Real Options — Expand / Abandon / Defer

Real Options Ch. 29 — CRR Binomial Lattice

Project Value ($M)

Volatility (%)

Time Horizon (yrs)

Risk-Free Rate (%)

Lattice Steps

Expansion Cost ($M)

Cost to invest and expand capacity

Salvage Value ($M)

Liquidation / salvage proceeds

Investment Cost ($M)

Cost to exercise (European — wait to invest)

Vol Min (%)

Vol Max (%)

Expand (Call)—

Abandon (Put)—

Defer (European Call)—

NPV (expand)—

NPV (defer)—

Abandon vs Hold—

Expand Premium—

Abandon Premium—

Defer Premium—

u (up factor)—

d (down factor)—

p (risk-neutral prob)—

u = e^{σ√Δt}, d = 1/u
p = (e^{rΔt} − d) / (u − d)
V_option = max(V_continue, V_exercise)

Ch. 29 — Real Options Lattice Ch. 29 — Option to Expand/Abandon/Defer