A company is considering a project which will initially cost $ 212776. It believes this project will generate a cash flow of $35135 in the first year, and the cash flow will increase at 2.2% annually forever. Calculate the IRR (%) of this project (round to 2 decimal places)

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BlackTom AI · Accepted Answer

To analyze this project, we need the rate r that makes the net present value (NPV) equal to zero.
The project is presented as a growing perpetuity starting with a cash flow of 35,135 in year 1, growing at g = 2.2% per year thereafter, with an initial cost (outflow) of 212,776 today.
For a growing perpetuity, the present value at time 0 is PV = CF1 / (r − g), where CF1 is the first-year cash flow.
Setting NPV to zero gives: -212,776 + 35,135 / (r − 0.022) = 0.
Rearranging yields r − 0.022 = 35,135 / 212,776, so r = 0.022 + (35,135 / 212,776).
Compute the ratio: 35,135 / 212,776 ≈ 0.1651.
Add the growth rate: 0.1651 + 0.022 ≈ 0.1871.
Converting to a percentage, IRR ≈ 18.71%.
Thus, the internal rate of return implied by these cash flows is approximately 18.71%.
Note: this approach relies on the standard formula for a growing perpetuity, which requires r > g; the result 18.71% comfortably exceeds 2.2%, satisfying the condition for convergence.
If one were to approach this from a numerical guess-and-check standpoint, you would iteratively adjust r until -212,776 + 35,135 / (r − 0.022) is close to zero, and you would converge near 0.1871.
In problems with perpetuities, recognizing the PV formula for a growing perpetuity often saves time compared to evaluating many cash flows explicitly.

MCD2170 - T2 - 2025 Week 4 post class homework

A company is considering a project which will initially cost $ 212776. It believes this project will generate a cash flow of $35135 in the first year, and the cash flow will increase at 2.2% annually forever. Calculate the IRR (%) of this project (round to 2 decimal places)

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