) +e. Deposit the Xe-r(T-t) in the bank to complete the hedge. The remaining e is profit. • The position is riskless because at expiration s + p = X + c. i.e., • s+max(0,X-s) = X + max(0,s-X)

45. Money pump either way • If the prices persist, do the same thing over and over – a MONEY PUMP. • The existence of the e violates no arbitrage pricing. • Similarly if inequality is in the other direction, pump money by the reverse transaction.

46. Review • Count all incremental cash flows • Don’t count sunk cost. • Understand the real rate. • Compare EAC’s.

48. Exam question • The current machine has annual cost of$55 (end of year). • Next year’s cost will be $60. • The alternative has EAC $56.6. • When should the current machine be replaced?

49. Answer • Start of next year. • That costs 55, 56.6, 56.6, … • instead of 55, 60, 56.6, … • or 56.6, 56.6, 56.6, ...