Question

Your firm is considering introducing a new product for which returns are expected to be as follows:

Year 1 to Year 3 (Inclusive): $2,000 per year

Year 4 to Year 8 (Inclusive): $5,000 per year

Year 9 to Year12 (Inclusive): $3,000 per year

The introduction of the product requires an immediate outlay (expenditure) of $15,000 for equipment estimated to have a salvage value of $2,000 after 12 years. Compute the Internal Rate of Return (IRR) for the launch of this product. Write your answer to two decimal places.

Answer 1

IRR is the rate at which NPV is zero.

Lets compute NPV at 19% as shown below:

= - $ 15,000 + $ 2,000 / 1.19 + $ 2,000 / 1.19² + $ 2,000 / 1.19³ + $ 5,000 / 1.19⁴ + $ 5,000 / 1.19⁵ + $ 5,000 / 1.19⁶ + $ 5,000 / 1.19⁷ + $ 5,000 / 1.19⁸ + $ 3,000 / 1.19⁹ + $ 3,000 / 1.19¹⁰ + $ 3,000 / 1.19¹¹ + $ 3,000 / 1.19¹² + $ 2,000 / 1.19¹²

= $ 568.50179

Lets compute NPV at 20% as shown below:

= - $ 15,000 + $ 2,000 / 1.20 + $ 2,000 / 1.20² + $ 2,000 / 1.20³ + $ 5,000 / 1.20⁴ + $ 5,000 / 1.20⁵ + $ 5,000 / 1.20⁶ + $ 5,000 / 1.20⁷ + $ 5,000 / 1.20⁸ + $ 3,000 / 1.20⁹ + $ 3,000 / 1.20¹⁰ + $ 3,000 / 1.20¹¹ + $ 3,000 / 1.20¹² + $ 2,000 / 1.20¹²

= - $ 103.1613503

It means the IRR lies between 19% and 20% since the initial investment of $ 15,000 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)

= 19 + [ ($ 568.50179) / ($ 568.50179 - (- $ 103.1613503) ] x (20 - 19)

= 19.84% Approximately

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