Garcia Developers will erect a small office building at a cost of $4,500,000. They have a client who will lease the space for 5 years at a price that will produce free cash flows of $150,000 per year. For approximately how much would they need to sell the building for at the end of the 5th year to reach break-even NPV? Garcia uses a discount rate of 10% for projects of this type.
A) $3,750,000
B) $5,755,936
C) $6,331,530
D) $6,964,683

Question

Quizplus · Accepted Answer

To find the break-even sale price at the end of the 5th year, we first calculate the present value (PV) of the free cash flows over the 5 years, and then determine how much the sale price needs to be to make the NPV equal to zero. The formula for the present value of an annuity is PV = C * [(1 - (1 + r)^-n) / r], where C is the annual cash flow, r is the discount rate, and n is the number of periods.For the annual cash flows of $150,000 over 5 years at a 10% discount rate, the PV is approximately $568,807. Then, to break even, the total of this PV and the sale price in the 5th year, discounted back to present value, must equal the initial investment of $4,500,000.The equation to solve for the sale price (S) at the end of the 5th year is: $4,500,000 = $568,807 + S / (1 + 0.10)^5. Solving for S gives a value close to $6,331,530, which is option C.

Garcia Developers Will Erect a Small Office Building at a Cost