A project costs $12,500 to initiate. Cash ﬂows are estimated as $2,500 a year for the ﬁrst two years and $3,100 a year for the next three years. The discount rate is 11.25%. The net present value for
This project is _____ and the internal rate of return is _________ the discount rate.
A) -$2,138.52; more than
B) -$2,138.52; less than
C) $1,800.00; more than
D) $1,800.00; less than
E) $2,138.52; less than

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV), we need to discount each cash flow to its present value and then subtract the initial cost of the project:

NPV = -$12,500 + ($2,500/(1+0.1125)^1) + ($2,500/(1+0.1125)^2) + ($3,100/(1+0.1125)^3) + ($3,100/(1+0.1125)^4) + ($3,100/(1+0.1125)^5)

NPV = -$2,138.52

To calculate the internal rate of return (IRR), we need to find the discount rate that makes the NPV equal to zero. We can do this using a financial calculator or by trial and error:

At 11%, NPV = -$583.66
At 12%, NPV = $68.05

Therefore, the IRR is between 11% and 12%, which is less than the discount rate of 11.25%.

The correct answer is B because the NPV is negative, indicating that the project is not profitable after considering the cost of capital. In addition, the IRR is less than the discount rate, which further supports the conclusion that the project should not be accepted.

A Project Costs $12,500 to Initiate