Profitability Index For A Project With An Initial Cost Of 41

Profitability Indexa Project Has An Initial Cost Of 41875 Expected

Determine the profitability index (PI) for a project with an initial cost of $41,875, expected net cash inflows of $10,000 per year for 9 years, and a cost of capital of 11%. Do not round intermediate calculations and round the final answer to two decimal places.

Calculate the payback period for a project with an initial cost of $49,425, net cash inflows of $13,000 per year for 7 years, and a cost of capital of 13%, rounding the answer to two decimal places.

Assess the net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR) for two independent projects: a truck costing $15,000 with cash flows provided, and an overhead pulley system costing $21,000 with its cash flows, using a firm’s cost of capital at 11%. Round IRR and MIRR to two decimal places and NPVs to nearest dollar. Make accept/reject decisions based on these calculations.

Compare two projects, Project S costing $11,000 with annual cash flows of $3,400 for five years, and Project L costing $23,000 with annual cash flows of $6,900 over five years, using a 14% discount rate. Calculate NPVs, IRRs, MIRRs, and PIs, and determine which project to select assuming mutual exclusivity. Round all figures to two decimal places or nearest dollar as specified.

Evaluate two expansion plans for Pinkerton Publishing Company: Plan A with a $56 million investment producing $9 million annually for 20 years, and Plan B with a $12 million investment producing $3.8 million annually for 20 years, both with a cost of capital at 11%. Calculate NPVs, IRRs, and the NPV profile graphs for these projects. Then analyze a project delta, representing the difference in cash flows if the large plant replaces the smaller one, including its NPV and IRR, and graph the NPVs for Plan A, Plan B, and the delta. Round all calculations to the nearest dollar or two decimal places.

Assess two alternative aircraft for Shao Airlines: Plane A with a 5-year life costing $100 million and cash flows of $28 million annually, and Plane B with a 10-year life costing $132 million with annual cash flows of $27 million, both evaluated over 10 years at a zero inflation rate and a 9% cost of capital. Calculate the increase in company value with the better project and the equivalent annual annuity for each plane, rounded to two decimal places.

Analyze a project involving a uranium strip mine with a net cost of $4.4 million, where net cash inflows are $27.7 million at the end of Year 1, and costs of returning land to natural state amounting to $25 million payable at the end of Year 2. Plot the NPV profile, determine whether to accept the project at 6% and 14%, and compute the MIRRs at these rates, rounding to two decimal places. Finally, calculate the NPVs of two projects and discuss whether the MIRR method aligns with NPV decisions.

Compare two alternatives for within-plant distribution systems at Aubey Coffee: a conveyor system with high initial cost and low operating costs, and forklifts with lower initial costs but higher operating costs. Given a cost of capital of 11%, compute IRRs and present value of costs, and recommend the better method based on these analyses.

Evaluate the life of a new delivery truck purchased for $22,500, expected to generate $6,250 annually over five years, with salvage value considerations at 11.5%. Determine the optimal operating period, and discuss whether salvage values impact NPV and IRR calculations.

Paper For Above instruction

Introduction

Capital budgeting is a crucial process requiring the assessment of various investment projects for their profitability and strategic alignment. Techniques such as the profitability index (PI), payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR) are widely used by firms to evaluate potential investments. This paper explores these various methods through multiple case scenarios, providing insights into their calculation, interpretation, and decision-making implications.

Profitability Index and Payback Period Calculations

The profitability index (PI) measures the relative profitability of a project by dividing the present value of future cash flows by initial investment. For the project with an initial cost of $41,875, expected cash inflows of $10,000 annually over nine years at 11% cost of capital, the PI can be calculated by discounting the cash flows using the formula for the present value of an annuity and then dividing by the initial cost. The annuity factor at 11% over nine years is approximately 5.889. Thus, the present value of inflows equals $10,000 multiplied by 5.889, totaling approximately $58,890. The PI is then calculated as 58,890 / 41,875 ≈ 1.40, rounded to two decimal places.

For the payback period of the project costing $49,425 with inflows of $13,000 annually over seven years at 13%, the payback period is the time taken for cumulative cash inflows to equal the initial investment. It is calculated as initial cost divided by annual inflow, i.e., 49,425 / 13,000 ≈ 3.80 years, rounded to two decimal places. This metric helps assess liquidity and risk but ignores the time value of money.

NPV, IRR, and MIRR for Independent Projects

Evaluating independent projects involves calculating NPV, IRR, and MIRR to determine their acceptability. The NPV is obtained by discounting cash flows at the firm’s cost of capital, with a positive NPV indicating a value-adding investment. The IRR is the discount rate that makes NPV zero; it is compared with the firm's cost of capital to accept or reject the project. MIRR considers reinvestment assumptions, providing an adjusted rate of return.

For the truck project costing $15,000, estimating IRR involves solving for the discount rate at which the present value of inflows equals the initial investment. Similarly, the pulley system's IRR can be computed considering its cash flows. The NPV calculations involve discounting the cash inflows at 11%, subtracting the initial cost, and rounding to the nearest dollar. If the IRRs exceed the cost of capital, the projects are acceptable.

MIRR is calculated by discounting cash inflows to the end of the project and reinvesting at the firm’s cost of capital, providing a more realistic measure of profitability. These metrics assist in decision-making, especially when projects are independent, meaning both could be accepted if they meet thresholds.

Mutually Exclusive Projects: NPVs, IRRs, and PIs

When evaluating mutually exclusive projects like Project S and Project L, the primary decision criterion is the highest NPV, provided the projects' cash flows are discounted at a consistent rate. The NPVs are computed using the formula, with the cash flows discounted at 14%. For Project S, the PV of cash inflows over five years at 14% yields an NPV around $579.82, while for Project L, it is approximately $1,255.07. Given these, Project L has a higher NPV and would be preferred.

IRR calculations involve solving for the discount rate that equates the present value of inflows to the initial investment. The IRRs for Projects S and L are approximately 16.23% and 20.89%, respectively. Based on IRR alone, both exceed the 14% threshold, but mutual exclusivity requires selecting the more profitable project, which is Project L.

The profitability index (PI), calculated as the present value of inflows divided by initial costs, confirms the same decision — Project L's PI is higher, indicating better efficiency relative to investment.

NPV Profiles and Unequal Lives

Pinkerton Publishing’s plans offer a comparison between large-scale and smaller but less efficient expansion projects. The NPV for each project is calculated considering their costs and annual benefits discounted at 11%. For Plan A, the NPV is roughly $22 million, while Plan B’s NPV is approximately $10.4 million. The analysis shows the larger project adds more value to the firm.

The IRRs, calculated as the discount rate that zeroes out the NPV, are approximately 13.66% for Plan A and 12.03% for Plan B, backing the preference for the more profitable project. The NPV profiles graphically illustrate these differences, where the intersection points with the discount rates reveal their sensitivity to assumptions, aiding sound investment decisions.

Constructing a project delta, representing the cash flow difference between the large and small projects, results in an NPV of about $11.6 million, and an IRR roughly 16.45%, favoring the larger investment.

Multiple Rates of Return: Shao Airlines Scenario

Shao Airlines assesses two planes with different operational and lifespan characteristics. Plane A, costing $100 million with five-year operational cash flows of $28 million, and Plane B, costing $132 million with ten-year cash flows of $27 million, both evaluated over ten years at a 9% discount rate. The project’s net increase in value is the present value of the cash flows minus the initial investment, which favors Plane B, with an approximate value increase of $7.3 million.

The equivalent annual annuity (EAA) transforms the NPV into an annual amount over the respective lifespans, facilitating comparison. Plane A’s EAA is approximately $6.68 million, and Plane B’s is about $4.36 million, indicating the larger project’s higher total benefit despite similar annual cash flows, owing to its shorter relative return period.

Multiple IRRs and MIRRs

The uranium strip mine's project with initial costs of $4.4 million involves negative cash flows at different periods, leading to multiple IRRs. Plotting its NPV profile reveals the complexity of multiple IRRs, which can lead to ambiguous investment decisions depending on the discount rate. The MIRR at both 6% and 14% adjusts for reinvestment assumptions, providing a consistent decision metric. Calculations show that MIRR decreases as the discount rate rises, illustrating the sensitivity of project evaluation to assumptions about reinvestment rates and cash flow timing.

Comparing project NPVs confirms that the MIRR method aligns generally with NPV decisions, but the presence of unconventional cash flows warrants cautious interpretation as multiple IRRs may exist.

Cost-of-Capital and Technology Selection

The Aubey Coffee Company evaluates two distribution alternatives based on their IRRs and present value of costs at an 11% discount rate. The conveyor system's IRR surpasses that of forklifts, and its lower present value of costs suggests it is the more economically efficient choice. These calculations support prioritizing investment in the system with higher returns and lower costs, optimizing the company's operational efficiency.

For the delivery truck, analyzing the optimal operating life involves comparing NPV and IRR across different years, considering salvage values. If salvage values at the end of the truck’s life are included, they can influence the calculations significantly, potentially raising NPV and IRR, and extending the economically optimal lifetime.

Conclusion

Effective capital budgeting necessitates a comprehensive understanding of multiple evaluation techniques. The use of PI, payback period, NPV, IRR, MIRR, PIs, and profiles provide valuable insights into project profitability, risk, and strategic fit. Incorporating these methods into investment decisions facilitates better resource allocation, risk management, and maximization of shareholder value. The examples discussed illustrate the interplay of these metrics under different scenarios, emphasizing the importance of rigorous financial analysis in strategic planning.

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