Capital Projects as Real Options: An Introduction

The Traditional Approach: An Irreversible Commitment to Invest Invest Don’t Invest Good News Bad News Good News Bad News Cash Flow

The Alternative Approach: An Option to Invest Good News Bad News Cash Flow Invest Don’t Invest

Definitions of Terms Option Pricing –Payoff Diagrams –Determinants of Value –Comparative Statics –Put-Call Parity –Complications: Dividends Early Exercise Basic Capital Budgeting –Incremental Cash Flows –Opportunity Cost –Basic Discounting Time Value Risk –NPV Rule

Mapping Project Characteristics Onto Call Option Contracts ProjectVariable Call Option Cost of Project XExercise Price Value of Assets SStock Price Length of Time tTime to Expiration Decision May be Deferred Risk of Assets  2 Variance of returns Time value of money rRisk-free rate of return

Expressing NPV as a Quotient Rather than a Difference NPV q = PV(Expected Cash Flows)/PV Cost = S/PV(X) NPV q < 1NPV q > 1 Projects here have negative NPVs; call options here are out of the money Projects here have positive NPVs; call options here are in the money

Pricing Call Options: NPV q and Cumulative Variance Black Scholes value of European call option, expressed as a percentage of underlying asset value Call option value increases in this direction NPV q Out of Money In Money Low High

Mapping Projects Into Call Option Space NPV q = 1.0In MoneyOut of Money VI. Exercise NeverI. Exercise Now II. NPV > 0 and NPVq > 1 Wait if possible, otherwise exercise early III. NPV < 0, but very promising because NPVq > 1 and cumulative variance is high IV. NPV < 0 and NPVq <1 Less promising, but high cumulative variance. These projects require active development V. NPV < 0 and NPVq < 1, and cumulative variance is low. Doubtful prospects

Quiz on Real Options 1. Exclusive use of a discounted cash flow (NPV) approach to capital budgeting will _____________ the value of a high-variance project that can be deferred. A. OverstateB. UnderstateC. Fairly Represent 2. Exclusive use of a discounted cash flow (NPV) approach to capital budgeting will _____________ the value of a high-variance project that cannot be deferred. A. OverstateB. UnderstateC. Fairly Represent 3. According to the “real options” approach to capital budgeting, a high-risk negative NPV project that can be deferred should be A. Immediately rejected by the firm B. Immediately accepted by the firm C. Neither A nor B 4. According to the “real options” approach to capital budgeting, a high-risk positive NPV project that can be deferred should be A. Immediately rejected by the firm B. Immediately accepted by the firm C. Neither A nor B