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Mike is investing in a new commercial meat grinder. It will cost $27,130 and last for 10 years. There is no salvage value, but he expects the new grinder will save him $5,000 per year. What is the internal rate of return of the new grinder?

A) 5.4%
B) 13.0%
C) 54.3%
D) 542.6%

Answer :

To find the Internal Rate of Return (IRR) for Mike's investment in the new commercial meat grinder, we need to determine the discount rate that makes the net present value (NPV) of the investment cash flows equal to zero.

Here's how you can calculate it:

  1. Understand the Cash Flows:

    • Initial investment at Year 0: [tex]-\$27,130[/tex].
    • Annual savings (cash inflow per year) for the next 10 years: $5,000.
    • No salvage value at the end of 10 years.

  2. Set Up the Net Present Value Equation:
    The NPV of the investment is calculated by summing the present values of all cash flows.

    [tex]NPV = -27,130 + \sum_{n=1}^{10} \frac{5,000}{(1 + r)^n} = 0[/tex]
    where [tex]r[/tex] is the IRR we want to find.

  3. Solve for IRR:
    Manually solving this equation for [tex]r[/tex] can be complex, so typically this calculation is done using financial calculators or spreadsheet software like Excel, where you can use the IRR function.

    However, given the options, we can also test which rate will result in an NPV close to zero.

  4. Evaluate the Options:

    • Option A: 5.4%
    • Option B: 13.0%
    • Option C: 54.3%
    • Option D: 542.6%

    By using a financial calculator or software, you can determine which option will zero out the NPV.

    In this case, the correct answer is:

    • Option B: 13.0%

    This implies that the IRR for this investment is 13.0%, meaning a 13.0% rate makes the present value of future savings equal the initial investment of $27,130, indicating it is a profitable investment given this IRR exceeds typical inflation and loan interest rates.

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Rewritten by : Barada