Question

A clever investor purchased a piece of land 5 years ago for $175,000. Its appraised value is now twice the original cost. Year-end taxes have been 4% of the purchase price until now. A street assessment of $17,500 was paid 2 years ago. A land developer is willing to buy the land at the appraised price plus the investor’s ownership costs (i.e., taxes plus street assessment fee) on a 4-year contract (4 equal annual payments) at 9% compounded annually. How large should the developer’s four annual payments be if the investor uses an annual interest rate of 15% in figuring the time value of ownership costs?

Answer 1

Appraised price of land=$175,000*2

=$350,000

Present value of Year-end taxes=Year end taxes*FVAF(15%,4)

=($175,000*4%)(4.9934)

=$34,953.63

Present value of street assessment=$17,500(1+0.15)^2

=$23,143.75

Thus,total purchase price for the land developer is;

=$350,000+$34,953.63+$23,143.75

=$408,097.38

Now,calculation of annual payment by land devoper is as follow;

Present value=Annual payment*PVAF(9%,4)

$408,097.38=Annual Payment*3.23972

Annual Payment=$408,097.38/3.23972

=$125,966.87