Real Options Valuation of R&D Projects
R&D buys the right to implement, not the obligation, and discounted cash flow prices that asymmetry at zero. A 2000 practitioner source builds the valuation instead from two distributions most firms already forecast — and both of its worked examples are reproduced here with their numbers.
The call-option analogy, and the one place it breaks
R2 is a practitioner methods article from 2000. It proposes a valuation model, derives a closed-form result and demonstrates it on two examples; it reports no empirical study. Its opening move is a structural comparison, not a metaphor.
R2'S STRUCTURAL COMPARISON — STOCK OPTION AGAINST R&D PROJECT
| Stock option | R&D project | |
|---|---|---|
| What the owner gets | The right, not the obligation, to buy stock at a stated price — the striking price | The right, not the obligation, to implement the R&D results at some future time |
| First decision | Whether to buy the option, on estimates of uncertain future benefits | Whether to invest in the R&D project — the same logic |
| Second decision, at expiry | Exercise, or let the option lapse | At R&D completion: implement by investing in production and marketing, or terminate if results are not promising |
| Downside | Limited to the option premium | Limited to the amount invested in the R&D phase |
| Number of uncertainties | One — the future stock price. The striking price is known in advance | Two — expected revenues and expected production and marketing costs |
Close paraphrase of R2's own comparison. The last row is the row the rest of the paper is built on.
The consequence R2 draws is directional, not incidental. Traditional net present value analysis ignores the flexibility, systematically undervalues R&D, and causes valuable projects to be rejected on negative NPV — a claim about method bias, not estimator error. For the discounted-cash-flow toolkit it argues against, see financial techniques for R&D project selection, and for the frame that toolkit sits in, the financial frame for R&D management.
Four objections to the classical closed-form model
R2 does not reject the classical model as wrong in its own domain. It states four reasons the model's required inputs are ones R&D cannot supply.
The four stated objections
The distributional assumption
The model assumes the future value of the underlying — for R&D, the cash flows received if the results are implemented — is lognormally distributed and cannot be negative. R2 says this may not hold for every R&D project.
The value of the underlying asset
If the underlying asset is not traded in the market, as with R&D projects, it is difficult if not impossible to establish its value. This is the parameter-determination problem the real-options literature raises.
Volatility
Volatility derives from the price relative — final stock price divided by initial stock price — obtained from historical data, which does not usually exist for R&D projects.
A point-estimate exercise price
The model uses a point estimate for the exercise price, so it cannot recognise uncertainty in production and marketing costs. This is the structural break above, restated as a parameter failure.
R2 also objects to the alternative already in circulation. A decision-analysis approach removes some of the possibly unrealistic assumptions, but it still requires management to estimate the distribution of net cash flows. R2's premise is that management is more likely to hold two separate estimates — production and marketing costs, and anticipated revenues — than a single net-cash-flow distribution.
The model — inputs, equations and outputs
Notation, as R2 sets it out
- V*
- Value of the R&D project at completion of the R&D phase.
- R
- Net present value of the anticipated revenues — the analogue of the terminal underlying price.
- K
- Net present value of production and marketing costs — the analogue of the exercise price.
- X
- Net cash flows, defined as R − K.
- f_X(x)
- Probability density function of the net cash flows X.
- k, t
- Discount rate, and time to completion of the R&D phase.
The verbal rule comes first. At the implementation decision, the value of the R&D project is the difference between the NPV of anticipated revenues and the NPV of production and marketing costs. If revenues exceed costs the project has a positive value; otherwise it has none — and because the firm need not make the additional investment when costs exceed revenues, it never realises a loss from that decision.
- Equation 1, value at completion:
V* = max[0, R − K] - Equation 2, the same rule as a conditional:
V* = R − K if R > K, andV* = 0 if R < K - Equation 3, expected value at completion:
E[V*] = ∫₀^∞ x · f_X(x) dx - Equation 4, what the firm would pay for the R&D at the start:
V = e^(−kt) · ∫₀^∞ x · f_X(x) dx
Equation 5 is the closed form for the case R2 argues is the realistic one. Let R and K be independent, normally distributed random variables with means μ_r and μ_k and variances σ_r² and σ_k². Then X = R − K is normally distributed, with mean μ_x = μ_r − μ_k and variance σ_x² = σ_r² + σ_k².
The expected value of the R&D project at completion is then E[V*] = (σ_x / √(2π)) · e^(−μ_x² / (2σ_x²)) + (μ_r − μ_k) · P(X > 0). Discounting that back over the R&D phase by equation 4 gives what the firm would be willing to pay for the R&D at the beginning.
The conditions under which the normal version holds
Gates R2 states before you use equation 5
- Costs and revenues can be modelled as normal only if the distribution lies far enough right of zero that the probability of negative values is approximately zero.
- R and K must exceed zero; the net quantity X may be positive or negative, which is why a lognormal assumption on the net quantity is inappropriate.
- R and K are assumed independent. Correlated cost and revenue shocks are not handled.
- Average sales must be expected to exceed average production and marketing costs — otherwise, as R2 puts it, the firm will eventually go out of business.
- If the data for the two distributions are approximately normal, the model may be used. If not, fall back on the general integral in equations 3 and 4 with whatever density applies.
- A real, exercisable abandonment option must exist at R&D completion.
R2 also states where the two distributions come from. Depending on the project, the technology and market conditions, the cost distribution could be estimated from data for similar projects or products, and the revenue distribution from sales figures for related products and from market research. That is a historical-baseline method, carrying the same weakness it has elsewhere in R&D financial analysis — it works least well where the technology is most novel.
The model-selection logic
Which valuation to run, following R2's stated sequence
Worked example 1 — a like-for-like comparison
R2 states this example is adapted from a real-options textbook and based on a project at a large pharmaceutical company. Treat every figure as a worked illustration built on figures reported for one case — not a finding of R2, and not a benchmark.
WORKED EXAMPLE 1 — ILLUSTRATIVE FIGURES, NOT BENCHMARKS
| Quantity | Value as printed | Provenance |
|---|---|---|
| Duration of the R&D phase | Four years | Illustrative |
| Cost to implement the results, in year 4 | $1.5 billion | Illustrative, reported case figure |
| Discounted cash value of expected revenues | $1,332 billion as printed — the arithmetic that follows implies $1,332 million | Illustrative; printed inconsistency flagged, not corrected |
| Discount rate k | 20 percent | Illustrative |
| Current value of the project, S = 1332·e^(−kt) | 598.5 | Illustrative, derived in text |
| Cost to implement, K | 1500 | Illustrative |
| Time to expiration, t | 4 | Illustrative |
| Risk-free discount rate, r | .10 | Illustrative |
| Relative volatility, σ | .35 | Illustrative, given rather than estimated |
| Option value from the classical formula | $70 million | Illustrative, computed for comparison |
| Expected value of R, assumed lognormal, for R2's model | $767 million | Illustrative |
| Result of applying equation 3 to that lognormal density | 208 | Illustrative, computed |
| Option value from R2's model after discounting | $93.5 million | Illustrative, computed |
R2's stated conclusion is that its own model returns a value slightly higher than the classical formula's on the same case.
Worked example 2 — the case the classical model cannot take
R2 states this second example is the one used by the earlier decision-analysis authors, although the results are slightly different. Illustrative figures only.
WORKED EXAMPLE 2 — THE NORMAL-DISTRIBUTION DEMONSTRATION
| Quantity | Value as printed | Provenance |
|---|---|---|
| Time to project completion | Three years from now | Illustrative |
| Revenues: mean μ_r | $10M | Illustrative |
| Revenues: standard deviation σ_r | $1.732M | Illustrative |
| Production and marketing costs: mean μ_k | $9M | Illustrative |
| Production and marketing costs: standard deviation σ_k | $1M | Illustrative |
| Net cash flows: mean μ_x | $1M | Illustrative, derived as μ_r − μ_k |
| Net cash flows: standard deviation σ_x | $2M | Illustrative, derived as √(1.732² + 1²) |
| P(X > 0) | 0.69 | Illustrative, derived |
| E[V*] at completion, and willingness to pay at the start | Not recoverable from the extract | Lost in a column break — see the gap note above |
The derived standard deviation shows the variance-addition rule working: two modest spreads combine into a $2M spread on a $1M mean.
The payoff of Example 2 is its closing statement rather than its arithmetic: the classical model could not be used here, because the revenues are not lognormally distributed. That is the demonstration Example 1 could not provide.
What follows, and what the model does not settle
- Implement if and only if R > K at R&D completion. If R < K, terminate; the value is zero and no loss is realised beyond the R&D investment.
- Value the R&D itself with equation 4 and compare it to the cost of the R&D phase. That comparison, not the raw NPV, is the buy decision.
- Do not use a point estimate for implementation cost when that cost is genuinely uncertain. Model it as a distribution.
- Given equal average returns, prefer the project with the larger variance — a much larger payoff is possible at no additional cost, because the loss is capped at the R&D investment.
- Do not reject an R&D project solely on negative NPV.
What to carry forward
- The option analogy is structural and breaks in one place: R&D has two uncertainties, revenues and implementation costs, where a stock option has one.
- The four objections to the classical model are objections about available inputs — untraded underlying, no historical volatility, a lognormal assumption that may not hold, a point-estimate exercise price.
- The proposed model needs only what a forecasting cycle already produces. Its output is the amount the firm should be willing to pay for the R&D phase.
- Cost uncertainty raises the computed value, because variances add. Say so explicitly when you present a number, or it will look like an error.
- Both examples are illustrations. The first borrows the rival model's assumptions on purpose; two figures in the second are not recoverable from the extract.
Frequently asked questions
Does this replace net present value for R&D?
No. It changes what you do with a negative NPV. R2's position is that conventional NPV ignores the right to walk away at R&D completion, and so systematically undervalues R&D projects. The model uses the same cost and revenue projections a firm already builds for NPV, but integrates only the positive part of the resulting net-cash-flow distribution.
Why can't I just use the standard closed-form option-pricing formula?
R2 gives four reasons. The underlying asset is not traded, so its value cannot be established. Volatility in that model comes from historical price relatives that do not exist for R&D. The lognormal assumption on the underlying may not hold. And the formula takes the exercise price as a point estimate, so it cannot represent uncertainty in production and marketing costs.
Why does more cost uncertainty make the project look more valuable?
Because revenues and costs are assumed independent, their variances add, so uncertainty in either raises the spread of net cash flows. A wider spread raises the volatility term in the closed form, and the downside is capped by the option to abandon. It is a genuine consequence of the model, not an artefact, but expect to have to explain it — it inverts the usual capital-budgeting instinct.
How do I estimate the two distributions?
R2 states the sources: production and marketing costs from data for similar projects or products, and revenues from sales figures for related products and from market research. Whether normality then holds is an empirical check on your own data, and the model's gate is that both distributions sit far enough to the right of zero that the probability of negative values is approximately zero.
Are the numbers in the two examples usable as benchmarks?
No. Both are illustrative worked examples. The first is adapted from a textbook case and deliberately adopts the classical model's assumptions so the two methods can be compared like for like, so the $93.5 million against $70 million result is a controlled comparison rather than evidence of general superiority.
What if implementation is already committed?
Then the model does not apply. The whole approach presupposes a real, exercisable abandonment option at R&D completion. If the organisation is contractually or strategically bound to implement whatever the R&D produces, there is no option to value and the downside is not capped.
References and source attribution
- R2 - capturing the option value of R&D. Practitioner methods article in a journal for research and technology management, July-August 2000; 4 printed pages. Proposes a valuation model, derives a closed-form result for the normal case, and demonstrates it on two worked examples. Not an empirical study; 12 references; two figures.
- The real-options textbook case and the earlier decision-analysis treatment that R2 compares itself against are cited within R2 and were not supplied to this library. They are recorded as R2 describes them and are not summarised independently.
- Eleven copyrighted journal articles on R&D project management, supplied as a reading set for a literature review and profiled for this library. Front matter, abstracts, framework sections, tables and figures were read; article bodies were not reproduced, and all content here is paraphrase. The set is a reading list, not a systematic survey of the field.
- Supplied teaching source for this library (research methods and research process materials). Used here for page conventions and voice only; it does not treat R&D valuation.
Suggested questions for Ask KEVOS
- Walk me through equation 5 using my own revenue and cost estimates.
- My project has a negative NPV. Show me how the option frame would change the case I put to the board.
- How do I test whether my cost and revenue forecasts are close enough to normal to use the closed form?
- Draft the explanation I will need when someone asks why more cost uncertainty raised the valuation.
- What would I have to be able to observe before the classical option-pricing model became usable here?
- Compare this model with the decision-analysis approach it positions itself against.