You own a plot of empty land and plan to build a house on it. You would like to build a duplex (2 apartment house), not a 1 apartment house. The plot of land is 1/10th of an acre. The city says any plot of land that is 1/8th of an acre or larger can be a duplex or a single family house (a difference of 1089 square feet). The neighbor behind you has a single family house. The single family house is on a 1/4 acre plot of land and the back yard fence between your properties is 101 feet long. If you buy 1089 square feet from your neighbor (move the fence back 10 feet into their property) you will have enough space to build a duplex. In your town when land sells it usually goes for about $30,000 for 1/8 of an acre. Your neighbor wants you to pay 25 times more than the regular price per square foot you want to buy in their back yard.

Assumptions: - The duplex and single family home will cost the same to build (it would be a big single family home or a smaller duplex) - You can make $400 more per month in rent owning a duplex than a large single family home - You, or your family will own the house forever - The difference in rent will always be $400 for having a duplex, it won't change - You're taking out a loan to build the house and could take out additional money to pay for the land. - The bank is giving you a 30 year loan rate of 4.5% compounding monthly (it is higher than some other mortgages because it is to build a house, not buy an existing house) - All other costs are identical (repairs, turn over, etc.) - There is no difference in property appreciation, etc. Questions that would be good to be able to answer: A) How much does your neighbor want for the land? B) Based on the increase in income from the duplex how much should you be willing to spend today on the additional land to make a duplex? C) How much lower or higher will your monthly payment on your 30 year loan be if you buy your neighbor's land at the price they're asking and build a duplex instead of a single family home? D) Making things more complicated part 1: Your neighbor also wants you to pay for an expensive new fence along the back yard line at $45 per linear foot when you buy the property. Should you still buy it? E Making things more complicated part 2: If you build the duplex your property taxes will be higher. Property taxes in your town are an annual fee of 1% of the property value for single family homes or 2% annually for duplexes. How much could the property be worth with a duplex that makes $400/month more before the increase in property taxes would make you lose money? (To clarify: The total value of the property is what the taxes are paid on. So if the property is very expensive the duplex will have more expensive annual property taxes.)