To calculate the internal rate of return (IRR) for the purchase of manufacturing equipment, we need to find the discount rate ($i$) at which the present value of future cash inflows equals the initial investment.

Here's the data provided:

• Initial Investment: $72,000
• Annual Cash Inflows:
  • Year 1: $36,000
  • Year 2: $34,000
  • Year 3: $29,000

Approach to Calculate IRR

We aim to find the IRR by setting up the following equation, where $i$ is the IRR:

$72,000 = \frac{36,000}{(1 + i)^1} + \frac{34,000}{(1 + i)^2} + \frac{29,000}{(1 + i)^3}$

1. Using Approximate Values: Appendix B and Appendix D provide present value factors for various rates and time periods. We would normally use these tables to estimate the range of $i$ values for IRR.
2. Using Financial Calculator: We then refine our answer by using a financial calculator to solve precisely for $i$, given the cash flows.

Since the specific calculations with a financial calculator involve trying values iteratively or through calculator functions, here’s the IRR calculation directly:

Solution with Financial Calculator Steps

1. Enter the cash flows as follows:

   • CF0 (initial investment): -72,000
   • CF1: 36,000
   • CF2: 34,000
   • CF3: 29,000

2. Calculate IRR using the calculator’s IRR function.

Using these steps, you should find an IRR of approximately 18.56%.

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Would you like further steps or details on any part of this calculation?

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1. What is the significance of IRR in investment decisions?
2. How does IRR differ from Net Present Value (NPV)?
3. How would IRR change if one of the cash flows was delayed by a year?
4. Can there be multiple IRRs for non-standard cash flow projects?
5. How would changing the initial investment affect the IRR?

Tip: When interpreting IRR, remember that it represents the discount rate where the project breaks even in terms of NPV, helping compare the profitability of different investments.