Your Division Is Considering Two Investment Projects Each Of

Your Division Is Considering Two Investment Projects Each Of Which Re

Your division is considering two investment projects, each of which requires an up-front expenditure of $25 million. You estimate that the cost of capital is 10 percent and that the investments will produce the following after-tax cash flows: a. What is the regular payback period for each of the projects? b. What is the discounted payback period for each of the projects? c. If the 2 projects are independent and the cost of capital is 10 percent, which project or projects should the firm undertake? d. If the two projects are mutually exclusive and the cost of capital is 5 percent, which project should the firm undertake? e. If the two projects are mutually exclusive and the cost of capital is 15 percent, which project should the firm undertake? f. What is the crossover rate? g. If the cost of capital is 10 percent, what is the modified IRR (MIRR) of each project?

Paper For Above instruction

Introduction

Investment decision-making is fundamental to corporate financial management, focusing on selecting projects that maximize shareholder wealth. Critical to this process are various financial metrics such as payback period, discounted payback period, net present value (NPV), internal rate of return (IRR), modified IRR (MIRR), and crossover rate. This paper analyzes two proposed projects using these criteria, considering the implications of project independence, mutual exclusivity, and varying discount rates.

Project Evaluation Metrics

The initial investment for each project is $25 million, with an expected series of after-tax cash flows. The evaluation begins with calculating the payback period, which measures the time required to recover the initial investment through cash inflows. Next, the discounted payback period considers the present value of cash flows, providing a more accurate measure when cash flows are discounted at the project's cost of capital. NPV analysis further assesses project profitability by subtracting the present value of cash inflows from the initial investment, while IRR determines the discount rate that equates the present value of cash inflows with the initial outlay.

Calculation of Payback Periods

The payback period is calculated simply by dividing the initial investment by the annual cash inflow. For example, if a project generates annual after-tax cash flows of $X million, the payback period will be $25 million / $X million. The discounted payback period involves discounting each year's cash flow at 10% and then summing until the initial investment is recovered.

Decision Rules Based on Investment Criteria

- Independent Projects: Projects are undertaken if their NPV is positive at the firm’s cost of capital.

- Mutually Exclusive Projects: The project with the higher NPV or IRR is selected, considering the discount rate.

- Crossover Rate: The discount rate at which the NPVs of two projects are equal, useful for understanding project rankings at different discount rates.

- Modified IRR (MIRR): Adjusts IRR to provide a more conservative and accurate measure of a project’s profitability, especially when cash flow patterns are unconventional.

Analysis and Results

Without the explicit cash flow data, general formulas and methodology are discussed. For example, the payback period formula for each project, discounted payback, and the calculation of NPV and IRR are explained. When cash flows are known, these formulas enable precise decision-making.

- Independent Projects: Both are accepted if their NPVs are positive.

- Mutually Exclusive Projects at 5%: The project with the higher NPV at a 5% discount rate is preferred.

- At 15%: The choice depends on which project's IRR exceeds 15%.

The crossover rate can be derived by setting the NPVs of both projects equal and solving for the discount rate, typically involving trial-and-error or financial calculator functions.

The MIRR accounts for the reinvestment rate and finance rate, providing a better measure than IRR, especially for projects with non-conventional cash flows.

Discussion

Analysis reveals that project selection heavily depends on the discount rate and project relationships (independent vs. mutually exclusive). A lower discount rate favors projects with higher initial cash flows, while higher rates penalize later cash flows more severely. The crossover rate indicates the sensitivity of project rankings to the discount rate, guiding strategic decision-making under varying economic circumstances.

Conclusion

Evaluating investment projects requires a comprehensive approach considering multiple financial metrics. While payback periods provide liquidity insights, NPV and IRR measure profitability more accurately. For independent projects, both must be profitable; for mutually exclusive projects, the decision depends on which project yields higher NPV or IRR relative to the discount rate. The crossover rate offers additional insight into project comparability, and MIRR provides a realistic profitability measure. Ultimately, integrating these metrics guides sound investment decisions aligned with corporate financial goals.

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