Suppose that an income producing property is expected to yield cash flows for the owner of $10,000 in each of the next five years, with cash flows being received at the end of each period. If the opportunity cost of investment is 12% annually and the property can be sold for $100,000 at the end of the fifth year, determine the value of the property today.
A) $36, 047.76
B) $56,742.69
C) $83,333.33
D) $92,790.45

Question

Quizplus · Accepted Answer

The value of the property today can be calculated using the formula for the present value of an annuity plus the present value of a lump sum. The present value of the annuity (cash flows of $10,000 for 5 years at 12%) is calculated using the formula PV = P * [(1 - (1 + r)^-n) / r], where P is the payment ($10,000), r is the annual interest rate (12% or 0.12), and n is the number of periods (5 years). This calculation gives us a present value of the annuity of approximately $36,047.76. The present value of the lump sum ($100,000 to be received at the end of the 5th year) is calculated using the formula PV = F / (1 + r)^n, where F is the future value ($100,000), r is the annual interest rate (12% or 0.12), and n is the number of periods (5 years). This calculation gives us a present value of the lump sum of approximately $56,742.69. Adding these two values together gives us the total present value of the property today, which is approximately $92,790.45.

Suppose That an Income Producing Property Is Expected to Yield