CAPITAL BUDGETING · FORMULA AND EXCEL
1. From a fixed plan to managerial flexibility
Traditional DCF values a specified cash-flow strategy. A real option is the right to change that strategy as information arrives. Flexibility can be valuable when the decision is partly irreversible, uncertainty resolves over time and management can act on it.
Do not add an option already included in scenario cash flows or a decision tree. Exclusivity, patents, permits, access and execution capability determine whether the business actually owns an opportunity.
CAPITAL BUDGETING · FORMULA AND EXCEL
2. Four real options and their applications
| Option | Management action | Example | Cost or trade-off |
|---|---|---|---|
| Expand | Invest more after favourable information | Add a second plant module | Reserve capacity, permits and expansion capex |
| Abandon | Sell or stop when continuation is unattractive | Sell a pilot asset or close an outlet | Closure costs and loss of future upside |
| Delay | Wait before committing the outlay | Develop land after demand becomes clearer | Lost early receipts and competitor entry |
| Switch / flexibility | Change input, output or operating mode | Fuel-switching generation or flexible production | More expensive equipment and switching costs |
When it is useful
Use an explicit option framework when flexibility changes the investment decision materially. Avoid calling an optimistic forecast an “option” if the firm must pay the cost regardless of the outcome.
CAPITAL BUDGETING · FORMULA AND EXCEL
3. Abandonment option: an original two-state illustration
At year 1, the project’s remaining continuation value is either 80 or 30. Management can instead sell it for 45 net of taxes and closure costs. In the high state choose 80; in the low state choose 45. The option adds 0 or 15 at year 1.
For a one-period risk-neutral pricing illustration, assume high-state risk-neutral probability q = 50% and a risk-free rate of 5%. PV of the option = [0.5 × 0 + 0.5 × 15]/1.05 = 7.14. q is assumed, not estimated from historical frequencies.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 80 | High continuation value at year 1 |
| B3 | 30 | Low continuation value |
| B4 | 45 | Net abandonment proceeds |
| B5 | 0.5 | Assumed risk-neutral high-state probability |
| B6 | 0.05 | Risk-free rate |
| B8 | =MAX(B4-B2,0) | High option payoff = 0 |
| B9 | =MAX(B4-B3,0) | Low option payoff = 15 |
| B10 | =(B5*B8+(1-B5)*B9)/(1+B6) | Option PV = 7.14 |
For a traded or replicable underlying asset, q can be derived from state returns. Many real projects are not readily replicable. Then a simple risk-neutral calculation may be an approximation requiring judgement, market calibration and sensitivity analysis.
CAPITAL BUDGETING · FORMULA AND EXCEL
4. Expansion and switching: evaluate state-by-state decisions
Switching benefit = max(value in alternative mode − switching cost − value in current mode, 0)
An expansion opportunity at year 1 has incremental value 90 in a strong state and 40 in a weak state, with optional cost 60. Its payoffs are 30 and zero. With assumed risk-neutral q = 0.5 and risk-free 5%, its PV is 14.29 before any up-front cost of reserving that opportunity.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 90 | High incremental expansion value |
| B3 | 40 | Low incremental value |
| B4 | 60 | Expansion cost at decision date |
| B5 | 0.5 | Assumed risk-neutral probability |
| B6 | 0.05 | Risk-free rate |
| B8 | =(B5*MAX(B2-B4,0)+(1-B5)*MAX(B3-B4,0))/(1+B6) | Expansion option PV = 14.29 |
Model operational constraints and interactions. Switching fuels can change emissions, throughput and maintenance, so compare total incremental cash consequences rather than input prices alone.
CAPITAL BUDGETING · FORMULA AND EXCEL
5. Delay: waiting has a price
Waiting preserves the choice to invest after learning about demand or costs. It can also sacrifice early cash flows, allow competition or lose a permit. Compare invest-now and wait strategies at the same date.
Investing now has NPV 8. Waiting one year allows a payoff of 30 in a strong state or zero in a weak state. Assume risk-neutral q = 0.5, risk-free 5% and an up-front holding cost 2. The wait-strategy NPV is −2 + 15/1.05 = 12.29. Under these assumptions waiting dominates immediate investment by 4.29.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 8 | Invest-now NPV |
| B3 | 2 | Immediate holding cost |
| B4 | 30 | Strong-state net investment payoff in year 1 |
| B5 | 0 | Weak-state net payoff if not investing |
| B6 | 0.5 | Assumed risk-neutral probability |
| B7 | 0.05 | Risk-free rate |
| B9 | =-B3+(B6*B4+(1-B6)*B5)/(1+B7) | Wait-strategy NPV |
| B10 | =B9-B2 | Incremental advantage of waiting |
The year-1 payoffs already incorporate the delayed cash-flow opportunity and investment cost. Do not subtract the investment cost a second time or append the waiting value to the invest-now NPV.
REAL OPTIONS · VISUAL AND EXCEL
6. Recognise a genuine real option
Uncertainty + information arriving later + an actionable right creates the setting for a real option. Management must identify the asset or opportunity, the allowed action, the exercise cost, the decision deadline and who controls the right.
| Question | Expansion example |
|---|---|
| What is the underlying? | Value of extra capacity, not automatically the whole existing business |
| What is the exercise price? | Incremental expansion capex and associated cash needs |
| When can we act? | Only at year 1, or at multiple specified review dates |
| What information changes the decision? | Demand, margins, permits or technical results |
| What makes the right defensible? | Land, spare infrastructure, a licence, contract or protected know-how |
Option value and the investment decision differ
An option may be valuable while the full investment package is unattractive. Subtract the price of acquiring the right and any enabling investment. A delay option can increase the opportunity’s value while making immediate commitment less attractive.
Three valuation levels
Start with a qualitative option map, then a transparent state-by-state decision tree. Use a calibrated lattice or option-pricing model when the decision is material and the inputs can be defended. Simulation without an exercise policy does not by itself value managerial flexibility.
REAL OPTIONS · VISUAL AND EXCEL
7. A complete binomial expansion case
A base project is worth 100 today. Over one year it becomes 130 or 80 with no interim payouts. A one-year risk-free investment grows by 5%. Assume the project’s risk can be priced using a replicating-asset model. These are new case assumptions, separate from the preceding examples.
q = (R − d)/(u − d) = (1.05 − 0.80)/(1.30 − 0.80) = 0.50
The pricing condition d < R < u holds. Under q, the base project reconciles: [0.5×130 + 0.5×80]/1.05 = 100. q is a pricing weight that incorporates risk adjustment; actual investors need not be risk-neutral.
Management may add 50% of the base capacity at year 1 for 55. Incremental payoff is max(0.5V−55,0): 10 in the up state and zero in the down state.
Reproduce it in Excel
Use a separate worksheet for this illustration. Values are ₹ lakh unless stated otherwise.
| Cell | Input / Excel formula | Meaning |
|---|---|---|
| B2 | 100 | Current base project value |
| B3 | 1.3 | Up multiplier |
| B4 | 0.8 | Down multiplier |
| B5 | 0.05 | Effective annual risk-free rate |
| B6 | 0.5 | Expansion fraction |
| B7 | 55 | Expansion cost at year 1 |
| B8 | 102 | Base project acquisition cost today |
| B9 | 1 | Separate fee for expansion right |
| B11 | =(1+B5-B4)/(B3-B4) | Risk-neutral q = 0.50 |
| B12 | =MAX(B6*B2*B3-B7,0) | Up-state option payoff = 10 |
| B13 | =MAX(B6*B2*B4-B7,0) | Down-state option payoff = 0 |
| B14 | =(B11*B12+(1-B11)*B13)/(1+B5) | Option PV = 4.7619 |
| B15 | =B2-B8+B14-B9 | Expanded NPV = 1.7619 |
Base NPV is 100−102 = −2. Adding the expansion right and subtracting its fee gives −2 + 4.7619 − 1 = +1.7619. The conditional right changes the decision under these assumptions.
For real projects with non-traded risks, this replication assumption may not hold exactly. Use market calibration, alternative risk adjustments and sensitivity analysis rather than inserting historical success probabilities into the risk-neutral formula.
REAL OPTIONS · VISUAL AND EXCEL
8. Early exercise: a two-step abandonment tree
A different project is worth 100 today, with annual up/down multipliers 1.25 and 0.80, risk-free 5% and no interim payouts. It can be sold for a fixed net 90 at each review date. Assume replication-based pricing is applicable. Here q = (1.05−0.80)/(1.25−0.80) = 55.56%.
Before expiry: flexible value = max(immediate exit value, discounted risk-neutral continuation value)
Reproduce it in Excel
Use a separate worksheet for this illustration. Values are ₹ lakh unless stated otherwise.
| Cell | Input / Excel formula | Meaning |
|---|---|---|
| B2 | 100 | Current base value |
| B3 | 1.25 | Up factor |
| B4 | 0.8 | Down factor |
| B5 | 0.05 | Annual effective risk-free rate |
| B6 | 90 | Net sale value |
| B8 | =(1+B5-B4)/(B3-B4) | q = 0.555556 |
| B10 | =MAX(B2*B3^2,B6) | Final up-up = 156.25 |
| B11 | =MAX(B2*B3*B4,B6) | Final up-down = 100 |
| B12 | =MAX(B2*B4^2,B6) | Final down-down = 90 |
| B14 | =(B8*B10+(1-B8)*B11)/(1+B5) | Continuation at year-1 up = 125 |
| B15 | =(B8*B11+(1-B8)*B12)/(1+B5) | Continuation at year-1 down = 91.0053 |
| B17 | =MAX(B6,B14) | Flexible up value |
| B18 | =MAX(B6,B15) | Flexible down value |
| B20 | =MAX(B6,(B8*B17+(1-B8)*B18)/(1+B5)) | Today’s flexible value = 104.6583 |
| B21 | =B20-B2 | Incremental abandonment-option value = 4.6583 |
Both year-1 nodes favour waiting in this example. In other cases immediate exercise may dominate. Review exercise and continuation values at each permitted date; a European option allows exercise only at expiry, while an American-style opportunity permits earlier exercise.
REAL OPTIONS · VISUAL AND EXCEL
9. Operating flexibility: switching and contraction
Switching fuel or output
A plant can use fuel A, or pay a switching cost to use B. In a high-price-A state, next-year cash costs are A=30 and B=18 plus switching cost 2, so switching saves 10. In a low-price-A state, costs are A=15 and B=19 plus 2, so keep A and save zero.
For a simple planning example, assume actual state probabilities are 40%/60% and an explicitly assumed 10% risk-adjusted rate for these savings. PV of flexibility is (0.4×10+0.6×0)/1.10 = 3.64. If flexible equipment costs 3 more today, net value is 0.64. The assumed rate must suit the option-like payoff; this expected-value illustration is not an arbitrage-free price.
Reproduce it in Excel
Use a separate worksheet for this illustration. Values are ₹ lakh unless stated otherwise.
| Cell | Input / Excel formula | Meaning |
|---|---|---|
| B2 | 30 | Cost of A in high-price state |
| B3 | 18 | Cost of B in high-price state |
| B4 | 15 | Cost of A in low-price state |
| B5 | 19 | Cost of B in low-price state |
| B6 | 2 | Switching cost |
| B7 | 0.4 | Actual probability of high-price state |
| B8 | 0.1 | Assumed risk-adjusted rate |
| B9 | 3 | Extra flexible-equipment cost today |
| B11 | =MAX(B2-B3-B6,0) | High-state saving = 10 |
| B12 | =MAX(B4-B5-B6,0) | Low-state saving = 0 |
| B14 | =(B7*B11+(1-B7)*B12)/(1+B8)-B9 | Net expected-value benefit = 0.6364 |
Contract or temporarily shut down
Contraction reduces scale while preserving part of the business. Compare released capital and avoided costs against the value of cash flows given up. Temporary closure differs from permanent abandonment because reopening costs and restart rights matter.
For example, releasing capital worth 12 while giving up a segment worth 8 creates an immediate incremental contraction payoff of max(12−8,0)=4 at the decision date. Include severance, taxes and restart costs where applicable.
REAL OPTIONS · VISUAL AND EXCEL
10. Option value drivers and a Black–Scholes illustration
For a simple expansion call with other assumptions held fixed, more underlying value, lower exercise cost and greater volatility generally increase option value. More time can help a right that preserves the same earlier exercise opportunities, but real-project competition, lost operating cash flows and rising costs can offset that benefit. Greater uncertainty can raise option value while making the overall business less attractive.
| Option input | Real-project interpretation |
|---|---|
| S | PV of incremental capacity cash flows |
| K | Cost required to exercise the expansion |
| T | Time until the expansion right expires |
| σ | Volatility of incremental project-value returns; not simply sales volatility |
| r | Maturity-consistent risk-free rate |
| Payout / carrying effect | Cash flows or opportunity benefits lost while waiting |
A separate European expansion illustration
Assume S=50, K=55, T=1 year, σ=25%, continuously compounded r=5% and no interim payouts. This is a separate lognormal model, not the discrete tree above.
d₂ = d₁ − σ√T
Call value = S N(d₁) − K e−rTN(d₂)
Reproduce it in Excel
Use a separate worksheet for this illustration. Values are ₹ lakh unless stated otherwise.
| Cell | Input / Excel formula | Meaning |
|---|---|---|
| B2 | 50 | PV of incremental project cash flows |
| B3 | 55 | Expansion cost |
| B4 | 1 | Years to exercise |
| B5 | 0.25 | Annual value-return volatility |
| B6 | 0.05 | Continuously compounded risk-free rate |
| B8 | =(LN(B2/B3)+(B6+B5^2/2)*B4)/(B5*SQRT(B4)) | d1 = −0.056241 |
| B9 | =B8-B5*SQRT(B4) | d2 = −0.306241 |
| B11 | =B2*NORM.S.DIST(B8,TRUE)-B3*EXP(-B6*B4)*NORM.S.DIST(B9,TRUE) | Option value = 4.0132 |
Black–Scholes requires restrictive assumptions. It does not directly value arbitrary early exercise, several linked management decisions or changing operating modes. A lattice is often easier to adapt. State how non-traded risks, competition, development time and project payouts are treated.
REAL OPTIONS · VISUAL AND EXCEL
11. Use the result as an operating decision rule
- Define the base strategy and a genuine right to change it.
- Estimate incremental state-dependent values and all exercise costs.
- Use consistent probabilities, risk adjustments and compounding.
- Value backwards and record the action at each node.
- Subtract the cost of creating or acquiring flexibility.
- Set review dates, measurable triggers, accountable owners and execution limits.
Options can interact: abandonment can remove future expansion rights, and switching can change the benefit of later expansion. Their separately calculated values are therefore not automatically additive.
Reviewed references for this expansion
Guthrie (2009), Real Options in Theory and Practice, selected modelling-framework discussion (printed pp. 22–23); Brach (2003), Real Options in Practice, selected staged-investment and switching discussion (printed pp. 36–38); Mun, Real Options Analysis, opening abandonment-model discussion (printed pp. 171–172). The uploaded three-case article was reviewed as a comparison; inconsistent inputs and formula typography were not copied. All numerical cases added here are original.
Further reading: Damodaran, The Promise and Peril of Real Options.
CAPITAL BUDGETING · FORMULA AND EXCEL
12. Inflation: match nominal and real quantities
CFnominal,t = CFreal,t(1 + inflation)t
For a separate one-year project, the current-price receipt is 110, initial outlay 100, general inflation 5% and real required return 8%. Nominal receipt = 115.5; nominal rate = 13.4%. Both routes give NPV = 1.85.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | -100 | Initial cash flow |
| B3 | 110 | Year-1 cash flow in today’s purchasing power |
| B4 | 0.05 | Inflation |
| B5 | 0.08 | Real required return |
| B7 | =(1+B4)*(1+B5)-1 | Nominal rate = 13.4% |
| B8 | =B3*(1+B4) | Nominal receipt = 115.5 |
| B9 | =B2+B8/(1+B7) | Nominal NPV |
| B10 | =B2+B3/(1+B5) | Real NPV; same 1.85 |
Differential inflation and taxes
Sales prices, wages and input costs can inflate at different rates. Build their nominal paths separately; compute cash taxes from the applicable nominal tax rules. Historic-cost tax depreciation does not automatically rise with inflation. Then discount nominal after-tax cash flows at a nominal required return.
CAPITAL BUDGETING · FORMULA AND EXCEL
13. International appraisal: currency and perspective
Use an exchange-rate quote defined as parent currency per unit of foreign currency.
A one-year project costs US$1 million today and pays US$1.2 million next year. Spot is ₹83/US$; the assumed future conversion rate is ₹85/US$. Cost = ₹83 million; receipt = ₹102 million. At a stated INR required return of 12%, NPV = 102/1.12 − 83 = ₹8.07 million.
Reproduce it in Excel
Use a separate worksheet for this illustration.
| Cell / range | Enter / formula | Meaning |
|---|---|---|
| B2 | 1 | Initial USD million |
| B3 | 1.2 | Year-1 USD million |
| B4 | 83 | Spot INR per USD |
| B5 | 85 | Assumed future INR per USD; not a live quote |
| B6 | 0.12 | INR required return |
| B8 | =-B2*B4+B3*B5/(1+B6) | NPV in INR million |
Expected future FX and the discount rate must form a coherent valuation model. A forward rate is a hedge price, not automatically an unbiased forecast. A foreign-currency valuation converted at spot agrees with a parent-currency route only when rates, FX and risk assumptions are consistent.
Parent versus subsidiary
Consider withholding taxes, remittance limits, blocked funds, transfer-pricing effects, local borrowing, country risk, closure costs and convertibility. Use the parent’s incremental remittable cash flows when answering a parent investment question. Do not multiply tax or country-risk charges already captured elsewhere.
Sources and further reading
Selected relevant sections of the supplied materials informed this series. Prasanna Chandra’s planning framework also informs the emphasis on estimation and strategic fit. These are original explanations and teaching cases, not reproduced textbook examples.
- Prasanna Chandra (2019), Projects: Planning, Analysis, Selection, Financing, Implementation, and Review, 9th edition, McGraw Hill. The uploaded 150-page scan was visually checked in selected opening sections: importance and difficulties of capital investment, project categories, planning–analysis–selection–financing–implementation–review, strategy and demand forecasting. It ends during Chapter 4; later detailed appraisal chapters appear in its contents but are not present in this extract.
- Dayananda, Irons, Harrison, Herbohn and Rowland (2002), Capital Budgeting: Financial Appraisal of Investment Projects, Cambridge University Press. Reviewed selected passages on relevant cash flows, appraisal methods, sensitivity, simulation and capital constraints. The chapter structure also guides further reading.
- Dr. Vijay Shankar Pandey, Capital Budgeting Techniques, uploaded as “Basics of Capital Budgetings”: process, payback, ARR, NPV, IRR and comparison. Rounded examples and conventions are checked independently rather than copied.
- Professor James P. Dow Jr., FIN 303, Part 8: Topics in Capital Budgeting: uncertainty, flexibility and unequal project lives.
- Capital Budgeting – Risk Analysis, uploaded five-page extract: probability, certainty equivalents and risk-adjusted approaches.
For continued study: Dayananda Chapters 1–2 for foundations; 5–6 for appraisal; 7–9 for risk; 11–12 for constrained selection; 16 for international appraisal. Review here is targeted, not a claim that the entire 343-page book was read.
Prasanna Chandra: further-reading map
The 9th-edition contents identifies Chapter 8 (Investment Criteria), Chapter 9 (Project Cash Flows), Chapter 10 (Cost of Capital), Chapter 11 (Project Risk Analysis), Chapter 12 (Project Rate of Return) and Chapter 13 (Special Decision Situations). These are reading directions, not claims that their absent pages were consulted.
Public reference links
All rates, taxes, exchange rates and business figures in the examples are teaching assumptions. Results use unrounded calculations and are rounded for display. Excel formulas use English function names and commas.