Reading: Startups as Real Options

We have seen that the value of an option can roughly be assessed with the following six parameters:

• S: Current value of the underlying asset
• X: Exercise price; Price at which we can buy (call option) or sell (put option) the underlying asset
• T-t: Time to maturity; For how many periods the right is valid
• r: Risk-free rate of return in continuous compounding (r = ln(1+R))
• y: Dividend payments of the underlying asset (in continuous compounding)
• σ: Volatility of the return of the underlying asset (i.e., to what extent we expect the value of the underlying asset to fluctuate in the future).

In the context of real options, most of these parameters are not necessarily fixed and management can take actions to influence them.  It is therefore important to understand how changes in the individual value drivers affect the resulting option value. With this knowledge, management can then manage the options so that they might become more valuable.

The purpose of this section is to briefly illustrate the sensitivity of option values (both call and put options) to changes in the value drivers. For a more comprehensive discussion of these so-called "Greeks," see, for example here.

The following table summarizes the main sensitivities of call and put option values with respect to increases in the corresponding value drivers (decreases in the respective value drivers then have the opposite effect on option values):

We can easily verify these sensitivities with the two options that we have considered when discussing the Black-Scholes-Merton model.

Sensitivities of Call Options

The first option we considered there was a the right to buy a license (call option) with the following specifications:

Under the assumptions we made, the value of that license was roughly 20.33 million. How does this value now change when the value drivers change? We can easily test this in our Excel file. Let us assume the following:

• Volatility (σ) increases from 40% to 50%: The resulting call value increases to 23.4 million
• Time to maturity (T-t) increases by 1 year from 1 to 2 years: The resulting call value increases to 26.6 million
• The dividend of the underlying asset (y) increases from 0% to 10%: The resulting call value drops to 14.8 million
• The value of the underlying asset (S) increases from 90 to 100: The resulting call value increases to 27.9 million
• The exercise price of option (X) increases from 80 to 90: The resulting call value drops to 15.4 million

What does this imply for the management ("all else the same" considerations)?

• As long as we hold the right to buy (as opposed to the obligation), risk is actually good. The reason is that a higher risk increases the dispersion of the possible future values of the underlying asset. Thereby, it increases the upside potential. The downside potential, in contrast, is factually unaffected, since we do not exercise the option if the value of the underlying asset drops below the exercise price (therefore, the outcome to us is the same whether the value of the underlying asset is 79 or 10 at the time of expiration: We do not exercise!). Because of this asymmetry in the payoff at maturity, the value of the option increases if risk goes up.
   
  When holding options, managers should therefore try to implement these options in an uncertain (dynamic) market environment. For example, they could try to address customer segments that are more volatile or market segments that are more dynamic.
   
  Note that traditional investment projects typically have an opposite exposure to risk. After all, higher risk increases the cost of capital and therefore reduces the present value of future earnings. This is because once we invest, we actually own the underlying asset and therefore fully participate in the value movements of that underlying asset (after exercising the option, the asymmetry described above disappears).
   
• Time is valuable. For a given project, we should try to postpone major investment decisions to the future so that we maintain the flexibility to walk away if the project develops unfavorably. 
   
• We should try to avoid value depletion of the underlying asset during the life of the option. As we will discuss in the next section, many market opportunities have a finite lifetime. If we do not invest today, we might forego valuable positive cash inflows. 
   
• S matters (obviously). The right to buy an asset at a predefined price becomes more valuable if the value of the asset increases. It can therefore make sense for the owner of the right to try and take measures to improve the value of the underlying asset, for example by trying to establish market entry barriers, lobbying for a favorable regulatory environment, etc. A case in point are the producers of "House of Cards," who lobbied for a favorable tax treatment before deciding where to produce the next season.
  
  
• X obviously matters, too. The more we have to invest, the less attractive an investment opportunity. It might therefore make sense to take initiatives during the lifetime of the option to lower the required investment at the time of exercise, for example by searching for alternative suppliers.

Sensitivities of Put Options

For completeness, let us also briefly discuss the value sensitivities of put options. In the previous section, we have considered a situation where we want to protect the value of an investment with a right to sell it at a predefined price. The put option in question had the following characteristics (values in thousands):

Based on the available information, we have concluded that the right to sell the plant at 1.8 million in 2 years has a value of roughly 66'000 today. Let us investigate as before how the value of this right changes when the value drivers change. Let us assume the following:

• Volatility (σ) increases from 15% to 20%: The resulting put value increases to 110'000.
• Time to maturity (T-t) increases by 1 year from 2 to 3 years: The resulting put value increases to 88'000.
• The dividend of the underlying asset (y) increases from 2% to 5%: The resulting put value increases to 97'000
• The value of the underlying asset (S) increases from 2'000 to 2'200: The resulting put value drops to 31'000
• The exercise price of option (X) increases from 1'800 to 2'000: The resulting put value increases to 143'000

The management implications these sensitivities bring about are similar to the ones discussed above in the context of call options.