1. Rents and market values are closely related. a. Consider a vacant acre of land that rents for $5000 per year after taxes. Your discount rate is 10%. What should be the market value of this parcel? b. Give a general expression for the market value of a property that promises to yield a series of after tax rents, r1, r2, r3, r4,… 2. Suppose the gross population density function for an urban area is estimated to be: D(x) = 7500*e^(-0.2x), where e is the base of the natural logarithms and x is distance to downtown in miles, and D(x) is the population density in people per square

Rents and market values are closely related.

For a vacant acre of land that rents for $5000 per year after taxes. Your discount rate is 10%.

What should be the market value of this parcel? 50,000

Explanation:

So for this present value valuation, consider  that the discounted cash flow as a standard method of investment valuation to estimate the stream of cash flows expected from the investment and the suitable discount rate and calculate the discounted present value of the cash flow.

The market value of the parcel is the discounted present value. The cash flows from the land, which annuity´s of 5,000 per year.

Undertaking that the rent is for life, the cash flows are a perpetuity, so the present value of a perpetuity is the periodic payment divided by the discount rate, as follows:

Present Value of Rent  =  5,000 / 10%  =  50,000

Concluding that the price of the land or the market value od this parcel is:     $50,000.