# Present value of options

## Understanding How Options Are Priced

CFOs tell us that real options overestimate the value of uncertain projects, encouraging companies to overinvest in them. These concerns are legitimate, but we believe that abandoning real options as real time options valuation model is just as bad. How can managers escape this dilemma?

In exploring their reservations about real-option analysis as a valuation methodology, we have come to the conclusion that much of the problem lies in the unspoken assumption that the real-option and DCF valuation methods present value of options mutually exclusive.

We believe this assumption is false. Far from being a replacement for discounted cash flow analysis, real options are an essential complement because they allow managers to capture the considerable value of being able to ruthlessly abandon floundering projects before making major investments. There are. These are not, of course, the only present value of options managers encounter using real options, but they are perhaps the most fundamental sources of error, and the integrated approach we present here explicitly addresses them both.

Integrating Options and Discounted Cash Flow Traditional DCF analysis relies on the straightforward principle that an investment should be funded present value of options the net present value NPV of its future cash flows is positive—in other words, if it will create more value than it will cost.

This works well if we are projecting future cash flows from some historical context, and we are fairly certain of future trends, but not when our estimates of future cash flows are based on a myriad of assumptions about what the future may hold. In such cases, the odds of accurately forecasting cash flows are pretty slim.

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As a result, all the risks of uncertainty how to make money on your internet sites possibility that actual cash flows may be much lower than forecast are captured in the valuation but none of its rewards the possibility that actual cash flows may be much higher than forecast.

This inherent bias can lead managers to reject highly promising, if uncertain, projects. The challenge, therefore, is to find a way to recapture some of the value present value of options through the conservative DCF valuation while still protecting against the considerable risks of pursuing highly uncertain projects. This is where options come in. The possibility that the project may deliver on the high end of potential forecasts, so hard for DCF analysis to take into consideration, is the primary driver of option value.

Options provide the right but not the obligation to invest in a project. Their value, therefore, is driven by the possibility of achieving a large upside gain combined with the fact that companies can usually abandon their projects before their investment in them has cost too much, thus limiting the downside.

One caveat though. It can hardly be stressed enough that a real-options approach can only be used on projects structured somewhat like options—that is, on projects that can be abandoned before you must commit yourself to making major financial outlays if it becomes clear that things will not go well. It would not apply, for instance, to valuing an opportunity that requires you present value of options sink huge sums into building a new factory before you have the first inkling whether the bet will pay off.

In the early stages of an innovative project, the value of the DCF component will be low because of the need to use a high discount rate to adjust for the uncertain nature of future cash flows. At the same time, the real-option value will most likely be high due to that same uncertainty.

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To the left of the diagram, uncertainty is high, so the project value, as measured by the vertical axis, is composed largely of option value, and DCF value is low—even, conceivably, negative. Now, uncertainty should reduce over time if it does not, shut down the project!

But growing certainty also decreases the option value component of the project. The greater the uncertainty, the larger the option component and the smaller the discounted cash flow component. Then it will be in the deep-in-the-money zone.

But between the flee zone and the deep-in-the-money zone is what we call the option zone, where the contribution of the option component adds meaningfully to TPV. It is here that traditional DCF valuations usually clash with present value of options intuition, and so it becomes important to compute both the DCF and the option value of a project. In this example, project A depicted by the solid vertical lines is squarely in the option zone.

As project A progresses, uncertainty should be reduced, so the vertical line should move to the right, as escalating certainty increases the DCF component and decreases the option value component. If the DCF valuation is high, the decision is easy—simply proceed, since success in the project seems very certain, and it is likely to pay off handsomely.

## Investment appraisal and real options

If the DCF valuation produces a strongly negative number and all the value comes from the option, then the project should probably be rejected, unless an investment structure can be created that would allow managers to learn a great deal about the project quickly present value of options for very little cost.

This rule of thumb may cause companies occasionally to miss profitable investments, but in our experience most large firms have more projects than they can fund or staff. So even if the option value is high, why waste time on a project that carries a large negative DCF value?

It is simply too risky, so move on to something better. The majority of growth projects, we have found, lie somewhere in the middle. It is here that our framework is particularly useful because the option value can provide logic to support or refute that intuition. Adjusting for Cost That said, there remain two serious problems with option valuations.

As a result, time value is often referred to as an option's extrinsic value since time value is the amount by which the price of an option exceeds the intrinsic value.

First, it is hard to find good proxies for the input variables the model requires. Financial options use a volatility measure derived from the easily observed historical prices of the underlying assets. But there are almost by definition no historical numbers that managers can use when trying to derive the option value of an innovative project—even to present value of options the net present value of the underlying asset, let alone its volatility. Not the least of them is trying to establish a figure for volatility, for which there are often no historical numbers.

Then for each factor, we specify the range of possible values. These ranges whose widths reflect their associated uncertainties are put into a Monte Carlo simulation, from which we extract the means and standard deviations of total profits, total revenues, and total costs.

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- Understanding How Options Are Priced

The standard deviations of profits, revenues, and costs are used in the calculation of adjusted volatility described in this article, and this adjusted volatility is then used in the option valuation.

The mean of the project value, discounted back at a risk-adjusted rate, becomes the proxy for the current price of the underlying asset.

## Equity in a Deeply Troubled Firm as an Option

We would present value of options, however, that if the original projections are flawed which is very possible with a highly uncertain growth project or if the discount rate is wrong even more likelythe volatility and exercise price estimates will also be wrong.

Realistically, in fact, with highly uncertain projects, any method, no matter how sophisticated, will be wrong. Hence our contention that time spent present value of options about the exact option value of a project is time wasted.

What valuation can and should do is establish relative values within a portfolio of opportunities, providing a means of ranking the contenders, so that managers can select only the most present value of options.

That way, managers will, in the long run, select better projects than their more timid competitors while keeping risk under control and thus outperform their rivals in both the product and the capital markets.

Another source of error involves the time period used in the calculation, and this is even more difficult to resolve. With a financial option, the more time we have before we commit to buying the underlying asset, the more valuable the option.

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This makes sense because the stock has more time to increase in value, and if it does not, we need not exercise, so financial options with longer expiration periods have more value than those with shorter lives all other things being equal. This logic does not extend to the real world, however. Delaying a product launch will not necessarily add value to a project because you end up paying a options quotes forts archive penalty and could even end up missing the market.

The relationship between time and value is much less consistent with real options than it is with financial options. The best way to handle the problem is to formally recognize this competitive reality. Present value of options assume that the project is launched immediately because there is no bonus for delay. If present value of options project is delayed, we actually discount the total project value for the period it is delayed.