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Practice of Capital Budgeting Finding the cash flows for use in the NPV calculations Topics: Incremental cash flows Real discount rates Equivalent annual cost Incremental cash flows Cash flows that occur because of undertaking the project Revenues and costs. Focus on the decision Incremental costs are consequences of it Time zero is the decision point -- not before 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? 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. Sunk cost fallacy is to attribute to a project some cost that is already incurred before the decision is made to undertake the project. 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. 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. Opportunity cost is revenue that is lost when assets are used in the project instead of elsewhere. Example: The project uses the services of managers already in the firm. Opportunity cost is the hours spent times a manager’s wage rate. Example: The project is housed in an “unused” building. Opportunity cost is the lost rent. 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. 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. 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. 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. 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. 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 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) Real and nominal interest Time zero Money Food 1 1 Time one 1 r 1 R 1 r 1 R 1 i 1 r 1 i Upshot 1 r 1 R 1 i ri R 1 i 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) Why use real rates? Convenience. Simplify calculations if real flows are steady. Examples pages 171-174. Valuing “machines” Long-lived, high quality expensive versus … short-lived, low quality, cheap. Equivalent annual cost EAC = annualized cost Choose the machine with lowest EAC. Costs of a machine Time Purchase price Maintenance cost Salvage value 0 100 Total cost 100 1 2 3 20 20 20 12 20 20 8 Equivalent annuity at r = .1 Time Cost 1/(1+r)^t PV Total PV PVAF(.1,3) Equivalent 0 1 2 3 100 20 20 8 1 0.909091 0.826446 0.751315 100 18.18182 16.52893 6.010518 140.7213 2.486852 56.5861 56.5861 56.5861 Overlap is correct Time Machine 1 Machine 2 … EAC1 EAC2 0 1 2 3 4 5 6 100 20 20 8 100 20 20 8 56.6 56.6 56.6 56.6 56.6 56.6 Compare two machines Select the one with the lowest EAC Review Count all incremental cash flows Don’t count sunk cost. Understand the real rate. Compare EAC’s. No arbitrage theory Assets and firms are valued by their cash flows. Value of cash flows is additive. 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. 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. 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 No arbitrage pricing implies put 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. Money pump 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) If 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. .