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?

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 2 years ago

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