Problem 1 (Rent vs. Own)

You are considering an option to purchase or rent a single residential property. You can rent it for 2,000 per month and the owner would be responsible for maintenance, property insurance, and property taxes. Alternatively, you can purchase this property for 200,000 and finance it with an 80 percent mortgage loan at 6 percent interest that will fully amortise over a 30-year period. The loan can be prepaid at any time with no penalty.

You have done research in the market area and found that (1) properties have historically appreciated at an annual rate of 3 percent per year, and rents on similar properties have also increased at 3 percent annually; (2) maintenance and insurance are currently 1,500.00 each per year and they have been increasing at a rate of 3 percent per year; (3) you are in a 26 percent marginal tax rate and plan to occupy the property as your principal residence for at least four years; (4) the capital gains exclusion would apply when you sell the property; (5) selling costs would be 7 percent in the year of sale; and (6) property taxes have generally been about 2 percent of property value each year.

Based on this information you must decide: 1-

(a) In order to earn a 10% IRR after taxes on your equity, should you buy the property or rent it for a four-year period of ownership?

The return on equity is 31.18%, hence ownership is preferred.

(b) What if your expected period of ownership was to change to five years. Would owning or renting be better if you wanted to earn a 10% IRR after taxes?

The return on equity is 31.61%, hence ownership is preferred.

(c) Approximately what level of rents would make you indifferent between owning and renting for a four-year period? Assume a 4.5% after-tax IRR would be the minimum you would need to earn on capital invested in the home.

The annual rent should be approx. 12,355.

NOTE - do not use excel as i want to learn how to solve it by hand on paper.