Business Statistics and Decision Analysis

Subject Mathematics Applied Statistics

Question

Some investors prefer to invest in real estate rather than more liquid investments. They live by the principle that land is tangible, and will always be there regardless of the markets around it. And this is true, in large part, if the land owner has kept the land free of any significant liens. However, if capital is poured into real estate projects and can’t be readily realized, then the parcel becomes just like any other bad investment….it can take a downturn in value. And if the owner can’t cover the investments and there is no market for the parcel, then the owner must sell it for a loss, which is similar to a stock value plummeting below its purchase price.
Residential and commercial real estate investments are generally perceived as the most risky because there are more variables that create volatility in the market. Several conditions have to occur for a residential real estate development to be successful. One of the major variables is constant demand over a rather long period of time. It is not uncommon for a residential development project to span a period of 20 years. Obviously, the length is dependent on demand for housing. Demand for housing is influenced by a variety of things, and at the center of these things are jobs. Some will say that the type of jobs are important because one must plan for providing housing that suits a potential home owners ability to make mortgage payments. Thus the size of the house and lot is an important consideration when planning the development. In addition, the mortgage rates, mortgage type (fixed or adjustable rate); material costs are just a few of the variables that can influence potential homeowners, and make business good or bad for the developer. And each of these ‘dependent’ variables is driven by their own set of independent variables.
If all of these variables are fairly favorable, then the developer will have no problem in selling lots as quickly as he can prepare them. However, if any of these variables become unfavorable, then the project life begins to lengthen. When the project begins to grow in length, then the time value of money begins to diminish profits.
Another potential area of excessive cost is the installation of the infrastructure. Long term projections can be wrong, and the infrastructure costs can become overwhelming in the midst of a slowdown. Most developers will hedge against a slowdown in demand by managing the pace of the infrastructure.
Although timberland has its own associated risks, these risks are not as fatal as the risks seen in residential development. Since the end of World War II, the average value of rural timberland has increased during any 3-year window except for one period in the early 1980’s when interest rates skyrocketed and the value of crop production plummeted.
Prior to 1992, the value of timberland could easily be calculated by performing a cost-benefit analysis. In timberland investments, this valuation is computed by calculating a ‘Soil Expected Value”. The Soil expected value is merely the “present value” of the expenditures and income on a per acre basis. For example, just like any investment, the soil is expected to generate revenues, and we can measure the timing and magnitude of the revenue versus the initial costs using the time value of money. Up until the early 90’s, the soil expected value was the measure by which most timberland was valued. That meant that whatever the soil could produce, that was the value of the land.
Since the early 90’s, the value of the soil has increased because of its recreational value. In some southeastern states, bare timberland has increased in price five-fold as a result of this demand. Now the value of the land is largely determined by this demand rather than for its timber-growing ability. Prices fluctuate more as a result of the availability of capital rather than the demand for the timber. Timberland is still considered somewhat of a commodity of sorts, because location is not a major factor in the valuation. This land use is generally in the rural areas of the state. In other words, the price per acre in one rural part of the state or region is very similar to the price per acre in another rural part. This is unlike the value of developmental property where location is a major factor in the valuation process. Home owners prefer to live close to a city, so the closer the development property is to the city, the more it is worth.
Although the recreational demand plays a huge role in the valuation process, the actual price for the timber itself can fluctuate. The demand is driven largely by the pulp, paper, and lumber companies. And their demand is driven by the same factors that influence the overall economy, such as the number of new homes built and the need for pulp to make paper products. However, it appears that our society is pushing for a “greener” approach to energy, which could make the value of the pulp increase sharply as a result of this demand. Pulp could be used as a fuel source for the power-generating turbines, rather than petroleum and coal products alone. However this shift would have to be a result of new legislation at the federal level which might or might not happen. The underlying deciding factor could boil down to the legislature, and if the economic experts think the economy can handle an increase in energy costs. In the early 1990’s, a recycle initiative was enacted which drove the cost of ‘used’ paper, and fiber, to a level that was and still is higher on a per ton basis than paper that is made of virgin fiber. Obviously, the requirement for renewable energy sources is yet to materialize, but there is a chance it could happen, and if it happens, timberland owners could see the price of their products increase substantially, making the value of the soil increase.

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.
Deliverables:

1. Using Joe’s event probabilities, determine what he should do if he uses the expected value approach. Develop a decision tree and the payoffs using the information given. Your tree and payoffs should fit on one page. Provide your reasoning at the bottom of the page.
2. The most complicating thing about this deal is that there is another potential buyer that might be willing to buy the residential tract right away. This puts pressure on Joe’s firm to make a quick decision. One alternative Joe has is to purchase an option from the landowner for 4 months while they decide if they really want to purchase the tract. This option will prevent the owner from selling it to another party, and will freeze the price at \$25,000 per acre. If Joe purchases the option, and does not buy the tract, then he will forfeit the cost of the option.
During this 4 month period, Joe would like to hire a geological expert to study the extent of rock formations underneath the surface of the soil. The option and the expert will cost Joe \$100,000.
Although we don’t have specific reports of the geological experts past work, his approach to determining the rock formations is “excellent”. Is the cost of the option and the survey extreme? In other words, would you ever pay \$100,000 for this information, even it were perfect? Show your work and explain your reasoning. (Hint: Use the expected value of perfect information). Develop a decision tree and the payoffs using the information given. Your tree and payoffs should fit on one page. Provide your reasoning at the bottom of the page.
3. Suppose that you have been able to obtain information on the geologist in problem 2. You were able to obtain enough information to provide the following conditional probabilities that reflect the results of his past work.

P(Hard|R)    = 0.90 P(Soft|R)    = 0.10
P(Hard|NR) = 0.20 P(Soft|NR) = 0.80

In other words, the expert was right 90% of the time when saying that the underground conditions were “Hard” (or Rocky) when, in fact, it was Rocky (R). Likewise, he was right 80% of the time when saying that the underground conditions were “Soft” (or not rocky) when, in fact, it was Not Rocky (NR).

Given this information, how much would you be willing to pay for his information? Is it worth \$100,000? Develop a decision tree and the payoffs using the information given. Preferably, your tree and payoffs can fit on one page. However, you might need to use two pages for this one. Provide your reasoning at the bottom of the page.

Instructions:
1. Please create the trees using power point, excel, or some other package. No handwritten submittals.
2. Provide a decision tree for problems 1, 2, and 3. Fit each tree on a separate page. On problem 3 you might need two pages. You should submit no more than 6 pages. The first page should be a cover page, and on the last page, show your calculations for problem 3, as well as any other calculations you want to include. Avoid submitting more than a total of 6 pages.
3. Please put your name on each page.
4. Please consolidate this assignment into one pdf file. Do not send multiple files for each of the trees.

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