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Developing Decision Trees and Payoffs

How to develop a decision tree and the payoffs using the information given

The Problem:
Joe Morgan, an investment strategist has learned of a couple alternatives that his company can invest in. His firm has chosen to invest in real estate. Occasionally the firm will invest in commercial real estate, but mostly in residential development and timberland.
In general, there are two alternatives: one is to invest in residential real estate, the second is to invest in a more stable and less risky timberland asset. They have recently sold an asset that provided about $5 million for them to invest. The asset was a real estate investment property, and they want to buy another real estate investment property to avoid paying capital gains tax, in accordance with Section 1031 of the Internal Revenue Code.

The potential residential property, which consists of 200 acres, has recently become available for the asking price of $25,000 per acre. The firm will have to invest another $30,000 per acre to install the underground utilities required by the city planning authority. They believe, that when the market is strong, they will be able to sell approximately 200 three quarter-acre lots for $80,000 each. This would mean that there would be one lot per acre. The remaining quarter acre would be used for roads and common area. If the economy slows down, to say an average pace, then the returns will diminish the present value of the lots by $10,000. Joe believes that there is a 25% chance that the demand will be strong and a 60% chance of an average demand.

Another alternative would be to develop the property such that they could sell 400 one-third acre lots. The selling price in a strong market for these smaller lots will be $45,000. However, the price could be reduced in an average market by $5,000 each. In this plan, there will be about 2 lots per acre, while the balance of the acre will be used for road and common areas. Again, the probability of there being an average market is about 60%, while there is a 25% chance there will be a high demand for the smaller lots in the next 15 years. Joe's firm can make a nice profit on both of these scenarios, however if the market turns completely south, the firm will lose or come close to losing their investment. In the case of the smaller lots, the price per lot would drop to $30,000. Joe believes that there is a 15% chance of this market condition occurring regardless of which size lot they go with. The price would drop to $50,000 for the larger lots. Another factor for the residential tract is the underground utility cost. There is a 60% chance that Joe's firm could experience some difficulties due to the topography and excessive rock formation underneath the surface. This condition would add a $5,000 cost per acre for the plot with smaller lots. The cost for the plot with the larger lots would be $2,500 per acre. The timberland alternative is not as complicated as the residential property because there are not as many variables involved. The tract is 2000 acres and can be purchased for $2,500 per acre. This particular tract has some potential to be split into smaller tracts. There has been a trend in recent years for mini-farms. Joe believes that in the next 15 years this tract could be subdivided into 40 to 80 acre plots, and could sell for $6,000 per acre which would be a profit of $3,500 per acre. He believes that there is a 30% chance of this occurring. If this demand does not occur, then the tract will be used as originally intended, for recreation and timber production. In the next 15 years, the timber value, plus the appreciation on the investment will increase to $4,000 per acre. The infrastructure costs are negligible, and the potential for underground rock is not a factor.
In the coming years, there is a chance that the legislature will introduce and the president will sign into law that electricity must be produced, in part, by the use of renewable resources. This movement is being considered so that the carbon emissions in power generation will be reduced. There are several alternatives for this which includes wind, solar, and biomass. In the southern states, the burning of biomass is the most likely alternative for reaching the mandate. It's not clear what the renewable portfolio standard will be, but it could reach as much as 5% renewable resources. If this is the case, the value of the wood would increase the value of this investment. Joe believes that there is a 30% chance that this legislation will pass, and if it does, it will mean that the timberland value per acre would increase by $500. This price increase does not apply to the residential development property since Joe will be trying to leave as many trees in place as possible.

1. Develop a decision tree and the payoffs using the information given.
2. Using Joe's event probabilities, determine what he should do if he uses the expected value approach.

Solution Preview

1. Develop a decision tree and the payoffs using the information given.
Please see the excel spread sheet.

2. ...

Solution Summary

The expert develops decision trees and payoffs.