Growth Enterprises believes its latest project, which will cost $93,000 to insta

Question

Growth Enterprises believes its latest project, which will cost $93,000 to install, will generate a perpetual growing stream of cash flows. Cash flow at the end of the first year will be $6,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5%. 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 %

Explanation / Answer

Working:

Solutions: (a)                                   Amount in $ NPV = (PV of cash inflows) - (PV of cash out flows) = 120000 - 93000 = 27,000 So, the NPV of the Project is $ 27,000

Working:

Intial Out Flows = 93,000 Expected 1st year cash inflows (CF) = 6,000 Growth Rate (g) = 5 % Discount Rate (I) = 10 % Our cash inflow here is a perpetuity that is growing at a constant
annual rate. So, in our case the formula is: PV of growing perpertuity = CF/(I-G)                       =6000/(0.1-0.05)                       =1,20,000                                                 (b) 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: 6000 / (I - 0.05) = 93,000 Now we just need to solve for I : 6000 / 93000 = I - 0.05 0.0645 = I - 0.05 I = 0.0645 + 0.05 I = 0.1145 or 11.45 % So the IRR for this project would be 11.45 %

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