Chapter 23: Real Options in Capital Budgeting

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Okay, let's unpack this.

Think back to the very first time you learned about capital You were introduced to the bedrock of corporate finance,

discounted cash flow,

DCF.

You meticulously projected revenues, subtracted costs, plugged in a hurdle rate, and you got an answer net present value NPV.

But there's a massive tension at the heart of this whole method.

And that tension is management itself.

Exactly.

DCF, by its nature,

it assumes your firm is going to treat that project, be it a new factory, a product launch, or an oil field, as a completely static passive commitment.

Right.

You invest the initial capital and then you just sort of stand back.

You just let the cash flows roll out, regardless of how the market shifts over the next five, ten, or fifty years.

But that's not how business works, is it?

Not at all.

I mean, managers aren't passive automatons.

If sales are booming, they'll expand production.

Of course.

And if a pilot project completely flops, they'll shut it down early to recover the salvage value.

Or if the economy tanks, they might temporarily mothball a facility until conditions improve.

And those opportunities to make decisions to expand, delay, contract, or abandon are immensely valuable.

They let you capitalize on good fortune and mitigate loss when project outcomes are uncertain.

Right.

This flexibility, the option to act based on future information, is exactly what a simple DCF analysis just ignores.

It completely misses it.

And that, for our deep dive today, is the focus.

Real options.

We're taking the mathematical framework of financial options, you know, calls and puts, and applying it directly to real, non -traded business assets and strategic decisions.

It's the ultimate tool for capturing the value of management and flexibility.

Our mission today is to move methodically through this framework, explaining not just the models but the intuition behind them.

We'll be showing how these option principles can really revolutionize capital budgeting.

And we're going to cover six critical areas step by step.

That's right.

First, the classic option to expand the call option that transforms a losing project into a strategic winner.

Then second, how we can view massive R &D spending as just the purchase of contingent options.

Third, the invaluable timing option, which is the option to wait and gather information.

Fourth, what I like to call the insurance policy,

the abandonment option.

And fifth, the value you get from flexible production and procurement.

And finally, we'll tackle the conceptual foundations that actually allow us to value these non -traded assets, including some really critical concepts like option leverage and, of course, the practical challenges.

Perfect.

So where do we start?

Let's jump right in by looking at the option to expand, starting with a classic scenario from the early days of personal computing.

We are setting the scene in 1982 at a company called Blitzen Computers.

They are evaluating the launch of a new microcomputer, the Mark I.

And this is a huge strategic step.

It's positioning them in an explosively uncertain new market.

But when the CFO crunches the numbers for the Mark I project alone, the forecast is, well, it's grim.

It is.

That's because, given the uncertainty of the market at the time, Blitzen uses a very high hurdle rate, 20%, for a project of this risk profile.

20%, wow.

Yeah.

And looking at the numbers in table 23 .1, the initial investment is $450 million in 1982.

Okay.

They forecast five years of operating cash flows and adjustments for working capital, which are generally positive, but they're just offset by that huge initial cost.

And when you discount those expected cash flows back at 20%, that present value is unequivocally negative.

Right.

It's negative $46 million.

So a hard pass.

If the CFO only relied on a passive DCF, absolutely, the project would be dead on arrival.

But this is where the dynamic reality of management kicks in.

The conversation shifts.

Shifts immediately to, we've got to do it for strategic reasons.

And what we now know is that strategic reasons isn't just some hand -wavy excuse.

It's financial code for, this project buys us a valuable option.

Exactly.

The Markwise true value isn't its immediate cash flows.

It's the call option it provides on the future, more powerful Mark II model.

So the Markwise is the required Sump cost.

It's the entry ticket to the industry.

That's the perfect way to put it.

It enables Blitzen to invest in the Mark II three years later in 1985.

If the market validates their strategy and the Mark II looks profitable.

And if not.

If the market is a bust or the Mark I fails to catch on, Blitzen simply walks away from the Mark II commitment.

They're not locked in.

The flexibility is the source of the hidden value.

So we now need to value that flexibility using the Black Skulls options framework.

Right.

We're essentially valuing a three -year call option on the Mark II project.

Let's establish the inputs.

We're going to need them for the model.

Yep.

As laid out in table 23 .2.

We need the exercise price, which is EX, the asset value S, the time, T, volatility, sigma, and the risk -free rate.

Okay.

Starting with the easy ones.

The time T to expiration is three years.

Right.

And the risk -free rate is given as 10%.

Okay.

Now the exercise price, EX.

This is the total investment required in 1985 to launch the Mark II.

And how much is that?

Blitzen forecasts this will be $900 million.

So double the scale of the Mark I.

Wow.

Okay.

Now for the tricky part, the underlying asset value S.

Yes.

This is the present value calculated today in 1982 of the Mark II's future cash flows, assuming we do decide to commit in 85.

Exactly.

And that underlying value S is calculated using traditional DCF, but only on the cash inflows of the Mark II starting in 1986.

If you look at the table, the expected PV of those inflows calculated in 1985 is $807 million.

Hang on.

Wait.

If the value in 1985 is $807 million and the investment required is $900 million, the Mark II project itself has an expected NTV of negative $93 million in 1985.

The expectation is that the Mark II will lose money.

Exactly.

And when you bring that value back to today, to 1982, the Mark II inflows are worth only $467 million.

Okay.

So that's $807 million discounted back three years at that 20 % cost of capital.

This value, $467 million, is our current underlying asset value S.

The fact that the forecasted NPV is negative is precisely why the option framework is so powerful.

So we are valuing a call option on an underlying asset worth $467 million that is currently deeply out of the money compared to the $900 million investment cost.

That's it.

But we need one more key input.

Volatility.

Oh, the uncertainty.

Because the Mark II is a real asset with no publicly traded market, we have to estimate its volatility.

Blitzen does this by looking at the stock prices of comparable high -tech growth firms,

the market's best guess is about risk, and estimates the annual volatility at 35%.

And it's crucial that this is unlevered volatility, right?

Business risk, not financing risk.

Absolutely.

Okay.

Let's talk about the discounting.

The $467 million asset value was discounted at the 20 % hurdle rate, reflecting its high risk.

But for the black schools model, we need the present value of the exercise price.

Why do we discount that fixed $900 million at the lower risk -free rate of 10 %?

That's a fundamentally important conceptual point.

The $900 million is the required investment if we choose to exercise.

It's fixed.

It is a contractual fixed cash flow treated as a certain liability.

Since the cash flow amount is fixed and not subject to the market risk of the project's failure, we discount it at the risk -free rate.

Which is the appropriate rate for certain cash flows.

Exactly.

So the present value of that liability is $900 million divided by 1 .1 to the power of 3, which is $676 million.

That distinction risky asset at 20 % versus fixed liability at 10 % is so key to understanding this.

So black schools is valuing a call on an asset worth $467 million, with an effective strike price today of $676 million.

Yep.

And we use the standard black schools calculation.

The inputs lead us to calculate these normalization parameters, D1 and D2.

Okay.

So what are D1 and D2 really doing here?

You can think of D1 as a measure of the expected profitability of the option in a risk -neutral world adjusted for volatility.

It helps us find ND1, which is the probability weighted value of the underlying asset we expect to receive if the option finishes in the money.

Okay.

And D2.

D2 is similar and it gives us ND2, which represents the risk -neutral probability that the option will actually expire in the money, meaning the asset value will be higher than the exercise price back in 1985.

Okay.

So after running all those numbers through the model, what's the answer?

The resulting call value is $55 .1 million.

Wait, a passive project with an expected NPV of negative 46 million is saved by a flexibility value of 55 million.

That's right.

That's almost 120 % of the original passive value, and it's coming purely from management choice and the option structure.

Precisely.

We apply the finding using the adjusted present value or APV method.

So APV equals the passive project NPV plus the option value.

So negative 46 million plus 55 million.

Equals a positive $9 million.

The project is now a go.

The financial analysis justifies that strategic gut feeling.

It does.

This really highlights the power of uncertainty.

We said the Mark II was expected to be a loser.

How can its option be worth 55 million today?

Because the option has a non -linear payoff structure.

Figure 23 .1 shows this perfectly.

The downside, where the Mark II value in 1985 is, say, only 500 million, is completely irrelevant.

Right, because Blitzen just throws away the option.

They walk away, saving the $900 million investment, and the payoff is zero.

Their loss is limited to the initial Mark M investment.

But the upside, driven by that 35 % volatility, is uncapped.

If uncertainty resolves favorably and the Mark II is worth $2 billion in 1985.

The option holder captures $1 .1 billion of that.

The $2 billion minus the $900 million cost.

So the option holder gets to fully participate in those high upside scenarios, the shaded area in the figure, while being totally insulated from the downside.

And this is why, counter -intuitively, the higher the uncertainty, the higher the volatility, the more valuable the option becomes.

It increases the chance of a massive payoff without increasing the potential loss.

And I'd guess the 55 million likely understates the full strategic value, because the Mark II itself probably provides a future call option on a Mark III.

Creating a whole chain of growth opportunities.

Which leads us perfectly to our next segment, where sequential investments are the norm.

If the Blitz and Mark I was an entry ticket, then R &D in pharmaceuticals or advanced tech is like buying a whole portfolio of extremely expensive high -risk lottery tickets.

That's a great analogy.

The sheer scale of initial R &D investment, which often fails to generate any immediate revenue, makes traditional DCF incredibly challenging.

It seems almost impossible.

R &D spending is essentially the cost of purchasing a portfolio of real options to make potentially valuable follow -on investments.

The initial cost buys the firm information and the exclusive right to proceed.

Okay, so let's use the pharmaceutical case study to make this real.

We're recasting a simplified clinical trial process, which is illustrated in Figure 23 .2 as a two -stage option investment.

Right.

The initial commitment is $18 million at year zero, which funds Phase II trials.

This $18 million buys a contingent call option.

Contingent on what?

Contingent on success.

Success in Phase II, which we estimate happens with a 44 % probability,

then grants the firm the right to proceed to Phase III.

And the Phase III trials and pre -launch costs, which happen at year two, that's our exercise price, our EX.

Exactly.

And that cost is $130 million.

Okay, so now we need the underlying asset value S.

Right.

This is the value of the drug once it successfully launches, which is forecasted at $350 million in year five.

But here's the added wrinkle.

Clinical risk continues even after Phase II.

Of course.

We assume there's an 80 % chance the drug will successfully launch after the $130 million investment is made at year two.

So we have to probability weight that $350 million launch value by the 80 % success rate, and then discount that expected value back to year zero.

Right.

And for this discounting, we use the drug's cost of capital, which is assumed to be 9 .6%.

So the calculation is?

It's 0 .8 times $350 million, all divided by 1 .096 to the power of five.

This gives us the underlying asset value S in year zero of approximately $177 million.

Okay.

So now we have all the inputs for a two -year call option.

S is $177 million, EX is $130 million, volatility is 20%, and the risk free rate is 4%.

And running those figures through black schools, the resulting option value is $58 .4 million.

And that $58 .4 million, that's the value of the right to proceed with Phase III, but only if Phase II is successful.

Exactly.

Since Phase II only succeeds 44 % of the time, we have to probability weight that option value before we can add it back to our initial investment.

So the total project NPV at year zero is?

It's the initial cost, negative $18 million plus

44 % times that $58 .4 million option value.

Which gives us a positive NPV of $7 .7 million.

The R &D project is justified even though the initial cost has sunk and success is so far from guaranteed.

This structure seems relatively simple, but real R &D has many more stages.

Phase I, II, III, FDA approval, launch.

How do you model that?

That represents a chain of sequential decisions, which are modeled as compound call options.

Compound call?

Yes.

The option you buy at Phase I has a payoff that is the value of the option to proceed to Phase II.

The option at Phase II has a payoff that is the value of the option to proceed to Phase III, and so on.

That sounds incredibly complex to solve.

It is.

You solve these complicated systems, typically using a multi -step binomial tree, working backward from the final launch date to find the optimal decision at every single milestone.

Let's talk about the risk profile, because this is often misunderstood.

We are using probability weighting for the clinical risks, like that 80 % success rate.

Correct.

And that's because those risks are specific to the trial outcome and are likely diversifiable.

We use the cost of capital, the 9 .6%, to discount for market -related cash flow risk.

You don't arbitrarily jack up the discount rate for clinical failure, because that would double -count the risk.

Right.

But the option itself has a unique risk profile.

You mentioned that R &D investments demand higher expected returns than the products they eventually generate.

Why is that?

Because a call option, inherently, is riskier.

It has a higher beta than the underlying asset it is written on.

It's like a leveraged bet.

It's exactly like a leveraged bet.

The firm has limited liability.

They can only lose that initial 18 million.

But they gain exponentially if the drug succeeds.

This leveraged structure means the required return for the R &D option is much higher than the required return for the launched drug's cash flows.

So for CFOs managing R &D portfolios, they need to recognize that their initial investments, which are buying these leveraged options, are intrinsically the riskiest assets the firm holds.

Yes.

Even if the underlying product itself is only moderately risky, it's a crucial concept for high -growth firms.

The high volatility and leverage inherent in innovation requires a much higher expected payoff to justify that initial cost.

We've spent two segments talking about whether to invest and how much.

Now we tackle what is arguably the most common real option managers face.

The timing option.

Even if a project has a positive NPV today, it is often optimal to wait.

The rationale for delay is simple.

Waiting allows you to gather more information.

You resolve uncertainty before you make any reversible commitment.

You keep the call option alive.

Exactly.

And you pay nothing to keep it open while the world reveals its true market conditions.

But there's a critical trade -off, and you can visualize this using the stock option analogy again.

When you hold a call on a stock,

large dividend payments incentivize you to exercise early.

Right.

Because once the dividend is paid, the stock price drops, making your option less valuable if you hold onto it.

So in the world of real assets… The project's cash flows are analogous to the stock's dividends.

If the project's cash flows, the dividends you get by operating it, are large, you will want to invest immediately to capture them, even if you lose the flexibility of the option.

But if the cash flows are relatively small, the value you lose by waiting is minimal compared to the value you gain by holding onto the option.

That's it.

The flexibility to walk away if things go badly.

Or the option to choose a better alternative if one appears.

This is why rational managers delay projects that technically clear the hurdle rate.

Okay, let's look at the classic example, the Malted Herring Factory.

It's a simple project that helps us understand the math of delay.

Right.

The project costs $180 million to build.

If we build now,

the current expected project value is $200 million.

Giving it a positive NPV of $20 million?

Correct.

But if we wait one year, we forego the first year's cash flow, but we gain clarity.

The value next year will either be high demand, $250 million, or low demand, $160 million.

So to decide, we have to value the option to wait one year using the binomial method.

And for that, we need the first most critical input, the risk -neutral probability.

This sounds complex, but it's just a way to solve the problem without having to estimate the risk premium, right?

Precisely.

We calculate the returns in each state, including the first year's cash flow, which is our dividend.

So high demand gives a 37 .5 % return.

Right.

And low demand gives a negative 12 % return.

The risk -free rate is 5%.

We set up the standard risk -neutral equation.

The expected return must equal the risk -free rate.

5 % equals p times 37 .5 % plus 1 minus p times negative 12%, where p is our risk -neutral probability of high demand.

And when you solve for p?

We find the risk -neutral probability of high demand is 34 .3%.

So what does that 34 .3 % risk -neutral probability actually tell us about the market's expectation?

It's a theoretical construct that simplifies the valuation.

In a hypothetical world where investors are indifferent to risk -risk -neutral, the expected return on all investments is the risk -free rate.

So this probability is what makes that true for this project.

Exactly.

By finding p equals 34 .3%, we're finding the probability distribution that makes the expected outcome of the project equal to the risk -free return.

This means we can discount the expected payoff of the option using the risk -free rate, which simplifies the whole process.

Okay, so now we value the option to wait.

At year one, if demand is high, we exercise.

Two 50 million value minus 180 cost gives a 70 million dollar payoff.

And if demand is low, we don't exercise payoff is zero.

So we take those expected payoffs and discount them back one year at the risk -free rate.

The value of the option to wait equals 0 .343 times 70 million plus 0 .657 times zero, all divided by 1 .05.

And the resulting option value is 22 .9 million dollars.

Wow.

The conclusion is inescapable.

The option to wait at 22 .9 million is worth more than the NPV of now, which was 20 million.

You have to wait.

That is a dramatic.

Finding a positive NPV is not enough to commit capital.

It isn't.

And it also answers a genuine challenge a manager might pose.

They might say, but if cash is king, why do we use the risk -free rate to discount the option value instead of the project's real higher cost of capital?

Doesn't that just inflate the value of waiting?

That's a good point.

If we use the higher rate, the present value would drop, maybe making the immediate investment look better.

But the risk -neutral method mathematically compensates for this.

Since we use the risk -neutral probabilities rather than the real -world probabilities, we already adjusted for the risk by adjusting the probabilities.

I see.

So discounting those probability -adjusted certainty equivalents at the risk -free rate is sound financial theory.

We aren't inflating the value of waiting.

We're correctly valuing the flexible payoff.

So let's move this to a more complex scenario.

The choice between mutually exclusive projects on vacant land, a hotel,

or an office building.

Now, waiting means you lose cash flows from both options, but you gain clarity on which one is superior.

This is often called a compound timing option.

And figure 23 .4 shows the optimal decision thresholds.

I see the axes are cash flows for the hotel and the office.

And 100 on the axis represents the point where NPV would be zero.

Right.

And notice that the optimal cash flow level required to justify commitment immediately is around 240.

That's way above the NPV equals zero line of 100.

A massive commitment threshold.

It has to be.

You need two things.

First, the project needs strong enough cash flows to justify giving up the flexibility of waiting.

And second,

the chosen option must clearly dominate the mutually exclusive alternative.

So if the office building cash flow is 250 and the hotel is only 100, we build the office now.

You're far enough in the corner of the chart where one option is clearly superior and high enough to justify losing the flexibility.

But look at the large central wait and C region.

It expands right along that 45 degree line.

Right.

If both options are looking good, but similar, say 250 for the hotel and 245 for the office, you're extremely cautious because the penalty for choosing the slightly worse project and extinguishing the slightly better one is so high that you have to wait until one option clearly dominates.

I bet every real estate developer looks back and wishes they had used this model before committing to a massive office tower right before a market crash.

And you have to remember the competitive caveat.

This model assumes you can just relax and wait.

If a competitor can snap up the neighboring plot and build the hotel while you're waiting.

That threat dramatically shrinks the wait and C region.

It could force you to move immediately just to secure a position.

We focused on the upside,

the option to expand and the option to time an investment.

Now we flip the coin to the downside, the abandonment option.

This is the insurance policy every project needs.

It really is.

The abandonment option is equivalent to a put option.

If project performance deteriorates, the manager has the option to exercise the put.

Meaning they sell the assets for their salvage value.

And the exercise price, the EX of this put is the recovery value of those assets.

Okay, let's use the perpetual crusher example.

It was established years ago.

And now, due to market changes, the project value, the underlying asset, S has dropped to 4 .8 million dollars.

And suppose the recovery value, the salvage value of the equipment in real estate, is fixed at 5 .2 million.

So if we abandon immediately, we get 5 .2 million minus 4 .8 million.

That's 400 ,000 dollars.

The option is 400 ,000 in the money.

It is.

But just like the timing option, we have the option to wait and see if the project recovers before we abandon.

We need to value this right to wait.

And since Black Schools is primarily for call options, how do we value this put?

We can use put call parity.

The relationship is simple.

Put value equals the call value plus the present value of the exercise price minus the asset value.

So we first calculate the value of a comparable call option on the same asset.

Right.

We'll assume a one -year life, 30 % volatility, and a 4 % risk -free rate.

The call option on the 4 .8 million dollar asset with a 5 .2 million exercise price is calculated via Black Schools at about 490 ,000 dollars.

Now we plug that into parity.

The present value of the exercise price, that's 5 .2 million recovered one year from now, discounted at 4%.

Which is exactly 5 million dollars.

So the put value equals 490 ,000 plus 5 million minus 4 .8 million.

Which gives us a resulting put value of 690 ,000 dollars.

So the total value of the project with the option to abandon is its current operating value, 4 .8 million plus the put value 0 .69 million.

For a total of 5 .49 million dollars.

And since 5 .49 million is greater than the 5 .2 million we would get by abandoning today, the rational decision is to wait.

Exactly.

We keep the project alive because that 690 ,000 dollar option value provides substantial downside protection while allowing for the possibility of a recovery.

The value is in the protection.

This framework also addresses that traditional problem of just

arbitrarily fixing a project's economic life, say seven years.

Real options completely eliminate that arbitrary assumption.

Instead, we forecast cash flows out to the project's maximum feasible technical life, maybe 15 years.

And we value the put option that allows the firm to abandon at any time before that.

So the project life is linked dynamically to its performance.

Exactly.

Not a fixed schedule.

Okay.

Let's move to a specialized abandonment option.

Temporary abandonment or the option to mothball assets.

The example here is an oil tanker.

Yes.

An oil tanker operating on the short -term spot charter market.

This is a complex switch option driven by high fixed costs.

What are the costs?

Well, if charter rates fall slightly below operating costs, you might want a mothball, but that involves costs laying off the crew securing the vessel.

But then if rates recover next month, you regret it because there are also high costs to reactivate.

And figure 23 .5 captures this brilliantly.

It plots the value of an operating tanker versus a mothball tanker against the current charter rate.

And you can see the lines cross where the tanker's revenue exactly covers its operating costs.

But the decision thresholds, M for mothball and R for reactivate, are far apart.

M is the rate where the value of a mothball tanker is high enough above an operating one to cover the cost of switching.

And R is the rate where the value of an operating tanker is high enough above the mothballed one to cover the cost of switching back.

The key observation here is the massive gap between M and R.

Huge.

If the tanker is currently operating, rates have to fall all the way down to M before you incur that expensive switch to mothballing.

If it's already mothballed, rates have to recover all the way up to R before you pay the cost to reactivate.

This phenomenon is called hysteresis, right?

A reluctance to change states because of high switching costs.

That's it.

And the wider the gap between M and R, the higher the switching costs and the higher the volatility in charter rates.

High volatility actually increases the gap because the option to wait a little longer before incurring that switching cost becomes even more valuable.

We've seen options to enter, options to leave, and options to wait.

Now let's talk about options that are embedded in the very design of a plant or a supply chain.

The option to vary inputs or outputs.

And this often takes the form of an exchange option.

Right.

The right to exchange one risky asset, like natural gas, for another risky asset, like electricity.

And a textbook example is the CT, or Combustion Turbine Power Plant.

These plants are less efficient than traditional baseload plants, but they are incredibly flexible.

They can be turned on or off in minutes.

So their value isn't in continuous operation?

No.

It's derived from the fact that they hold a series of daily or even hourly call options to produce electricity.

And the decision to exercise that call is driven by the spark spread.

Which is just the electricity price minus the natural gas cost.

The CT plant is exercised only when that spread is high enough to cover its operating costs.

And figure 23 .6 shows this with UK electricity prices.

The prices are extremely volatile, often spiking over 100 pounds per megawatt hour.

Even though the average price might only be 45.

Right.

So if a plant with an operating cost of 60 pounds per megawatt hour was forced to run continuously,

it would lose money, about 1467 per megawatt hour on average.

But because the CT has the flexibility, the option, to operate only when the price is above 60, it captures those high spikes.

And the lower panel shows the impact of exercising that option.

By operating only when prices clear that 60 pound hurdle, the average realized profit jumps from negative 1467 to a highly positive 35 pounds and 41 pence per megawatt hour.

Wow.

So the plant may operate only 5 % of the time.

But the money made during those volatile peaks makes the entire, otherwise inefficient investment worthwhile.

And crucially, the value of this flexibility is almost entirely driven by the volatility of the spark spread.

If electricity and gas prices move perfectly together, the spread would be constant and the option would be worthless.

So high volatility, especially spikes, is what makes the plant valuable.

Exactly.

That's flexibility and output.

Let's look at flexibility in procurement and timing using the example of Hewlett Packard printers.

HP historically faced massive inventory risk.

They would customize printers, adding power supplies, manuals, regional plugs for European markets, ship them over and then find out they had too many German units and not enough French units.

Leading to markdowns and losses.

Big losses.

So their strategic shift was revolutionary.

Ship the printers partially assembled, what we call postponement, and perform the final customization only at the regional distribution centers when a firm order arrived.

This is an option to delay configuration costs.

That's right.

By delaying the commitment, they retain the flexibility to match specific market demand perfectly.

While manufacturing and shipping costs rose slightly, the value gained from better inventory matching far outweighed that expense.

They proved the option to postpone is a significant source of value in the supply chain.

Absolutely.

Okay, our final flexibility example involves buying options on massive capital goods, like airlines buying the Airbus A320.

We're the lead time stretch for several years.

An airline faces a difficult choice between immediate commitment, waiting and deciding later, or buying a purchase option today.

And that option requires an upfront fee.

But it fixes the purchase price, the exercise price, and critically, it fixes a guaranteed delivery date, say in year four.

The value of that guaranteed delivery date must be immense if the airline waits and decides to buy later without the option.

They might pay a higher price and even worse, join a long queue for delivery, possibly waiting until year five or even later.

And figure 23 .8 shows the value of this purchase option relative to a wait and decide later strategy.

The option's value actually peaks when the current NPV of purchasing the plane is near zero.

Right.

If the current NPV is highly positive, the airline would just commit immediately anyway.

And if it's highly negative, they won't exercise the option, so its value is low.

But when the project is marginal, near zero NPV, the option provides maximum flexibility.

If demand improves slightly, they exercise, securing the guaranteed price and that delivery slot.

If demand disappoints, they walk away.

Losing only the option fee.

And the option's value increases dramatically as the queue time for delivery without the option increases.

The option is effectively paying a premium to guarantee a spot on the production line, which is extremely valuable when capacity is constrained.

We've used black skulls, put call parity,

binomial trees, all tools designed for traded financial assets to value non -traded strategic business decisions.

This brings us back to the central theoretical question.

How can we justify using these models for a non -traded asset, like a chemical plant or a new technology patent?

This is the conceptual problem.

Since real options are non -traded, we can't rely on arbitrage arguments, which are the bedrock of financial option valuation, to prove our models are correct.

How do we justify it?

We justify the valuation method through the conceptual foundation of the double.

Okay, tell us more about the double.

The concept assumes that, conceptually, shareholders can buy a portfolio of traded financial assets, the double, that has the exact same systematic risk profile, the same beta, as the real investment opportunity being evaluated.

So you're saying if a specific investment has a market risk that demands a 12 % return, there must exist some portfolio of traded stocks and bonds out there that also demands a 12 % return.

Exactly.

And if the real investment has a double, then the required rate of return for that double is the cost of capital for the project.

By extension, the value of a real option on that project must be the same as the value of an identical traded option written on that theoretical double.

So we don't need the option to actually exist and trade.

We just need to assume it could exist and then value it using the risk -neutral method.

This assumption that traded securities exist with the same risk characteristics supports both DCF and real option valuation.

We're essentially calculating the value of the asset or the option as if it were traded.

And this is also why we use the risk -neutral method.

Yes.

We are, in essence, taking the cash flows and finding their certainty equivalents, which are then discounted at the risk -free rate.

It parallels standard capital budgeting.

The two methods have to yield the same result.

Let's get into the necessary financial mechanics that we've ignored for simplicity, specifically taxes.

How do they affect these calculations?

Taxes are critical.

They have to be accounted for in both the inputs and the discount rate.

First, the value of the underlying asset, S, must be calculated using after -tax cash flows.

Any tax shields from depreciation have to be factored in.

What about the exercise price, the EX?

Similarly, the exercise price must be calculated on an after -tax basis.

If the investment is tax -deductible over time, you subtract the present value of those resulting depreciation tax shields from the initial pre -tax outlay to get the effective after -tax cost.

And the risk -free rate?

Since we are dealing with corporate value, that rate must be the after -tax interest rate.

Why is that?

The logic stems from the structure of a call option.

A call is conceptually equivalent to owning the underlying asset and implicitly taking out a loan equal to the present value of the exercise price.

This implicit borrowing is a debt -equivalent obligation, and we discount safe, fixed obligations using the after -tax risk -free rate.

This idea of implicit borrowing leads directly to the concept of option leverage.

The borrowing doesn't show up on the balance sheet, but it's real financial leverage, isn't it?

Absolutely.

Think about the fundamental formula.

Call option value equals asset value minus the PV of the exercise price.

That PV of the exercise price is mathematically identical to an off -balance sheet zero -coupon loan that the firm implicitly takes out.

And the implication for growth companies, whose value often comes mostly from their PVGO present value of growth opportunities.

Which are, by definition, real options.

It's massive.

It means that a growth firm has substantial implicit financial leverage, even if their traditional balance sheet shows near zero debt.

This option leverage is highly sensitive to the volatility of the underlying asset, making the firm's total equity value much riskier.

So if a CFO at a high -growth tech company truly understands this, they should intentionally run their company with lower ordinary borrowing.

To compensate for the implicit off -balance sheet option leverage attached to their growth strategy.

If they didn't, they would be massively over -leveraged in reality.

So traditional metrics like the debt -to -equity ratio completely miss the financial risk embedded in strategic assets.

They do, if they don't account for this hidden option leverage.

Okay, let's pivot to the final segment.

Acknowledging the practical reality.

These models are elegant, but managers face some pretty big hurdles when trying to implement them.

There are three primary challenges.

The first is complexity.

Real -world decision trees can involve dozens of possible outcomes and decision points.

If the model becomes too intricate, it becomes an analytical black box.

And managers hate black boxes.

They do.

They often prefer a simpler, even if approximate, model they can communicate and trust over a theoretically perfect but inscrutable one.

Second is the lack of structure.

To run black skulls or a binomial tree, you need clear definitions.

A fixed exercise price, a set time horizon, a measurable asset value.

And many real strategic opportunities just don't have that predefined structure.

R &D and resource extraction fit well, but broader strategic moves like evaluating how a new marketing push might open follow -on investments lack the fixed roadmap required for quantification.

And third, the valuation becomes exponentially more difficult when we introduce competitor interactions.

Our models assume passive competitors.

But in concentrated markets, a competitive dynamic emerges.

Your decision to wait and learn might be rational from a single -player perspective.

Like in the malted herring example.

But waiting might mean a competitor gains first -mover advantage and corners the market, extinguishing your option entirely.

That requires layering game theory onto option pricing, which is a whole other level of complexity.

So the models are a conceptual framework for thinking strategically.

Even if the final decision can't always be boiled down to a specific number.

Exactly.

And this framework encourages managers to proactively create value through flexibility.

They can design modular production plants, opting for several smaller, sequentially built plants instead of one giant, efficient facility.

And that slightly higher initial operating cost is justified because they have embedded a cheap option to expand capacity incrementally.

Or like the example of overbuilding infrastructure.

Putting a wider diameter oil pipeline in the ground than currently needed.

The extra upfront cost is small, but it embeds a cheap valuable call option to increase capacity later if more reserves are found.

The value is always in the embedded choice.

So this deep dive has really, I think, fundamentally shifted our view of capital budgeting.

We replaced the static passive DCF assumption with the recognition and valuation of managerial flexibility.

We found that the key to valuation lies in identifying and pricing four key types of real options.

We looked at the call option to expand and capitalize on good news, like with Blitzen.

Right.

The call option to wait and defer commitment until uncertainty is resolved with multi -taring.

The put option to abandon a failing project and recover salvage value, like the perpetual crusher.

And finally, the exchange option inherent in flexible production and procurement, like with those CT power plants.

These methods use DCF as their starting point.

Define the value of the underlying asset, and then apply these sophisticated option pricing models to capture the strategic value of management decisions.

Ultimately, they ensure that capital budgeting accurately reflects the total strategic worth of a project.

And here's a final thought for you to mull over as you encounter finance in the real world.

Since high growth companies rely so extensively on embedded options for their value, their PVGO, and we've established that these options carry significant, implicit, off -balance sheet financial leverage.

What does this tell you about the true risk profile of the most successful, seemingly low -debt tech and growth firms?

Should traditional analysts and lenders adjust conventional metrics like debt -to -equity ratios to explicitly account for this option -based leverage when assessing the risk of innovation, or are they systematically underestimating the true financial volatility of growth?

Thank you for joining us for this deep dive into real options.

We'll see you next time.