Real Options

flexibility in network design, priced

What is flexibility in a network design worth?

A classic network study optimises for the expected forecast and commits. But demand grows, stalls or collapses. A real option is the right, not the obligation, to act later: build once demand is confirmed, or start small on a big site and expand in steps, or rent with the right to hand the space back. Those rights cost money today. This page prices them on a demand lattice and compares them with the best fixed design, not with a straw man.

No optionCommit nowBuild the full footprint today. Simple, but you carry unused capacity for years if demand is slow.
The fair baselineBest fixedBuild the single size that maximises NPV today. Flexibility is measured against this.
Deferral optionWait & seeServe demand through a 3PL and hold the permits; build once demand crosses a trigger. Later builds cost more.
Growth optionStage & expandBuild small on a big footprint and add capacity in steps where demand justifies it, at a premium per step.
Exit optionLease & breakRent instead of building, with break clauses to hand the space back. Owned sites can be sold too.
How financial options map onto network decisions
Financial analogueReal option in network designHow you build it in
Call optionOption to expandOversized land, utilities and permits; modular buildings; scalable automation; framework contracts with 3PLs
Option to waitDeferral of investmentAn interim 3PL or leased space; phased capital release; keep the incumbent site running one more year
Put optionOption to contract or abandonLeases over ownership; break clauses; shared facilities; shorter asset lives
Switching optionSource, product or mode flexibilityDual-qualified suppliers; multi-product lines; plants that can serve several regions
Compound optionStaged multi-region roll-outHub-by-hub expansion where each opening creates the option to open the next

Decision map: when to act

The shaded fan is where demand may go (the middle 50% and 90% of outcomes, and the median). The lines are the optimal triggers: inside the decision window wait & see builds once demand rises above its line and stage & expand adds its first step above its own; at any time the best fixed design is sold if demand falls below the dashed line (or, if it cannot be resold, mothballed below the dotted line and restarted above the thin one), and at each break date the lease is handed back below its dot.

Payoff by outcome

Each dot is one simulated demand path, with each strategy following its optimal policy. Flexible strategies give up a little in the middle and cut the losses when demand disappoints.

Distribution of NPV

The best fixed design against the best flexible strategy, over the same paths.

Uncertainty makes flexibility valuable

The value of each flexible strategy over the best fixed design, as demand volatility changes (everything else as set). The dashed line is your setting.

Table view

What moves the value of flexibility

Each bar moves one assumption down and up and shows the effect on the value of flexibility (best flexible minus best fixed). Pin down the long bars first.

Compare scenarios

Save the scenario you are looking at, change the assumptions, save again, and compare them side by side. Saved scenarios stay in this browser; each has a link and a decision report.

The model

One facility, one product, money in $M. Every number on this page comes from these equations, which run in src/model.js; the same file is checked by automated tests, including a lattice-against-Black–Scholes convergence test and a Monte Carlo replay of every optimal policy.

Demand moves up or down each step; the lattice recombines, so it stays small enough to solve exactly.
Each strategy is solved backwards from the end of the asset's life: at every node, act or wait, whichever is worth more.
The result: a flexible design gives up a little in the middle and cuts the losses when demand disappoints.

Demand lattice

u = e^(σ·√Δt) d = 1/u p = (e^(g·Δt) − d) / (u − d) D(t,i) = min(D₀·u^(2i−t), ceiling·D₀)

A recombining binomial tree over the whole asset life. The step Δt is a quarter, or monthly or weekly when needed so that p stays inside (0, 1) and the growth you set is reproduced exactly; the page says when that happens. Demand saturates at the market ceiling.

Cash flow per year

own = min(D, K) out = min(D − own, outCap·D₀) lost = D − own − out CF = margin·own + outMargin·out − penalty·lost − opcost·K

Unmet demand goes to a 3PL at a lower margin up to a limit, and the rest is lost with a penalty. The rule is the same for every strategy, including while waiting or while a site is being built.

Operating a capacity

R_K(t,i) = CF(D(t,i), K)·Δt + e^(−rΔt)·[p·R_K(t+1,i+1) + (1−p)·R_K(t+1,i)] R_K(N,·) = 0

The value of running capacity K to the end of the asset life, with no decisions. There is no terminal perpetuity: the asset life is explicit.

Committing with a lead time

commit(t,i) = R_old(t,i) − E_t[e^(−rL)·R_old(t+L)] + E_t[e^(−rL)·R_new(t+L)] − cost

A project started at step t keeps the old capacity running for the lead time L and the new one after it. The L-step expectation uses binomial weights.

Strategies

fixed(K) = commit(0,0; 0 → K) − (F + v·K) best = max over K of fixed(K) defer(t) = max(commit now − (F+v·K)(1+e)^t, wait) stage(t,k)= max(hold, max over k′>k of commit(k → k′) − (F/4 + v·ΔK·(1+premium)))

Decisions are possible only inside the decision window; after it the capacity stays as it is until the end of the asset life. Staging runs one project at a time.

Selling a site

resale(K,t) = salvF·(F + v·K)·(1 − t/N) R_K(t,i) = max(hold, resale(K,t) + R_0(t,i))

Any owned site can be sold at any time, irreversibly; demand is then served through the 3PL (R0). The resale value declines to zero at the end of the asset life. Staging can sell too, at whatever stage it has reached. This applies to the best fixed design as well, so the baseline is not penalised.

Mothballing and contraction

idle CF = CF(D, 0) − mothF·opcost·K A = max(hold_A, hold_B − c_moth, sell) B = max(hold_B, hold_A − c_restart, sell) contract k → k′: V(k′) + salvF·v·(K_k − K_k′)·(1 − t/N)

An idle site sends demand to the 3PL and keeps part of its holding cost; switching each way has a one-off cost, which opens a band between the demand at which it is idled and the demand at which it is restarted. Comparing continuation values means no switch-and-back within a step. A site that resells well is usually better sold than idled. The staged site can also sell capacity back in steps.

Lease with break clauses

CF_lease = CF(D, K) − rent·K at a break date b: R_L(b,i) = max(hold, R_0(b,i) − fee·rent·K) lease = commit(0,0; 0 → K, lead L_f) − fit·F

No capex: rent instead, plus a fit-out cost and time. Break dates fall at the minimum term after the lease starts and then at fixed intervals; breaking costs a fee in years of rent. The leased capacity is chosen to maximise NPV, and the break clauses' value is the lease with them minus the same lease without.

Valuation basis

WACC: drift g, discount at WACC Risk-neutral: drift g − λ·σ, discount at r_f

Discounting expected cash flows at a WACC is the practitioner's convention. Risk-neutral valuation is the theoretically consistent one for options: it reduces the drift by the market price of demand risk λ and discounts at the risk-free rate.

Value of flexibility

flexibility = max(defer, stage, lease) − best fixed

Measured against the best fixed design, which is what a competent planner would choose without options. The gap to the full footprint is shown as well, because that is the comparison most studies make.

Read it as

A decision-support model, not a project appraisal. Its value is the direction and rough size of the flexibility premium, the triggers, and which assumptions they hinge on. It does not yet model several sites, switching between sources or regions, competition, or correlated cost risks.