Skip to content

Strategic Financial Management · Evaluation of Risky Proposals for Investment Decisions

Simulation, Monte Carlo and Real Options in Capital Budgeting

Updated 11 October 2026 · Fact-checked

Simulation tests a project by repeatedly drawing random values for uncertain inputs, computing NPV each time, and studying the spread of results. Real options value management's flexibility to expand, abandon or defer. To solve: find the base NPV, then add the option value, or compare payoffs across choices.

Understand Simulation, Monte Carlo and Real Options

Most project inputs are uncertain: sales volume, price, cost, life. Sensitivity and scenario analysis change a few inputs by hand. Simulation goes further. It lets all uncertain inputs vary together, each following its own probability distribution.

Monte Carlo simulation works in a loop. You assign a probability distribution to each uncertain variable. You draw a random value for each one. You compute the cash flows and the NPV for that draw. You repeat this hundreds or thousands of times. The NPVs give you a distribution: mean NPV, standard deviation, and the probability that NPV is below zero. Software does the repeats. In the exam you will see only the logic or a small hand-run with a few random numbers.

Simulation has limits. The output is only as good as the assumed distributions. Relationships between variables (for example, price and volume) must be modelled, or the result misleads. It needs time and software, and it shows risk but does not give a single decision rule.

NPV treats a project as a now-or-never choice. In practice, management can change course later. Real options value that flexibility. A project with options is worth more than its plain NPV. Think of it as: Expanded NPV = Base NPV + Value of options.

The common options are three. Expansion option: invest more later if the market turns out good. Abandonment option: stop and sell assets if results are poor, which limits the downside. Deferral (timing) option: wait for information before committing. Each is like a financial option, so Black-Scholes or binomial models can value them. Exam questions usually use a simple payoff comparison or probability-weighted outcomes.

Key rules to remember

Expanded (strategic) NPV
Expanded NPV = Base NPV (without option) + Value of real option
Accept the project if expanded NPV is positive, even when base NPV is negative.
Expected NPV from simulation
Mean NPV = Σ NPVi ÷ n
n is the number of trials. Also report standard deviation and P(NPV < 0).
Abandonment decision
Abandon if salvage value > PV of continuing cash flows
Compare at the decision date using the same discount rate.
Value of abandonment option
Option value = Σ Probability × max(Salvage value − PV of continuing, 0)
Applies to each outcome at the decision date, then discount to today.
Expansion option payoff
Payoff = max(PV of expansion inflows − Expansion outlay, 0)
Exercise only when the payoff is positive.
Option analogy
Underlying = PV of project inflows; Exercise price = investment outlay; Time = decision window; Volatility = uncertainty of inflows
Use when Black-Scholes is asked for a real option. Higher volatility and longer time raise option value.

How to solve Simulation, Monte Carlo and Real Options questions

Use this method for any question on simulation or real options.

  1. 1Identify the type: simulation (random numbers, distributions) or real option (expand, abandon, defer).
  2. 2For simulation, list each uncertain variable and map random numbers to values using the cumulative probability ranges given.
  3. 3Compute cash flow and NPV for each trial, discounting at the stated rate. Show one full working and tabulate the rest.
  4. 4Find the mean NPV across trials and, if asked, the share of trials with negative NPV.
  5. 5For real options, compute the base NPV without any option first.
  6. 6At each decision point, compare the payoff of each action (continue, expand, abandon, wait) and choose the higher. Work backwards if there are two stages.
  7. 7Discount option payoffs to today, multiply by probabilities, and add to base NPV to get expanded NPV.
  8. 8State the recommendation in one line and note any key assumption or limitation.

Quickest way: Option value as a payoff gap

When to use it: Use when a question gives two outcomes with probabilities and asks for the value of an abandonment or expansion option.

  1. Compute base NPV without the option.
  2. In each outcome, pick the better of continue or exercise. The gain over the no-option case is the option's payoff there.
  3. Multiply each gain by its probability and discount it if it arises later.
  4. Add the total to base NPV. A positive result means accept.

Common mistakes in Simulation, Monte Carlo and Real Options

  • Treating simulation as giving one optimal answer

    Students expect a single NPV figure like in DCF.

    Fix: Present a distribution: mean, spread and probability of loss. Then link it to the accept or reject call.

  • Using random numbers outside the assigned ranges

    Cumulative probability ranges are set up carelessly.

    Fix: Build ranges from cumulative probabilities, for example 0.30 and 0.50 give 00-29 and 30-79. Check the last range ends at 99.

  • Ignoring the option and accepting or rejecting on base NPV

    Habit from plain NPV questions.

    Fix: If flexibility is mentioned, compute expanded NPV. A negative base NPV can still become a positive total.

  • Comparing undiscounted salvage value with PV of future flows

    Timing is overlooked.

    Fix: Put both on the same date, then compare. Discount to today only at the end.

  • Counting option value when the option is not exercised

    Adding the full payoff in every outcome.

    Fix: Use max(payoff, 0). Option value is zero in outcomes where exercising does not help.

  • Listing simulation advantages but forgetting limitations

    Theory answers are written from memory of one side only.

    Fix: Give both: it handles many variables and shows the full range, but depends on assumed distributions, correlations and effort.

Worked examples

Example 1

A project needs ₹10,00,000 now. Year 1 inflow is ₹6,00,000 with probability 0.5 (good) or ₹2,00,000 with probability 0.5 (poor). If good, inflows continue at ₹6,00,000 for years 2 and 3. If poor, the firm can abandon at the end of year 1 for ₹5,00,000 salvage, or continue with inflows of ₹2,00,000 in each of years 2 and 3. Cost of capital is 10%. Ignoring any salvage at the end of year 3, find the expected NPV with the abandonment option. Use discount factors: year 1 0.909, year 2 0.826, year 3 0.751.

Show the solution
  1. Good case: inflows ₹6,00,000 in years 1 to 3. PV = 6,00,000 × (0.909 + 0.826 + 0.751) = 6,00,000 × 2.486 = ₹14,91,600. NPV = 14,91,600 − 10,00,000 = ₹4,91,600.
  2. Poor case, decision at end of year 1: PV of continuing (years 2 and 3) at year 1 = 2,00,000 × (1/1.1 + 1/1.21) = 2,00,000 × (0.909 + 0.826) = 2,00,000 × 1.735 = ₹3,47,000.
  3. Salvage ₹5,00,000 is greater than ₹3,47,000, so abandon.
  4. Poor case PV today: year 1 inflow 2,00,000 × 0.909 = 1,81,800. Salvage 5,00,000 × 0.909 = 4,54,500. Total = ₹6,36,300. NPV = 6,36,300 − 10,00,000 = −₹3,63,700.
  5. Expected NPV with option = 0.5 × 4,91,600 + 0.5 × (−3,63,700) = 2,45,800 − 1,81,850 = ₹63,950.

Answer: Expected NPV with the abandonment option is about ₹63,950 (positive), so accept the project. Without the option the poor case would give a lower NPV, so abandonment adds value.

Example 2

A firm plans a pilot plant costing ₹50 lakh with PV of expected inflows ₹46 lakh, so base NPV is −₹4 lakh. If the market is strong (probability 0.4), the firm can spend ₹40 lakh on a full plant, whose inflows have a PV of ₹70 lakh at that time. If the market is weak, it will not expand. Ignoring discounting of the expansion decision, should the firm accept the pilot?

Show the solution
  1. Base NPV of the pilot = 46 − 50 = −₹4 lakh.
  2. Expansion payoff if strong = max(70 − 40, 0) = ₹30 lakh.
  3. Expansion payoff if weak = ₹0 because the firm does not expand.
  4. Value of expansion option = 0.4 × 30 + 0.6 × 0 = ₹12 lakh.
  5. Expanded NPV = −4 + 12 = ₹8 lakh.

Answer: Expanded NPV is +₹8 lakh, so accept the pilot. The expansion option more than offsets the negative base NPV.

Exam tips

  • Write the base NPV first, then the option value, then the total. Marks are given for each step.
  • Always state the decision rule in words: abandon if salvage exceeds the value of continuing; expand if payoff is positive.
  • For simulation, show the random-number ranges table clearly. A tidy table earns method marks even if arithmetic slips.
  • Expect a short theory part: explain Monte Carlo steps, or list advantages and limitations. Prepare both sides in four or five bullets each.
  • In case-based MCQs, match the wording: 'sell the plant if demand is low' is abandonment; 'wait a year for clarity' is deferral; 'add capacity if sales rise' is expansion.

Practice questions from Evaluation of Risky Proposals for Investment Decisions

Simulation, Monte Carlo and Real Options in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Simulation, Monte Carlo and Real Options: frequently asked questions

What is Monte Carlo simulation in capital budgeting?

It is a method that draws random values for uncertain inputs such as sales and cost, computes NPV for each draw, and repeats many times. The results form a distribution of NPV. You read the mean, the spread and the chance of a negative NPV.

What is the difference between an abandonment option and an expansion option?

An abandonment option lets you stop the project and sell its assets if results are poor, which limits losses. An expansion option lets you invest more if results are good, which captures extra gains. Both add to the base NPV.

What are the limitations of simulation in project appraisal?

The output depends on the distributions you assume, and poor assumptions give misleading results. Links between variables are hard to model. It needs time and software, and it does not give one clear accept or reject rule.

Can a project with negative NPV be accepted?

Yes, if the real options attached to it are valuable enough. Add the option value to the base NPV. If the expanded NPV is positive, the project can be accepted.