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8 July, 06:23

Growth Enterprises believes its latest project, which will cost $80,000 to install, will generate a perpetual growing stream of cash flows. Cash flow at the end of the first year will be $5,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5%. If the discount rate for this project is 10%, what is the project NPV?

What is the project IRR?

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  1. 8 July, 08:41
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    NPV = $20,000

    IRR = 11.25%

    Explanation:

    first we need to determine the present value of the cash flows using the growing perpetuity formula:

    PV = cash flow / (discount rate - growth rate) = $5,000 / (10% - 5%) = $5,000 / 5% = $100,000

    The NPV = PV of cash flows - investment = $100,000 - $80,000 = $20,000

    to determine the IRR we must find the discount rate that makes NPV = 0

    $5,000 / (r - 5%) = $80,000

    $5,000 = $80,000 (r - 5%)

    $5,000 = $80,000r - $4,000

    $5,000 + $4,000 = $80,000r

    $9,000 = $80,000 r

    r = $9,000 / $80,000 = 0.1125 or 11.25%
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