There is another tool we might consider using to help us with the fact that intangibles frequently change value over time: an option pricing model.
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After all, nearly every day we hear about some sports team picking up a player’s option. Are the fruits of that player’s labor not intangible assets?
Similarly, we read about a studio’s option to make a sequel, or to use a par- ticular actor, or to release a film for television. Does option mean the same thing in all these cases?
An option pricing model can be helpful when there is value associated with waiting to make some investment decision. The model also is helpful when investing in the asset has limited downside risk but unlimited upside potential. A financial option is thought of as an instrument that gives its holder the right, but not the obligation, to some future action. Usually it is the right to either buy or sell an asset. Let us think only of a call option, the right to buy something. Let us also consider only what is called a European call option, which is the type that can be exercised on only one date, the date of expiration.5
What is interesting for our purposes is that option pricing theory takes into account how the value of that right changes over time. A funda- mental difference from calculating value based only on discounted cash flows is that the options model—which in the context of corporate deci- sions is called a real option—also takes into account the value of the abil- ity to defer some investment decision. For intangibles, this comes up a lot.
The decisions when to commercialize a patent, when to license a trade- mark, when to pick up the rights to a sequel, are all examples of option- like thinking.
Example: The Baseball Player’s Contract
Let us think about a baseball player’s contract. Suppose the team owner is willing to pay $1 million for the first year of a new player’s contract, and also wants the option of signing him up for another year, at the end of the first season. The owner does not want to pay the player for a two-year contract because he is still unproven in the majors. The team’s financial advisor decides to value the player’s contract in this way: He calculates what they will have to pay the player in year 2; then he calcu- lates what the player is likely to return in terms of extra ticket sales in that year.
The team will pay the player $1 million the first year and then the probability-weighted salary for the second year of a home-run king ($5 mil- lion), an average player ($1 million), and a player with a career-ending injury (0). The respective probabilities of each scenario are 30 percent, 60 percent, and 10 percent. The present value of the second-year salary is dis- counted at the risk-free rate of 5 percent. (It is discounted only one period
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because the re-signing occurs right after the first year.) The advisor’s calcu- lations for the cost of acquiring this player are:
$1 million first year +(.3 ×$5 mil) +(.6 × $1 mil) +(.1 × $0)
=1 +(1.5 +.6 +0) =1 +(2.1)/1.05 =1 +2 =$3 million Because the owner already has decided to sign the player up for the first year, the cost of paying $2 million now for the second year is what really matters.
The value this player produces, which is the profit attributable to him through increased ticket sales, is estimated as 20 percent more than his salary. Obviously, if he turns out to be a home-run slugger, the team’s return will be much greater than if he is just average, or worse yet, should he wind up injured. So, sales given the three possible outcomes are: $6 million as a home run slugger, $1.2 million as an average player, and 0 if he is injured.
The value of the “investment” in the second year is $2.4 million, which is simply the expected $2.52 million discounted one period. Table 6.1 shows this calculation.
The net present value of signing this player for the second year is then
$400,000: $2.4 million less $2 million now. This does not sound like enough to the owner. Is there some other calculation the owner can use?
Real Options Calculation
This is where we might consider a real options valuation to quantify wait- ing to sign the player for the second year. The real option on this player requires the same five inputs that are necessary to value a financial option.
They are:
1.The value of the underlying asset (S), which is the expected year 2 value of $2.52 million
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TABLE 6.1 Expected Sales
Sales Probability Expected
6.0 0.3 1.8
1.2 0.6 0.72
0 0.1 0
2.52 Discounting rate of 5% gives $2.4 million.
2. The variance Vin the value of that asset, which is 0.82
3.The exercise price (X), which is the expected salary cost of $2.1 million 4.Time to expiration, or time until the decision can be deferred (1 year) 5.Riskless rate of return (5%)
We need to calculate the variance of the expected sales value of $2.52 mil- lion. In options language, what we want is the volatility associated with the different scenarios of this player’s success in the second year. Using the expected probabilities is likely our best source; it is based on the compara- ble historical volatility of the team’s other second-year players. Table 6.2 shows this calculation.
There are a couple of different ways to model this information, but the most widely used is probably the Black-Scholes options pricing model.6The details of how it works are beyond the scope of this text. Suffice to say that it was worthy of the 1997 Nobel Prize in economics.7 Given some rea- sonable assumptions, we find that the option of waiting to sign this player up for his second year is worth about $1 million. The time premium of
$600,000 is the difference between acting now, which is worth $400,000, and waiting, which is worth $1 million. This tells us that the team owner has up to that amount to negotiate as a signing bonus. For example, he can pay the player for the first year and also offer him $500,000 extra for the option to sign him for the next year. Even that would make the owner $100,000 better off than if he committed now to signing the player for year 2.
This example shows that when there is value in waiting to make deci- sions—as there often is with the changing quality of intangibles—an options pricing model is worth considering. To the pharmaceutical com- pany CEO, the option on the baseball player’s prospects in year 2 probably sounds a lot like an option on a new drug after it reaches Stage 3 Food and Drug Administration approval. In turn, those scenarios probably sound pretty familiar to movie studio executives who are trying to decide whether they want to buy the rights to make the sequel to next summer’s potential action blockbuster.
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TABLE 6.2 Option Calculation Expected
Salary Expected Standard
Cost Year 2 Sales Probability Sales Mean Variance Deviations
2.1 6.0 0.3 1.8
2.1 1.2 0.6 0.72 0.84 0.8208 0.90598
2.1 0 0.1 0
2.52
SUMMARY
In this chapter we learned about the basics of the income approach to val- uation. It relies on calculating discounted cash flows, so we examined how to calculate present value. We then applied the income approach to value soda revenues, the cost of worker inefficiencies, and the value associated with Test Company’s proto-asset: its corporate culture. We then thought about what contributed to corporate culture and hypothesized that some of it was represented by the soda machine. For Test Company’s CEO, remov- ing the machine became a more complicated decision once he could iden- tify that it added something positive along both dimensions of the PIE-B.
We also examined the idea of using an options methodology to value intan- gibles. Real options valuation helps address one of the frequent character- istics of intangible assets, namely their unpredictable cash flow outcomes.
It also helps when there might be value in waiting to exercise the option.
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