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P10-19 (similar to) Question Help NPV and IRR Benson Designs has prepared the following estimates for a long-term project it is considering
P10-19 (similar to) Question Help NPV and IRR Benson Designs has prepared the following estimates for a long-term project it is considering. The initial investment is $25,960, and the project is expected to yield after-tax cash inflows of $5,000 per year for 8 years. The firm has a cost of capital of 12%. a. Determine the net present value (NPV) for the project. b. Determine the internal rate of return (IRR) for the project. c. Would you recommend that the firm accept or reject the project? a. The NPV of the project is $ (Round to the nearest cent.)
Expert Solution
The NPV is as follows:
= - Initial cost + Annual amount x [ (1 – 1 / (1 + r)n) / r ]
= - $ 25,960 + $ 5,000 x [ (1 - 1 / (1 + 0.12)8 ) / 0.12 ]
= - $ 25,960 + $ 5,000 x 4.967639767
= - $ 1,121.80
IRR is the rate at which NPV is zero.
Lets compute NPV at 10% as shown below:
= - $ 25,960 + $ 5,000 x [ (1 - 1 / (1 + 0.10)8 ) / 0.10 ]
= - $ 25,960 + $ 5,000 x 5.334926198
= $ 714.6309895
Lets compute NPV at 11% as shown below:
= - $ 25,960 + $ 5,000 x [ (1 - 1 / (1 + 0.11)8 ) / 0.11 ]
= - $ 25,960 + $ 5,000 x 5.146122761
= - $ 229.3861954
So, the IRR is:
= Lower rate + [ (Lower rate NPV / (Lower rate NPV - Higher rate NPV) ] x (Higher rate - lower rate)
= 10 + [ ($ 714.6309895) / ($ 714.6309895 - (- $ 229.3861954) ] x (11 - 10)
= 10.75% Approximately
Since the NPV is negative, hence the project shall be rejected.
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