Theoretical Questions

• Higher level of uncertainty leads to later investment, but in larger capacity.

• More uncertainty requires the option to be deeper in money before exercise is optional.

• In conclusion the firm should invest more to capitalize on the higher spot price at exercise.

Tax credits meant to promote green investment can have the opposite effect by encouraging brown investment, as seen in the Koch Industries case.

• Koch used tax credit for producing coal briquettes from mining waste - technically alternative fuel, but still carbon-intensive

• Project became profitable mainly due to the tax break, not environmental benefit

• Transfered ressources to polluting activities, extended life of fossil fuels and crowded out truly green innovations

• Short-term tax incentives led to long-term “brown” infrastructure

• A construction delay leads to a later realization of FCFs, which means that the PVs of FCFs goes down.

• An immediate investment in a shell reduces delay (T2 -> T1), reduces the strike (k), since the cost of the shell has already been incurred.

• In conclusion the reduction of flexibility thus may, indeed create value.

• They are not priced, since they are correlted with stochastic discount factor, which make them diversifiable risks & not require a risk premium in complete markets

• -> firm specific & diversifiable accross a large portfolio

• -> In standard asset pricing theory (CAPM/APT), only systematic risk (correlated with overall market/economy) is priced

• -> requires dont require compensation for idiosyncratic risks

• The American Option is higher priced, since it offers higher flexibility as it can be exercised at any point, whereas the European Option can only be exercised at maturity

• Flexibility to time the decision is valuable in cases where early exercise may be benefitial due to favorable movements (market conditions, CF-considerations) in the underlying asset. -> P-k >= (q x X + (1-q) x Y) / DF

• We would never exercise an American Option early if there is no ncy, since delaying the options holds optionality, which has value in uncertain environments.

• Exercising early kills the option & potential upside convience income by holding the underlying, which is derived by them

NCY = opportunity cost of holding the option rather than the asset!

Different Forms:

• Storage Costs (commodities)

When there is no convenience income by holding the UND:

• Finite-life or finite tax credits

• opportunity cost of waiting

  -> each period of delay causes irrversible loss in value/profit (ex: mine cant produce immediantly)

• Erosion in the Underlying

  -> delay reduces lifetime / usuability of UND (ex: lease expiry)

• Shrinkage in the UND

  -> economic value dimishes over time (ex: expiring of tax credits / subsidies)

• Commodities act as dividend stocks, since you can either use them to produce something or to hedge the risk to be running out of them

• In environments of uncertainty & irreversible investments Real Options > DCF

  1. Uncertainty increases Option Value:

     -> as uncertainty (price volatility - ex: electricity, carbon costs) increases, the value of waiting grows, since the firm has the right to act when the information is clearer

  2. Real Options create the possibility of Strategic Delay:

     -> delay in investment in new technology (ex: wind) when it has long-term benefits (rational & strategic delay)

  3. Investment Trigger depends on Comparison Values:

     -> Compare

     1. Value of continuing with the current asset

     2. Value of switching to the new investment

     3. Value of keeping the option alive

  4. Policies can shift exercise-timing:

     -> Tools like carbon tax can the relative cost of old technologies (ex: fossil fuel) and effectively making the option to switch more valuable sooner

HIgher, since:

• Consumption is likely to be lower, so an investor with a concave utility function (decreasing marginal utility) values consumption more in bad states like a recession

• Therefore an additional unit of payoff in the recession state increases overall utility more than the same unit in a boom state

• In conclusion investors are willing to pay more to ensure consumption in bad times

• ß measures risk in an assets return relative to another asset (market index)

• Since market risk cant be avoided it is better to compare risk to a common base

CAPM can be used, if CMCFs are perfectly spanned by the risk-free asset & market index.

1. Growth Option (ex: Home Depot testing new store format to later roll out a chain of stores, European Call)

   -> m = test period, k = CAPEX, UND = PV of the FCFs of the expanded project

2. Staging Option (ex: Walmart rolling out new stores in phases, European Call)

   -> m = time of each stage, k = CAPEX of each step, UND = PV of the FCFs after all stages

3. Option to defer (ex: mining holding a lease, but waiting to operate, Amercian Call)

   -> m = end of lease, k = CAPEX, UND = PV of the FCFs of the mine, when exploited

4. Option to alter operating scale (ex: scaling up or down factory production depending on demand, American Call/Put Option)

   -> m = until project end, k = CAPEX to increase / savings when decreasing, UND = PV of FCFs from adjusted production

5. Option to abandon (ex: closing factory before it becomes unprofitable, American Put)

   -> m = until end of asset life, k = recovery value / cost saving when abandoning, UND = PV of the FCFs (current operations)

6. Option to Switch (ex: switching energy sources in a power plant (fossil fuel -> renewable, American Call Option)

   -> m = project end / technology changes, k = CAPEX of switching, UND = PV of FCFs of operations under new mode