A project has an anticipated stream of annual net receipts of $20,000. Its life is 6 years. No salvage value is expected at the end of the 6 years. Compute the net present value of the project, if its price is $80,000 and the applicable discount rate is 10%.
A) -68,710.00
B) -44,568.00
C) 7,106.00
D) 74, 312.00
E) 87,106.00

Question

Quizplus · Accepted Answer

The net present value (NPV) of a project is calculated by discounting the future cash flows back to their present value and then subtracting the initial investment. Here, the annual net receipts are $20,000 for 6 years, the initial investment is $80,000, and the discount rate is 10%. The formula for NPV is:$$ NPV = \sum \frac{R_t}{(1 + i)^t} - C_0 $$where $R_t$ is the net receipt at time $t$, $i$ is the discount rate, and $C_0$ is the initial cost.Using the formula for the present value of an annuity because the cash flows are the same each year:$$ PV = R \times \left( \frac{1 - (1 + i)^{-n}}{i} \right) $$where $R$ is the annual net receipt, $i$ is the discount rate, and $n$ is the number of periods.$$ PV = 20,000 \times \left( \frac{1 - (1 + 0.1)^{-6}}{0.1} \right) = 20,000 \times 4.35526 = 87,105.2 $$Subtracting the initial investment:$$ NPV = 87,105.2 - 80,000 = 7,105.2 $$Therefore, the closest answer is $7,106.00.

A Project Has an Anticipated Stream of Annual Net Receipts