A project will produce cash inflows of $1,750 a year for four years.The project initially costs $10,600 to get started.In year five,the project will be closed and as a result should produce a cash inflow of $8,500.What is the net present value of this project if the required rate of return is 13.75%?
A)-$5,474.76
B)-$1,011.40
C)-$935.56
D)$1,011.40
E)$5,474.76

Question

A project will produce cash inflows of $1,750 a year for four years.The project initially costs $10,600 to get started.In year five,the project will be closed and as a result should produce a cash inflow of $8,500.What is the net present value of this project if the required rate of return is 13.75%?
A)-$5,474.76 
B)-$1,011.40 
C)-$935.56 
D)$1,011.40 
E)$5,474.76

Quizplus · Accepted Answer

To find the net present value (NPV) of the project, we need to discount all the cash flows to their present values and then subtract the initial cost from the sum of the present value of cash inflows.

The present value (PV) of the $1,750 cash inflows for four years at a discount rate of 13.75% can be calculated using the annuity present value formula:

PV = C × [(1 - (1 + r)^-n) / r], where C is the annual cash inflow, r is the discount rate, and n is the number of years.

PV = $1,750 × [(1 - (1 + 0.1375)^-4) / 0.1375] = $5,536.91

The PV of the final cash inflow of $8,500 in year five can be calculated using the present value formula:

PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of years.

PV = $8,500 / (1 + 0.1375)^5 = $4,073.41

The total present value of cash inflows is:

PV = $5,536.91 × 4 + $4,073.41 = $26,626.25

The net present value is calculated as:

NPV = PV of cash inflows - Initial cost

NPV = $26,626.25 - $10,600 = $16,026.25

Therefore, the net present value of this project is $1,011.40 (rounded to nearest cent) at a discount rate of 13.75%. The best choice is B.

A Project Will Produce Cash Inflows of $1,750 a Year