A firm is evaluating a proposal which has an initial investment of $50,000 and has cash flows of $15,000 per year for five years. If the firm's required return or cost of capital is 10%, the NPV of the project is:
A) $5,000
B) $6,862
C) -$5,000
D) -$6,862

Question

Quizplus · Accepted Answer

We can calculate the present value of the cash flows using the formula:

PV = CF / (1 + r)^n

Where: 
CF = cash flow 
r = required return or cost of capital 
n = number of periods

Using the formula:

PV (year 1-5) = $15,000 / (1 + 0.10)^1 = $13,636 
PV (year 2-5) = $15,000 / (1 + 0.10)^2 = $12,396 
PV (year 3-5) = $15,000 / (1 + 0.10)^3 = $11,269 
PV (year 4-5) = $15,000 / (1 + 0.10)^4 = $10,244 
PV (year 5) = $15,000 / (1 + 0.10)^5 = $9,314

PV (total) = $50,000 + $13,636 + $12,396 + $11,269 + $10,244 + $9,314 = $106,859

Therefore, the NPV of the project is:

NPV = PV - Initial investment 
NPV = $106,859 - $50,000 
NPV = $56,859

The closest answer to $56,859 is B ($6,862), which means that the project has a positive NPV and should be accepted.

A Firm Is Evaluating a Proposal Which Has an Initial