An investment project has an initial cost, and then generates inflows of $50 a year for the next five years. The project has a payback period of 3.6 years. What is the project's internal rate of return (IRR)?
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A. B. C. D. E.A
Investment cost = $180.
CF(0) = -180 -
CF(1-5) = 50 -
Solve for IRR = 12.05%.
To calculate the internal rate of return (IRR) for the investment project, we need to find the discount rate that equates the present value of cash inflows to the initial cost of the project.
In this case, we have the following information:
Initial cost = ? Cash inflows = $50 per year for 5 years Payback period = 3.6 years
To find the initial cost, we can calculate the present value of cash inflows using the payback period as a guide. We'll discount each cash inflow back to the present using a discount rate and then sum them up until the total reaches the initial cost.
Let's calculate the present value (PV) of cash inflows using a discount rate of 0% (just as a starting point):
PV = $50 / (1 + 0%)^1 + $50 / (1 + 0%)^2 + $50 / (1 + 0%)^3 + $50 / (1 + 0%)^4 + $50 / (1 + 0%)^5
Simplifying the equation:
PV = $50 + $50 + $50 + $50 + $50 = $250
Since the payback period is 3.6 years, we know that the present value of cash inflows at the end of the third year must be equal to or greater than the initial cost. Therefore, we need to increase the discount rate until the present value reaches or exceeds $250.
We can use trial and error or financial calculators to find the discount rate that meets this condition. I will use trial and error to find the approximate discount rate.
Assuming a discount rate of 10%, let's calculate the present value of cash inflows:
PV = $50 / (1 + 10%)^1 + $50 / (1 + 10%)^2 + $50 / (1 + 10%)^3 + $50 / (1 + 10%)^4 + $50 / (1 + 10%)^5
Simplifying the equation:
PV ≈ $45.45 + $41.32 + $37.56 + $34.14 + $31.04 ≈ $189.51
Since $189.51 is less than $250, we need to increase the discount rate further.
Let's try a discount rate of 15%:
PV = $50 / (1 + 15%)^1 + $50 / (1 + 15%)^2 + $50 / (1 + 15%)^3 + $50 / (1 + 15%)^4 + $50 / (1 + 15%)^5
Simplifying the equation:
PV ≈ $43.48 + $37.85 + $32.91 + $28.55 + $24.74 ≈ $167.53
Again, $167.53 is less than $250, so we need to increase the discount rate further.
Let's try a discount rate of 20%:
PV = $50 / (1 + 20%)^1 + $50 / (1 + 20%)^2 + $50 / (1 + 20%)^3 + $50 / (1 + 20%)^4 + $50 / (1 + 20%)^5
Simplifying the equation:
PV ≈ $41.67 + $34.72 + $28.93 + $24.11 + $20.09 ≈ $149.52
Once again, $149.52 is less than $250, so we need to increase the discount rate.
Let's try a discount rate of 13%:
PV = $50 /