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Q: Net Present Value and IRR ( Answered,   1 Comment ) Question
 Subject: Net Present Value and IRR Category: Business and Money > Finance Asked by: inept-ga List Price: \$25.00 Posted: 27 Feb 2005 00:46 PST Expires: 29 Mar 2005 00:46 PST Question ID: 481674
 ```NPV/IRR. 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 this year will be \$5,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5 percent. a. If the discount rate for this project is 10 percent, what is the project NPV? b. What is the project IRR?``` ```Hi inept-ga, Net present value can be described by the following equation: NPV = (PV of Cash Inflows) - (PV of Cash Outflows) Our cash inflow here is a perpetuity that is growing at a constant annual rate. We calculate a perpetuity as described at the following link: http://www.netmba.com/finance/time-value/perpetuity/ So, in our case the formula is: PV of growing perpertuity = C / (i - g) Where: C = income at the end of the first period i = the current discount rate g = the growth rate per period PV of growing perpertuity = 5000 / (.1 - 0.05) = 5000/0.05 = \$100000 Now we can calculate NPV, since we know there is only one outflow which occurs immediately: NPV = (PV of Cash Inflows) - (PV of Cash Outflows) = \$100,000 - \$80,000 = \$20,000 So the NPV of this project is \$20,000 To calculate the IRR, we need to find the discount rate which would yield an NPV of 0. We can get the proper calculation using the above NPV calculations: 5000 / (i - 0.05) = 80,000 Now we just need to solve for i: 80000/5000 = i - 0.05 0.0625 = i - 0.05 i = 0.1125 So the IRR for this project would be 11.25%. This is the point at which the project would break even. Any rate above this would cause a negative NPV, and any rate below it would cause a positive NPV (as we saw with the original NPV calculation). Hope that helps you understand NPV and IRR - please post a clarification if anything above is unclear. Cheers! answerguru-ga``` ```It appears to me that the formula is incorrect. You say 80000/5000=i-.05. I think it should be 5000/80000=i-.05. Also, I'm confused. It seems to me that the "point at which the project would break even" is 10% - the discount rate. Furthermore, any rate above this would cause a positive NPV, not a negative one as you assert. What am I missing?``` 