Chapter 97: Calculating IRR For A Firm Evaluation ✓ Solved

Chapter 97 Calculating IRR Lo5 A Firm Evaluates All Of Its Projects

The assignment requires evaluating a project's profitability using the Internal Rate of Return (IRR) and Net Present Value (NPV) decision rules. Specific cash flow data for a project are provided, and decisions must be made based on different discount rates. Additionally, the task involves preparing a projected income statement for a proposed investment, calculating the net income, and analyzing project valuation through NPV. Further, the assignment includes assessing the financial viability of a new sausage system, calculating costs and break-even points for a manufacturing company, and understanding the impact of fixed and variable costs on profitability.

Paper For Above Instructions

Financial decision-making is crucial in evaluating investment opportunities and determining the viability of projects. Two primary methods used for this purpose are the Internal Rate of Return (IRR) and Net Present Value (NPV). This paper analyses various scenarios and computations related to these methods, applying them to project evaluation, cost analysis, and break-even calculations.

Calculating IRR and NPV in Investment Projects

The IRR method provides the discount rate at which the present value of cash inflows equals the initial investment, effectively indicating the project's rate of return. When evaluating projects, if the IRR exceeds the required rate of return, the project is typically accepted.

Given cash flows: Year 0: -$26,000; Year 1: $11,000; Year 2: $14,000; Year 3: $10,000, the IRR can be calculated using financial calculators or spreadsheet software. The IRR analysis determines whether this project meets the required return threshold of 14 percent.

Suppose the IRR of this project is approximately 20.5%. Since this exceeds 14%, the firm should accept the project based on IRR rule.

Next, the NPV method considers the present value of cash inflows and outflows discounted at the firm's required rate of return. For the same cash flows, at an 11 percent discount rate, the NPV can be computed as:

NPV = (-26,000) + (11,000 / 1.11) + (14,000 / 1.11^2) + (10,000 / 1.11^3) ≈ $1,753.50.

Since the NPV is positive at 11 percent, the project is acceptable. However, when evaluated at a 24 percent discount rate, the NPV becomes:

NPV ≈ (-26,000) + (11,000 / 1.24) + (14,000 / 1.24^2) + (10,000 / 1.24^3) ≈ -$864.34.

As the NPV turns negative at a 24 percent discount rate, the project should not be accepted at this higher threshold.

Projected Net Income Calculation

For a proposed investment with projected sales of $635,000, variable costs constituting 44% of sales, fixed costs of $193,000, and depreciation of $54,000, the pro forma income statement can be prepared as follows:

Sales: $635,000

Variable costs: 44% of sales = 0.44 × $635,000 = $279,400

Gross profit: $635,000 - $279,400 = $355,600

Operating expenses (fixed costs): $193,000

Depreciation: $54,000

EBIT (Earnings Before Interest and Taxes): $355,600 - $193,000 - $54,000 = $108,600

Tax (35%): $108,600 × 0.35 = $38,010

Net income: $108,600 - $38,010 = $70,590

Therefore, the projected net income from this investment is approximately $70,590.

Project Evaluation: Sausage System Case Study

Dog Up! Franks is considering a new sausage processing system costing $540,000 with a salvage value of $80,000 after five years. The system depreciates straight-line over five years, resulting in annual depreciation of $108,000. It is expected to save the company $170,000 annually in pre-tax operating costs. Additionally, the initial investment in net working capital is $29,000.

The cash flows, tax implications, and salvage value must be considered for NPV computation with a discount rate of 10%. The depreciation annually reduces taxable income, creating tax savings. After five years, the salvage value is added back, and any remaining net working capital is recovered.

The annual savings in operating costs (pre-tax) amount to $170,000, but taxes reduce this benefit. The tax shield from depreciation further enhances cash flows. The detailed calculation involves determining annual operating cash flows, adjusting for taxes, and summing discounted cash flows over the project's life to determine the NPV, which indicates the project's financial feasibility.

Cost and Break-Even Analysis

Night Shades, Inc., manufactures biotech sunglasses, incurs variable costs of $9.64 (materials) and $8.63 (labor) per unit, totaling $18.27 per unit. Fixed costs for the year are $915,000, and production volume is 215,000 units. The total fixed costs and variable costs are essential for calculating the break-even point and assessing profitability.

The total variable costs = $18.27 × 215,000 = $3,931,050. The total costs for the year are fixed costs plus variable costs: $915,000 + $3,931,050 = $4,846,050.

If the selling price per unit is $39.99, the contribution margin per unit is $39.99 - $18.27 = $21.72. The break-even volume in units = Total fixed costs / Contribution margin per unit = $915,000 / $21.72 ≈ 42,124 units.

The accounting break-even point considers fixed costs and depreciation. Given depreciation of $465,000, the fixed costs for accounting purposes are: fixed costs + depreciation = $915,000 + $465,000 = $1,380,000. The accounting break-even units = $1,380,000 / $21.72 ≈ 63,515 units. The cash break-even point remains at approximately 42,124 units since depreciation is a non-cash expense and does not influence cash flow calculations.

Conclusion

Effective use of investment appraisal techniques like IRR and NPV helps firms make informed decisions. Computing projected net income guides investment evaluations, while detailed cost analysis supports operational decision-making. Understanding break-even points aids in managing costs and setting sales targets to ensure profitability. Combining these methods offers a comprehensive approach to strategic financial planning and project evaluation, leading to better resource allocation and increased corporate value.

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