Real Options and Corporate Investment Decisions

Fundamental Concepts of Real Options

• Definition of Real Option: A real option is the right to make a particular business decision, such as a capital investment, after new information is learned. This differs from a financial option, which is the right to buy or sell a traded asset, such as a stock.

• Key Distinction: Unlike financial options, real options and the underlying assets on which they are based are often not traded in competitive markets.

• Types of Real Options: Corporations frequently encounter several types of options in their decision-making processes:

  • Timing Option: The option to delay an investment opportunity.

  • Growth/Expansion Option: The option to grow or increase the scale of a project.

  • Abandonment Option: The option to shut down or exit an investment.

• General Valuation Formula: The value of a real option is calculated as the difference between the Net Present Value (NPV) with the option and the NPV without the option:     $\text{Value of Real Option} = \text{NPV with option} - \text{NPV without option}$

The Option to Delay an Investment Opportunity (Timing Option)

• Scenario Overview: Consider an electric car project that can be invested in today ($t=0$) or in exactly one year ($t=1$).

  • Current Investment Cost: $180 \text{ million}$.

  • Current Project Value: $200 \text{ million}$.

  • Immediate NPV: $200 \text{ million} - 180 \text{ million} = 20 \text{ million}$.

• Future Uncertainty: Future cash flows vary based on consumer tastes and the state of the economy. Waiting allows for the resolution of uncertainty but results in the loss of the first year's cash flow.

• Expected Valuation ($t=1$):

  • High Demand: Generates $25 \text{ million}$ in cash flow and a project value of $250 \text{ million}$. Total Value: $275 \text{ million}$.

  • Low Demand: Generates $16 \text{ million}$ in cash flow and a project value of $160 \text{ million}$. Total Value: $176 \text{ million}$.

• Risk-Neutral Probabilities: These are the probabilities of the up and down states that make the price of the underlying asset equal to its expected future payoffs, discounted at the risk-free rate ($r_f$). Under risk-neutrality, all assets have an expected return equal to the riskless rate.

  • Risk-free rate: $5\%$ per annum ($p.a.$).

  • Calculation for Probability of High Demand ($p$):         $200 = \frac{p \times 275 + (1-p) \times 176}{1 + 0.05}$         $200 = \frac{275p + 176 - 176p}{1.05}$         $210 = 99p + 176$         $34 = 99p$         $p = 0.343$

  • Probability of High Demand: $0.343$.

  • Probability of Low Demand: $1 - 0.343 = 0.657$.

• Valuation with the Option to Wait:

  • If Demand is High ($t=1$): Invest $180 \text{ million}$. The NPV is $250 \text{ million} - 180 \text{ million} = 70 \text{ million}$.

  • If Demand is Low ($t=1$): Do not invest. The NPV is $0$.

  • Present Value of the Timing Option at $t=0$:         $\text{PV} = \frac{0.343 \times 70 + 0.657 \times 0}{1.05} \approx 22.9 \text{ million}$

• Calculating Option Value:     $\text{Option Value} = 22.9 \text{ million} - 20 \text{ million} = 2.9 \text{ million}$

The Option to Expand (Growth Option)

• Scenario Overview: An investment requires $10 \text{ million}$ today. In one year, the success of the project is revealed. The risk-neutral probability of success ($p$) is $50\%$.

  • If successful: The project generates $1 \text{ million}$ per year in perpetuity.

  • If failed: The project generates nothing ($0$).

  • Risk-free rate: $6\%$.

  • Expansion terms: At $t=1$, the project size can be doubled on the original terms (invest another $10 \text{ million}$ for an additional production line).

• NPV Analysis Without the Expansion Option:

  • Expected annual cash flows: $1 \text{ million} \times 0.5 = 0.5 \text{ million}$.

  • NPV calculation:         $\text{NPV} = \frac{500,000}{0.06} - 10,000,000 = -1.667 \text{ million}$

  • Decision without the option: The project should not be undertaken.

• NPV Analysis With the Expansion Option:

  • If the project is a success ($t=1$), the NPV of doubling the project size is:         $\text{NPV}_{\text{double}} = \frac{1,000,000}{0.06} - 10,000,000 = 16,666,667 - 10,000,000 = 6.667 \text{ million}$

  • Present Value of the Growth Option today:         $\text{PV}_{\text{growth option}} = \frac{0.5 \times 6.667 + 0.5 \times 0}{1.06} = 3.145 \text{ million}$

  • Total NPV with Expansion Option:         $\text{Total NPV} = -1.667 \text{ million} + 3.145 \text{ million} = 1.478 \text{ million}$

• Conclusion: Because the total NPV is positive, the project should be undertaken today specifically because of the existence of the future expansion option.

The Option to Abandon

• Scenario Overview: A CFO is considering opening a gourmet food store in the Boston Ferry Building.

  • Setup Costs: $400,000$.

  • Operating Costs: $10,000$ per month.

  • Revenue if Tourist Attraction (50% probability): $16,000$ per month in perpetuity.

  • Revenue if not a Tourist Attraction (50% probability): $8,000$ per month in perpetuity.

  • Cost of Capital: Based on the risk-free rate because the uncertainty is idiosyncratic.

  • Risk-free rate: $7\%$ per year ($0.565\%$ monthly).

• Analysis: Forced Operation (No Abandonment):

  • Monthly Net CF (Success): $16,000 - 10,000 = 6,000$.

  • Monthly Net CF (Failure): $8,000 - 10,000 = -2,000$.

  • NPV calculation:         $\text{NPV} = \frac{6,000 \times 0.5 + (-2,000) \times 0.5}{0.00565} - 400,000 = -46,018$

  • Decision: Do not open the store.

• Analysis: With Option to Abandon:

  • A lease clause allows breaking the lease at no cost after two years ($24 \text{ months}$). Success or failure is immediately obvious upon opening.

  • State 1: Tourist Attraction:         $\text{NPV} = \frac{6,000}{0.00565} - 400,000 = 661,947$

  • State 2: Not a Tourist Attraction:         The store will close after 24 months. Monthly losses of $2,000$ for 24 months plus setup costs:         $\text{NPV} = -400,000 + \frac{-2,000}{1 + 0.00565} + \frac{-2,000}{(1 + 0.00565)^2} + \dots + \frac{-2,000}{(1 + 0.00565)^{24}}$         $\text{NPV} = -444,770$

  • Total Project NPV:         $\text{NPV} = (0.5 \times 661,947) + (0.5 \times -444,770) = 108,589$

• Value of the Abandonment Option:     $\text{Option Value} = 108,589 - (-46,018) = 154,607$

Summary and Strategic Importance

• Real Options Have Value: An opportunity can be worth something today even if the static NPV is negative, provided there is a chance it could be positive in the future via management flexibility.

• Exploiting Real Options: To create value, firms must continually re-evaluate investment opportunities. This includes the flexibility to delay, abandon, create, or grow projects as new information is revealed.

Questions & Discussion

• Class Discussion: Costs and Benefits of Waiting:

  • Question: What are the benefits and costs of waiting in the electric car example?

  • Answer Context: Waiting helps resolve uncertainty (benefit) but results in the loss of initial cash flows (cost).

• Interactive Session:

  • Q&A Forum: Opportunity provided for students to ask questions regarding the material before the conclusion of the session.