Youare offered a chance to buy an asset for $4,000 that is expected toproduce...

You are offered a chance to buy an asset for $4,000 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset?

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Expert Solution

IRR is the rate at which NPV is zero.

Lets compute NPV at 27% as shown below:

= - $ 4,000 + $ 750 / 1.27 + $ 1,000 / 1.27² + $ 850 / 1.27³ + $ 6,250 / 1.27⁴

= $ 28.02349098

Lets compute NPV at 28% as shown below:

= - $ 4,000 + $ 750 / 1.28 + $ 1,000 / 1.28² + $ 850 / 1.28³ + $ 6,250 / 1.28⁴

= - $ 70.09291649

It means the IRR lies between 27% and 28% since the initial investment of $ 4,000 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)

= 27 + [ ($ 28.02349098) / ($ 28.02349098 - (- $ 70.09291649) ] x (28 - 27)

= 27 + [ $ 28.02349098 / $ 98.11640747 ]

= 27.28% Approximately

jeff jeffy answered 1 year ago

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