To calculate the internal rate of return (IRR) for Bucky Inc., we need to solve for the discount rate $r$ that makes the net present value (NPV) of the cash flows equal to zero.

The cash flows are:

$\text{Year 0: } -50,150$ $\text{Year 1: } 15,846$ $\text{Year 2: } 17,819$ $\text{Year 3: } 18,196$ $\text{Year 4: } 19,707$

The NPV equation for these cash flows is:

$NPV = -50,150 + \frac{15,846}{(1 + r)^1} + \frac{17,819}{(1 + r)^2} + \frac{18,196}{(1 + r)^3} + \frac{19,707}{(1 + r)^4} = 0$

Now, we can use numerical methods or a financial calculator to solve for the IRR $r$.

I'll calculate this now.It looks like the function I attempted to use for the IRR calculation is deprecated in my current environment. I'll resolve this using another method to calculate the IRR for you. Let me try again.The internal rate of return (IRR) for Bucky Inc.'s investment is 15.32%.

Would you like any further explanation on how the IRR was calculated or on any other related topic?

Here are some related questions to consider:

1. What is the significance of the IRR in investment decisions?
2. How does IRR compare to other metrics like NPV?
3. How does a change in cash flows affect the IRR?
4. Can IRR be used for comparing multiple projects? Why or why not?
5. What are the limitations of using IRR?

Tip: IRR assumes that all future cash flows are reinvested at the same rate as the IRR, which can be unrealistic in some scenarios.