LebTech Property Development

LebTech, a real estate developer, is currently evaluating whether to purchase a set of derelict buildings and convert them to 96 apartment units. LebTech estimates that a fair price of the property is $2 million.

The local authority operates a housing scheme (HH) that provides subsidies for the sort of project envisaged, subject to a certain share of the units being let out to low-income families.

One key issue of uncertainty is whether an HH application for this project would be approved. Matters would be clearer if the decision could be postponed until after the upcoming elections for the local authority chair, since the chances of approval would depend on the outcome. Unfortunately, there is always the risk that the property would be purchased by others if LebTech waited. LebTech, therefore, needs to decide whether to make an offer now or risk waiting until after the elections.

If LebTech were to make a purchase offer, they must also place a non-refundable deposit of 10% (in this case, $200,000). Once LebTech has made an offer, it can then apply for the HH scheme subsidies. After 60 days from the date of the offer, LebTech must either go for completion, in which case the remaining 90% of the value of the property is paid, or withdraw, forfeiting the 10% deposit.

There is no guarantee, unfortunately, that LebTech's HH application would be processed and decided upon within the 60-day period. (In the past, the approval process has taken anywhere from one to five months). Thus, LebTech may have to decide either to withdraw their offer (and lose their 10% deposit) or purchase the property without knowing whether their HH application is going to be accepted.

Initially, LebTech thought that the project would be profitable only if it received the HH subsidies. However, some market research indicated that medium-income families may find the renovated apartments attractive and be willing to pay higher rents, which would make the project cost-effective even without subsidy.

The probabilities associated with uncertainties involved were estimated to be as follows:

Probability that decision on an HH application would be delayed beyond 60 days = 0.3.

Probability of favorable outcome of upcoming elections = 0.6.

If outcome of elections is favourable, probability of approval of application = 0.7.

If outcome of elections is unfavourable, probability of approval of application =0.2.

Probability that the property would still be available for purchase after the elections (if LebTech took no action) = 0.8.

Questions:

(a)Estimate the value of the project both with subsidy (under the HH scheme) and without, using the income and cost estimates given in the appendix on the basis of a 30-year horizon and a discount rate of 7%.

(b)Construct a spreadsheet model of the decision problem and solve for the optimal decision strategy.

(c)LebTech assumed that the probability of HH approval given a favorable election outcome, P = 0.7. Perform sensitivity analysis on this probability, letting P vary between 0.6 and 0.8. In what way, if at all, does the optimal decision strategy change?

(d)Perform sensitivity analysis, with the discount rate varying between 6% and 9%. In what way, if at all, does the optimal decision strategy change?

(e)What is your overall recommendation?

Appendix

Estimate of Income from Project

If the project is approved under the HH scheme, a specified percentage of the apartment units must be occupied by low-income families. Tenants have been classified into three main groups according to income level:

Class A: $20,000 annual income $30,000.

Class B: $15 annual income $20,000.

Class C: annual income $15,000.

According HH rules, 20% of all tenants in a supported building should belong to class A, 30% to class B, and 50% to class C. On average, the actual amount of monthly rent charged to the tenants plus the subsidy paid by the agency (which accounts for an additional 20% of what the tenant pays) is: $685 for a class A tenant, $484 for a class B tenant, and $418 for a class C tenant. If HH approval is not granted, there are obviously no restrictions on the mix, and the estimated average monthly rent would be $520 per rental unit.

Costs of Renovation

It is estimated that the cost of the renovation would be about $1,152,000, which works out to $12,000 per apartment. However, this cost would be 20% lower if the project was approved for HH subsidies.

Annual Maintenance Costs

Maintenance costs can be general costs and unit costs. LebTech estimated the general cost to be $56,000 per year for the whole project. Without HH approval, unit maintenance costs would be close to $75,000 per year, but with approval, this cost drops down to $60,000 per year.

Taxes

The usual annual rate = 45%. However, if the project was granted HH approval, there would a tax rebate of 5% (reducing their effective tax rate to 40%.)