Growth Enterprises believes its latest project, which will cost $98,000 to insta
ID: 2632432 • Letter: G
Question
Growth Enterprises believes its latest project, which will cost $98,000 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 6%.
If the discount rate for this project is 10%, what is the project NPV? (Do not round intermediate calculations.)
What is the project IRR? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Growth Enterprises believes its latest project, which will cost $98,000 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 6%.
Growth Enterprises believes its latest project, which will cost $98,000 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 6%. a. If the discount rate for this project is 10%, what is the project NPV? (Do not round intermediate calculations.) NPV $ __ b. What is the project IRR? (Do not round intermediate calculations. Round your answer to 2 decimal places.) IRR 11.00 %Explanation / Answer
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.
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