Question

A company is considering purchasing equipment costing $ 92,000. The equipment is expected to reduce costs from year 1 to 3 by $22,000, year 4 to 9 by $9,000,and in year 10 by $2,000. In year 10, the equipment can be sold at a salvage value of $15,000.

Calculate the internal rate of return​ (IRR) for this proposal.

Answer 1

IRR is the rate at which NPV is zero.

Lets compute NPV at 9% as shown below:

= - $ 92,000 + $ 22,000 / 1.09 + $ 22,000 / 1.09² + $ 22,000 / 1.09³ + $ 9,000 / 1.09⁴ + $ 9,000 / 1.09⁵ + $ 9,000 / 1.09⁶ + $ 9,000 / 1.09⁷ + $ 9,000 / 1.09⁸ + $ 9,000 / 1.09⁹ + $ 2,000 / 1.09¹⁰ + $ 15,000 / 1.09¹⁰

= $ 2,045.036423

Lets compute NPV at 10% as shown below:

= - $ 92,000 + $ 22,000 / 1.10 + $ 22,000 / 1.10² + $ 22,000 / 1.10³ + $ 9,000 / 1.10⁴ + $ 9,000 / 1.10⁵ + $ 9,000 / 1.10⁶ + $ 9,000 / 1.10⁷ + $ 9,000 / 1.10⁸ + $ 9,000 / 1.10⁹ + $ 2,000 / 1.10¹⁰ + $ 15,000 / 1.10¹⁰

= - $ 1,285.47385

It means the IRR lies between 9% and 10% since the initial investment of $ 92,000 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)

= 9 + [ ($ 2,045.036423) / ($ 2,045.036423- (- $ 1,285.47385) ] x (10 - 9)

= 9.61% Approximately

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