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Practice of Capital Budgeting

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Practice of Capital Budgeting

Finding the cash flows

for use in the NPV calculations

- Incremental cash flows
- Real discount rates
- Equivalent annual cost

- Cash flows that occur because of undertaking the project
- Revenues and costs.

- Incremental costs are consequences of it
- Time zero is the decision point -- not before

- 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?

- It is a cost of the earlier decision to explore.
- It is not an incremental cost of the decision to raise the treasure.

- to attribute to a project some cost that is
- already incurred before the decision is made to undertake the project.

- Research to design a better hard drive is sunk cost when …
- the decision is made to invest in production facilities and marketing.

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

- revenue that is lost when assets are used in the project instead of elsewhere.

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

- The project is housed in an “unused” building.
- Opportunity cost is the lost rent.

- 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.

- = 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.

- 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.

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

- 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.

- 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

- 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

Time one

Money

Food

Upshot

- 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)

- Convenience.
- Simplify calculations if real flows are steady.
- Examples pages 171-174.

- Long-lived, high quality expensive versus …
- short-lived, low quality, cheap.

- EAC = annualized cost
- Choose the machine with lowest EAC.

- Select the one with the lowest EAC

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

- Assets and firms are valued by their cash flows.
- Value of cash flows is additive.

- 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.

- 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.

- 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

- Put call parity already holds by definition in expiration values.
- If the relation does not hold, a risk-free arbitrage is available.

- 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)

- 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.