Final answer:
The land capitalization rate can be calculated by dividing the value of the improvement by the building capitalization rate. The remaining economic life of the improvement is used to calculate the land value. By substituting the given values into the equations, we find that the land value is 0.048 times the value of the improvement.
Step-by-step explanation:
The land capitalization rate can be calculated using the formula: land value / present value of land income. In this case, the present value of land income is the value of the improvement over its remaining economic life. The land value can be found by subtracting the value of the improvement from the total property value. If the building capitalization rate is 12% and the remaining economic life of the improvement is 25 years, we can assume that the property value is the same as the value of the improvement. Therefore, to find the land value, we can multiply the value of the improvement by the reciprocal of the building capitalization rate:
Land value = Value of improvement / Building capitalization rate
Land capitalization rate = 1 / Remaining economic life of the improvement
Substituting the given values:
Land value = Value of improvement / 12% = Value of improvement * 100 / 12
Land capitalization rate = 1 / 25 = 0.04
Substituting the value of the land capitalization rate into the land value equation:
0.04 = Value of improvement * 100 / 12
Value of improvement = 0.04 * 12 / 100 = 0.048
Therefore, the land value is 0.048 times the value of the improvement.