The interest rate is 10%.A certain piece of land can be used for a parking lot, in which case there are no construction costs and it will yield a net return of $5,000 per year forever starting one year from now.Or it can have a house built on it.Building a house would cost $50,000 now.If a house is built on the lot, it will yield a stream of net income equal to $12,000 per year starting one year from now.No other uses are contemplated.The theory of asset markets predicts that the lot will sell for
A)$120,000 and a house will be built on it.
B)$50,000 and it will be used as a parking lot.
C)$70,000 and a house will be built on it.
D)$13,200 and a house will be built on it.
E)$80,000 and it will be used as a parking lot.

Question

Quizplus · Accepted Answer

To determine the best use of the land, we need to compare the present value of future cash flows from each option.

Option 1: Use as a Parking Lot

The annual net return is $5,000 forever, starting next year. We can use the perpetuity formula to calculate its present value:

PV = Net Return / Interest Rate
PV = $5,000 / 0.10
PV = $50,000

Therefore, if the land is used as a parking lot, its present value is $50,000.

Option 2: Build a House

The house will cost $50,000 now and generate an annual net income of $12,000 starting next year. We can use the formula for a growing perpetuity to calculate its present value:

PV = Net Income / (Interest Rate - Growth Rate)
PV = $12,000 / (0.10 - 0)
PV = $120,000

However, we also need to subtract the construction cost of $50,000:

PV = $120,000 - $50,000
PV = $70,000

Therefore, if a house is built on the land, its present value is $70,000.

Comparing Options

Since $70,000 is greater than $50,000, it is better to build the house on the land. Therefore, the answer is choice C: $70,000 and a house will be built on it.

The Interest Rate Is 10