To determine the internal rate of return (IRR) for the project, we need to identify the discount rate that results in a net present value (NPV) of zero. The formula for NPV is:

$\text{NPV} = \sum \left( \frac{\text{Net Cash Inflow}}{(1 + r)^t} \right) - \text{Initial Investment}$

Where:

• $r$ is the internal rate of return (IRR).
• $t$ is the year (1 to 5 in this case).
• Net Cash Inflow = Net Operating Income + Depreciation (because depreciation is a non-cash expense).

Step 1: Calculate the annual net cash inflows

From the given information:

• Net Operating Income = $830,000
• Depreciation = $1,170,000

The net cash inflow each year is:

$\text{Net Cash Inflow} = 830,000 + 1,170,000 = 2,000,000$

Step 2: Apply the formula for NPV

We know the initial investment is $5,850,000 and the project provides annual net cash inflows of $2,000,000 for five years. To find the IRR, we need to solve for the discount rate where the NPV equals 0:

$NPV = 2,000,000 \times \left( \frac{1 - (1 + r)^{-5}}{r} \right) - 5,850,000$

Step 3: Use the Present Value of Annuity formula

We need to find the discount rate ($r$) such that the present value of an annuity of $2,000,000 over five years equals the initial investment of $5,850,000.

Using annuity tables or trial and error, we can estimate the rate by checking the factor $\frac{1 - (1 + r)^{-5}}{r}$ that will yield:

$5,850,000 = 2,000,000 \times \text{Annuity Factor}$

$\text{Annuity Factor} = \frac{5,850,000}{2,000,000} = 2.925$

Step 4: Locate the corresponding IRR from Annuity Tables

By consulting the annuity tables, we look for a 5-year annuity factor close to 2.925. This factor corresponds to an interest rate of approximately 24%.

Conclusion:

The project’s internal rate of return (IRR) is approximately 24%.

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Would you like more details on any specific part of this process?

5 Related Questions:

1. How does the IRR compare to the company’s discount rate of 20%?
2. What would be the net present value (NPV) if the discount rate were 20%?
3. How does depreciation impact the cash flow of a project?
4. What are the risks of relying solely on IRR for capital budgeting decisions?
5. What other financial metrics could Casey use to evaluate the project?

Tip:

When evaluating a project, it’s essential to consider both the IRR and the NPV to get a full picture of its potential profitability.