“I have a friend who wants to put up the 20 percent down payment I need to purchase my house. It would be an investment by him, which he would recover when I sell the house or in seven years, whichever comes first. Our problem is in determining the percent of the house value at that time to which he would be entitled. He owns 20 percent coming in, but how much should he own going out?”

The investor should receive more than 20 percent of house value when he exits the relationship because you get to live in the whole house, not just in the 80 percent of the house that you paid for. The challenge is to calculate that amount in a fair way, without making it too complicated.

The key is the rental value of the house – what the house could be rented for if you put it on the market. This is the best measure of the value to you of being able to live in the house. From this, deduct the costs of maintenance, which you are responsible for, to obtain the net rent. You owe the investor 1/5 of the net rent every month.

Note that you do not deduct the mortgage payment from the rent, because that is solely your responsibility. If you had paid cash for your 80 percent share instead of borrowing it, you would owe the investor the same amount.

It is important for you and the investor to agree on an initial rental value, or on a procedure for determining it. This includes agreement on whether the initial rent will hold for seven years, or if the rent is to be adjusted over time. If it is to be adjusted, furthermore, you must agree on an adjustment procedure. As an illustration of one possibility, the rental value could be adjusted every year in line with changes in the rental component of the Consumer Price Index.

The amount due the investor each month can be handled in at least three different ways. The simplest way is for you to pay it in cash. If you did that, his share of ownership would remain at 20 percent. In all probability, however, both of you will prefer to defer any payments until the house is sold or the seven-year settlement point has been reached.

Assuming payment is deferred, you could treat it as a debt to him that accumulates over time. If you adopt this approach, you both need to agree on the interest rate that is applied to this debt. Then at termination, he would get 20 percent of the property value plus the accumulated value of the debt. With this procedure, the investment is a combination of equity plus debt.

A second way, which the investor will prefer if he wishes a strictly equity investment, is to use the amount due each month (or each year) to purchase an additional share of the equity. In this case, you have to agree on whether the value of the house used in this calculation is the initial value or the current value.

This decision is related to the earlier decision regarding rental value. If the rent is adjusted every year, the property value should be as well. Much the simplest approach, however, is to use both the initial rental value and the initial property value throughout the term of the deal. It isn’t as accurate but it is simpler and less costly. It avoids having to get the house appraised every year.

A potentially thorny issue that ought to be faced at the outset is how you treat an improvement in the house that enhances its value. If you pay the entire cost of an improvement, the investor receives an unjustified windfall. You would expect the investor to contribute to the cost in proportion to his ownership share.

From the investor’s point of view, however, there is a danger that an improvement will not increase the value of the house by enough to cover the cost. You might want to build a swimming pool, for example, but as an investment, pools are a loser. It may be OK with you because you like to swim, but the investor will not want to subsidize an enhancement to your lifestyle.

It follows that the investor is unlikely to agree in advance to contribute to any improvements that you might want to make. You are going to have to negotiate these when they arise. For the deal to work for both parties, you should have a good relationship.

The writer is Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at www.mtgprofessor.com.

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