Practice of capital budgeting
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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.

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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

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.


  • 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.

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.


  • 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

Time one





  • 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

Equivalent annuity at r = .1

Overlap is correct

Compare two machines

  • Select the one with the lowest EAC


  • 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 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.

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)

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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