Question

roject L requires an initial outlay at t = 0 of $69,922, its expected cash inflows are $11,000 per year for 11 years, and its WACC is 11%. What is the project's IRR? Round your answer to two decimal places.

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Answer 1

IRR is the rate at which NPV is zero.

Lets compute NPV at 10% as shown below:

= - $ 69,922 + $ 11,000 / 1.10¹ + $ 11,000 / 1.10² + $ 11,000 / 1.10³ + $ 11,000 / 1.10⁴ + $ 11,000 / 1.10⁵ + $ 11,000 / 1.10⁶ + $ 11,000 / 1.10⁷ + $ 11,000 / 1.10⁸ + $ 11,000 / 1.10⁹ + $ 11,000 / 1.10¹⁰ + $ 11,000 / 1.10¹¹

= $ 1,523.671057

Lets compute NPV at 11% as shown below:

= - $ 69,922 + $ 11,000 / 1.11¹ + $ 11,000 / 1.11² + $ 11,000 / 1.11³ + $ 11,000 / 1.11⁴ + $ 11,000 / 1.11⁵ + $ 11,000 / 1.11⁶ + $ 11,000 / 1.11⁷ + $ 11,000 / 1.11⁸ + $ 11,000 / 1.11⁹ + $ 11,000 / 1.11¹⁰ + $ 11,000 / 1.11¹¹

= - $ 1,650.331421

It means the IRR lies between 10% and 11% since the initial investment of $ 69,922 is recovered between them and same is shown below:

= Lower rate + [ (Lower rate NPV / (Lower rate NPV - Higher rate NPV) ] x (Higher rate - lower rate)

= 10 + [ ($ 1,523.671057) / ($ 1,523.671057 - (- $ 1,650.331421) ] x (11 - 10)

= 10.47% Approximately

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