IMPORTANT ASSUMPTIONS

Assumptions are the Mother's Milk of Theory. Irritating though they may be, they are needed to simplify the discussion. The key is to make assumptions that do not impair realism. Let's see if we can agree on the following:

1. Use of this material is governed by the mathestate.com legal restrictions where you will note the usual disclaimers and exculpatory language that are vital to the functioning of our society.
2. We assume the current borrower is at least struggling to make his payments on a loan that has had an interest rate adjustment that lead to an increased (and unaffordable) payment.
3. We assume that homeownership is good for society, that the present borrowers wish to remain homeowners and displacement of them from their present home has a costly net negative effect on all concerned.
4. The basic value of the real estate is its value in use, the lower bound of which is its rental value. The upper bound is an owner's value in use. The present occupant needs time to allow his personal economics to move from the lower bound to the upper bound where he will be able to afford to own the property. The task calls for a quasi-tenant, quasi-owner arrangement facilitated by an investor.
5. The present owner/occupant was a tenant prior to purchase and if foreclosed will again become a tenant.
6. Income taxes are ignored. Occupant tax benefits can be included but considered superfluous in a setting that includes possible foreclosure.
7. The transaction costs of displacement are considerable, uncertain and assessed unevenly and inefficiently against both current parties (borrower and lender).
8. A well run condominium homeowner's association can operate the building or the unit at an overall expense ratio that is not different if the units are tenant occupied or owner occupied (this is perhaps the most heroic assumption but not really central to our point).
9. The lender has decided that "half a loaf is better than none" and will consider a discounted payoff that is some fraction of the present balance.
10. The occupant, after paying a number of years at a lower level will still wish to own his unit and will exercise his option to purchase; in the alternative, the condominium market recovers to put the option "in the money" at the end of the arrangement.
11. Annual compounding to compute yield, despite monthly payments.
12. Tenant payments are indexed over the period of the lease-option arrangement with annual adjustments at the safe rate.
13. During the period of the lease-option arrangement the tenant will accumulate funds at the safe rate by making a monthly sinking fund payment to allow for a down payment at the time of option exercise that is 20% of the option price.
14. No economies of scale or scope are considered should this concept be applied to all loans affecting a particular building.
15. There are a host of ways to model this process. The one chosen takes inputs and produces the option price, necessary growth rate and sinking fund payment required. In this approach the yield is fixed. Alternatively, the option price can be chosen and a variable yield produced at different option exercise times. Permutations are endless, what is important is full disclosure and full understanding of the parties to the revised situation.

The basic idea is that it is more efficient to leave the present owner/occupant in place as a tenant with an ownership stake (essentially his position now) than displace him and find a new owner occupant. Although a third party investor is implied by the structure of this demonstration, an enlightened existing lender could do this with his borrower as part of a recast of the loan terms.