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?

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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