You are the judge in a settlement case You need to compute t

You are the judge in a settlement case. You need to compute the value of a piece of land in Denver Co. The valuation is subject to the following conditions

The settlement will take place at the end of 2019

The current appraised value of the land on 1/1/2018 is $500.000

The piece of land has a building on it that is uninhabitable . It takes one year to bring the building down at a cost of $100,000. That money must be paid now.

The land can be rented in 2019 at a net proceeds of 40,000

While rented the land cost $20,000 in property taxes

Your real estate adviser notes that selling prices of comparable lands in Denver have declined, in real terms, at an average rate of 3% per year over the last 5 years.

The cost of capital is 10%

The sale of the land at the end of 2019 is subject to a 10 % commission.

What should someone pay today for this land if given the choice?

Solution

Today\'s Net Value of Land =
Present value of Land worth at the end of 2019
+ Present value of Gains from the land till the end of 2019
- Present Value of Commission for sale of land at the end of 2019
- Present Value of all related expenses till the end of 2019

1)
Land worth at the end of 2019 by declining at 3% for 2 years = 500000*(1-3%)² = 470,450
Present Value of Land Now = Future Value /(1+Cost of Capital)ⁿ = 470450/(1+10%)² = 388,802

2)
Net Gain in 2019 = Rent - Property Taxes = 40000 - 20000 = 20000
Present value of Gains now = Future Value /(1+Cost of Capital)ⁿ = 20000/(1+10%)² = 16,529

3)
Commission for sale of land at the end of 2018 = 10% of 470,450 = 47045
Present value of commission now = Future Value /(1+Cost of Capital)ⁿ = 47045/(1+10%)² = 38,880

4)
Present Value of all expenses to ttake down building now = 100,000

So,

Today\'s Net Value of Land = 388802 + 16529 - 38880 - 100000
Today\'s Net Value of Land = $ 266,451

What should someone pay today for this land if given the choice? = $ 266,451