Casey Nelson is a divisional manager for Pigeon Company. His annual pay raises are largely determined by his division’s return on investment (ROI), which has been above 24% each of the last three years. Casey is considering a capital budgeting project that would require a $5,850,000 investment in equipment with a useful life of five years and no salvage value. Pigeon Company’s discount rate is 20%. The project would provide net operating income each year for five years as follows:

Sales	 	$ 5,200,000
Variable expenses	 	2,320,000
Contribution margin	 	2,880,000
Fixed expenses:	 	 
Advertising, salaries, and other fixed out-of-pocket costs	$ 880,000	 
Depreciation	1,170,000	 
Total fixed expenses	 	2,050,000
Net operating income	 	$ 830,000
Click here to view Exhibit 7B-1 and Exhibit 7B-2, to determine the appropriate discount factor(s) using tables.

Required:

 What is the project’s internal rate of return to the nearest whole percent?

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%**.

---

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.

Casey Nelson is a divisional manager for Pigeon Company. His annual pay raises are largely determined by his division’s return on investment (ROI), which has been above 24% each of the last three years. Casey is considering a capital budgeting project that would require a $5,850,000 investment in equipment with a useful life of five years and no salvage value. Pigeon Company’s discount rate is 20%. The project would provide net operating income each year for five years as follows: Sales $5,200,000, Variable expenses $2,320,000, Contribution margin $2,880,000, Fixed expenses: Advertising, salaries, and other fixed out-of-pocket costs $880,000, Depreciation $1,170,000, Total fixed expenses $2,050,000, Net operating income $830,000. What is the project’s internal rate of return to the nearest whole percent?

Learn how to calculate the internal rate of return (IRR) for a 5-year capital budgeting project with a $5,850,000 investment. This step-by-step guide covers key concepts like Net Present Value (NPV) and Present Value of Annuity to help determine the IRR, which is approximately 24%. Ideal for finance students or professionals evaluating capital investments.

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