Practice of Capital Budgeting

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

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

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

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

5. 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?

6. 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.

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

8. 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.

9. 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.

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

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

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

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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

19. 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)

20. Real and nominal interest Time zero Time one Money Food

21. Upshot

22. 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)

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

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

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

26. Costs of a machine

27. Equivalent annuity at r = .1

28. Overlap is correct

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

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

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

32. 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.

33. 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.

34. 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

35. 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.

36. 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)

37. 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.

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