What is the present worth of an independent project that requires initial investment of $50 000 and annual maintenance costs of $4 000 for 10 years at a 4% minimum acceptable rate of return?
A)-$4 000
B)-$32 444
C)-$54 000
D)-$82 444
E)-$17 556

Question

Quizplus · Accepted Answer

The present worth of an independent project can be calculated using the formula for the present value of a series of cash flows. The initial investment is a cash outflow of $50,000. The annual maintenance costs of $4,000 for 10 years can be considered as an annuity. The present value of this annuity can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($4,000), r is the annual interest rate (4% or 0.04), and n is the number of periods (10 years). The present value of the maintenance costs is $4,000 * [(1 - (1 + 0.04)^-10) / 0.04] = $33,444.24. Adding this to the initial investment of $50,000 gives a total present worth of $50,000 + $33,444.24 = $83,444.24. Since the closest option is D) -$82,444, it is considered the correct answer. This calculation takes into account the time value of money, showing the total cost of the project in today's dollars, considering both the initial investment and the ongoing maintenance costs.

What Is the Present Worth of an Independent Project That