Sheet1solutioninitial Investment 200000000savings Every Year ✓ Solved

Sheet1solutioninitial Investment 200000000savings Every Year

Calculate the Net Present Value (NPV), Internal Rate of Return (IRR), and Payback period based on the given investment details. The initial investment is $2,000,000.00, with annual savings of $500,000.00 over a period of 10 years, using a cost of capital of 14% and 25% to determine the financial viability of the investment.

Paper For Above Instructions

The financial analysis of a project is critical for understanding its viability and long-term benefits. This paper will calculate the Net Present Value (NPV), Internal Rate of Return (IRR), and Payback period for an investment scenario involving an initial investment of $2,000,000 and annual savings of $500,000 over 10 years.

Investment Summary

The investment details are as follows:

  • Initial Investment: $2,000,000.00

  • Annual Savings: $500,000.00

  • Investment Duration: 10 years

  • Cost of Capital: 14% (Scenario 1) and 25% (Scenario 2)

Calculating NPV

The NPV is calculated as the present value of cash flows minus the initial investment. The formula for NPV is:

NPV = PV of Cash Flows - Initial Investment

Scenario 1: Cost of Capital at 14%

The cash flows over the 10 years are:

  • Year 0: -$2,000,000

  • Year 1: $500,000

  • Year 2: $500,000

  • Year 3: $500,000

  • Year 4: $500,000

  • Year 5: $500,000

  • Year 6: $500,000

  • Year 7: $500,000

  • Year 8: $500,000

  • Year 9: $500,000

  • Year 10: $500,000

Using present value factors (PVF) for 14%, the present value for each year can be calculated:

  • Year 1: $438,596.49

  • Year 2: $384,733.76

  • Year 3: $337,485.76

  • Year 4: $296,040.14

  • Year 5: $259,684.33

  • Year 6: $227,793.27

  • Year 7: $199,818.66

  • Year 8: $175,279.53

  • Year 9: $153,753.97

  • Year 10: $134,871.90

The total present value of cash flows is $2,608,057.82. Thus, the NPV calculation is:

NPV = $2,608,057.82 - $2,000,000 = $608,057.82.

Scenario 2: Cost of Capital at 25%

The process is similar for the second scenario with a higher cost of capital:

  • Year 0: -$2,000,000

  • Years 1-10: $500,000 annually.

Using PVF at 25%, we see:

  • Year 1: $400,000.00

  • Year 2: $320,000.00

  • Year 3: $256,000.00

  • Year 4: $204,800.00

  • Year 5: $163,840.00

The present value of cash flows totals $1,785,251.64. Therefore, the NPV calculation is:

NPV = $1,785,251.64 - $2,000,000 = -$214,748.36.

Calculating IRR

The IRR is calculated as the discount rate where NPV equals zero. For the initial scenario with a cost of capital of 14%, the IRR calculated is approximately 21%. For the second scenario, the IRR also remains approximately 21%, indicating that even with different costs of capital, the project’s profitability is similarly measured.

Payback Period

The payback period is the time taken for cumulative cash flows to offset the initial investment. In both scenarios, the payback period is about 4 years, meaning the investment recovers its cost within this timeframe based on the cash inflows of $500,000 annually.

Conclusion

The analysis shows that at a 14% cost of capital, the investment is viable, yielding a positive NPV of $608,057.82 and an acceptable IRR. However, at a cost of capital of 25%, the NPV turns negative, indicating that this investment would not be recommended under those conditions. This analysis underscores the importance of selecting an appropriate cost of capital when evaluating potential investments.

References

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