A developer is interested in a parcel of land for a small mixed use development. Similar developments are worth $15 million and require the following sequential investments to complete:
Phase Description
1 Purch. land, permitting, utilities
2 Build retail
3 build apartment
Cost Time to complete
3 million 1 year
10 million 2 years
7 million 2 years
The volatility of the development value is 25% and the risk-free rate of interest is 3%. Due to competition the developer knows that the project will have to be completed in the next 6 years or not at all.
1. If the developer has to make a decision today (ie. invest today or do not invest at all) and assuming that a suitable discount rate for the project is the risk free rate plus 3% premium, should the project be undertaken?
2. Using the data provided above, give the developer some advice on how to proceed with this opportunity?
3. What is the probability that the development will actually be completed?
4. Suppose that after a careful examination of the data, the volatility is though to be lower than first anticipated for this project. What level kills the optionality in the investment and will force the developer to walk away from this opportunity?
5. Explain why your answer to number 4 above makes sense. That is, what is the relationship between volatility and the value of an option in the context of this investment decision?
1. To determine if the project should be undertaken, we need to calculate the net present value (NPV) of the project and compare it to zero. The suitable discount rate for the project is the risk-free rate plus a premium of 3%. In this case, the discount rate would be 3% + 3% = 6%.
To calculate the NPV, we need to discount each cash flow at the appropriate time period. The cash flows for this project are:
- Year 0: Initial investment of $3 million for land, permitting, and utilities
- Year 1: Cash flow of -$3 million (assuming no income yet)
- Year 2: Cash flows of -$10 million and -$7 million for building retail and apartments, respectively
- Year 3 and beyond: No cash flows mentioned, so we assume no income or expenses
To calculate the NPV, we discount each cash flow at a rate of 6% and sum them up:
NPV = (-$3 million) / (1 + 0.06) + (-$10 million) / (1 + 0.06)^2 + (-$7 million) / (1 + 0.06)^2
Computing this will give us the NPV for the project. If the NPV is positive, then the project should be undertaken. If it is negative, the project should not be undertaken.
2. If the NPV is positive, the developer should proceed with the project. However, given the time constraints of completing the project within 6 years, the developer needs to carefully plan the scheduling of each phase to ensure timely completion.
The developer should conduct a thorough analysis of the local market conditions, including demand for retail and apartments in the area, and the potential for rental or sale income from the development. It may also be prudent to consult with experts in the field (such as real estate agents, construction professionals, and financial advisors) to gain a better understanding of the risks and opportunities associated with the project.
Additionally, the developer should consider potential contingencies, such as cost overruns, delays in construction, and changes in market conditions, and factor them into the financial projections and decision-making process.
3. The probability of the development being completed depends on various factors, such as the developer's commitment, availability of financing, market conditions, and ability to execute each phase on schedule. Without specific information about these factors, it is difficult to provide an accurate probability.
However, the fact that the developer is considering the project suggests a certain level of intention and motivation to complete it. A thorough analysis, proper planning, and diligent execution can certainly increase the probability of successful completion.
4. The level of volatility that would kill the optionality in this investment depends on the developer's risk tolerance and the potential consequences of the investment not being profitable.
If the developer determines that the potential downside risks outweigh the potential upside potential, they may decide to walk away from the opportunity. This threshold will be subjective and depend on the specific circumstances and the developer's risk appetite.
5. In the context of investment decisions, volatility has a significant impact on the value of an option. In this case, the development project can be seen as an option to invest, as the developer has the choice to proceed or not based on market conditions and projected returns.
Higher volatility increases the potential range of outcomes (both positive and negative) for the project's value. This makes the option to invest more valuable because there is a higher chance of favorable outcomes. On the other hand, lower volatility reduces the potential range of outcomes and decreases the uncertainty associated with the investment. This can reduce the value of the option and may push the developer to walk away if the remaining potential return doesn't justify the risks involved.