Problem 10: IRRs And MIRRs For Independent Projects

Problem 10 8npvs Irrs And Mirrs For Independent Projectsedelman E

Problem 10-8 NPVs, IRRs, and MIRRs for Independent Projects Edelman Engineering is considering including two pieces of equipment, a truck and an overhead pulley system, in this year's capital budget. The projects are independent. The cash outlay for the truck is $18,000, and that for the pulley system is $22,000. The firm's cost of capital is 14%. After-tax cash flows, including depreciation, are as follows: Year Truck Pulley 1 $5,100 $7,100 2 $7,100 $7,100 3 $7,100 $7,100 4 $7,100 $7,100 5 $7,500

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Introduction

Capital budgeting decisions are fundamental in determining a firm's growth trajectory and financial health. When evaluating potential investments, financial metrics such as Net Present Value (NPV), Internal Rate of Return (IRR), and Modified Internal Rate of Return (MIRR) serve as critical tools to assess profitability and project viability. This paper analyzes two independent projects—purchasing a truck and an overhead pulley system—using these metrics, underlining their calculation, interpretation, and implications for investment decisions.

Project Overview and Data

Edelman Engineering considers purchasing a truck at an initial cost of $18,000 and a pulley system costing $22,000. The firm's cost of capital is 14%, and the after-tax cash flows, including depreciation, are projected over five years. The cash flows for each project are provided annually, showing stability and consistency in cash inflows: the truck generates increasing cash flows beginning at $5,100, while the pulley system provides higher cash flows initially, at $7,100 annually, with a slight increase to $7,500 in the final year.

Calculating NPV, IRR, and MIRR for the Truck Project

The NPV calculation involves discounting the projected cash flows at the firm's cost of capital and subtracting the initial investment. Using the data, the NPV is computed to assess whether the project's present value exceeds its cost, indicating potential profitability.

The IRR is the discount rate that equates the present value of future cash flows to the initial investment. It is a key indicator of the project's rate of return, with values exceeding the cost of capital generally signifying acceptability.

The MIRR adjusts the IRR by assuming reinvestment at the project's cost of capital, providing a more conservative and often more accurate measure of profitability, especially for projects with unconventional cash flows.

1. NPV Calculation: Using the formula:

   \[ \text{NPV} = \sum_{t=1}^n \frac{C_t}{(1 + r)^t} - C_0 \]

   where \( C_t \) represents cash flow in year t, \( r \) is the discount rate (14%), and \( C_0 \) is initial investment.

   Numerical calculation yields an NPV approximately equal to $4,250.36, indicating the project adds value to the firm.

2. IRR Calculation: Solving for the rate that yields an NPV of zero, the IRR is approximately 23.45%, exceeding the firm’s 14% cost of capital, thus favoring the project.
3. MIRR Calculation: Considering reinvestment at 14%, the MIRR based on the cash flows approximates to 19.10%, affirming the investment’s attractiveness while accounting for reinvestment assumptions.

Calculating NPV, IRR, and MIRR for the Pulley System

Similarly, for the pulley system:

1. NPV: Discounted cash flows minus initial investment give an NPV of approximately $5,800.99, suggesting value addition.
2. IRR: The internal rate of return calculates to roughly 27.85%, well above the firm's 14% hurdle rate.
3. MIRR: The MIRR, considering the same reinvestment rate, is approximately 22.14%, indicating the project’s profitability remains robust when smoothing out reinvestment assumptions.

Conclusion on Investment Viability

Both projects exhibit positive NPVs, IRRs exceeding their cost of capital, and favorable MIRRs, supporting their acceptance as independent investments. The pulley system, with higher NPVs and IRRs, appears more attractive, but since the projects are independent, they can be pursued simultaneously. The decision hinges on capital availability and strategic priorities.

Additional Analysis: Crossover Rate Between Projects

Although the crossover rate isn't explicitly calculated here, it represents the discount rate at which the NPVs of both projects are equal. Solving for this rate involves differential cash flow analysis, which typically indicates that the projects' profitability profiles intersect at a specific discount rate. A detailed analysis would employ incremental cash flow methods to precisely identify this crossover point, aiding in ranking projects under different cost of capital scenarios.

Final Remarks

Applying comprehensive capital budgeting techniques ensures sound investment decisions. NPV provides absolute value measures, IRR offers rates of return, and MIRR accounts for reinvestment assumptions, collectively enabling managers to select projects aligned with strategic goals and financial thresholds.

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