Problem 10 19a Using Net Present Value And Internal Rate Of

Problem 10 19a Using Net Present Value And Internal Rate Of Return To

Using net present value and internal rate of return to evaluate investment opportunities

Dwight Donovan, the president of Donovan Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $400,000 and for Project B are $160,000.

The annual expected cash inflows are $126,000 for Project A and $52,800 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Donovan Enterprises' desired rate of return is 8 percent.

Paper For Above instruction

In evaluating proposed investment projects, organizations often rely on financial metrics such as Net Present Value (NPV) and Internal Rate of Return (IRR) to guide decision-making. These metrics provide insightful data about the profitability and efficiency of investments, helping firms allocate limited resources to the most promising opportunities. This paper applies these techniques to two hypothetical projects considered by Donovan Enterprises, which faces the decision to invest in either automation equipment (Project A) or employee training (Project B).

Calculating Net Present Value

The NPV method involves discounting the estimated cash inflows generated by a project to their present value at the company's desired rate of return and subtracting the initial investment. The formula used is:

NPV = Present Value of Cash Inflows – Initial Investment

Given that both projects generate annual cash inflows for four years and have a stated discount rate of 8%, the present value of an annuity formula is employed:

PV = Cash Flows × Annuity Factor (at 8%, 4 years)

The annuity factor for 8% over four years is approximately 3.3121 (from standard financial tables). Applying this to each project:

Project A

  • Initial investment: $400,000
  • Annual cash inflow: $126,000
  • Present value of inflows: $126,000 × 3.3121 ≈ $417,102.60
  • NPV: $417,102.60 – $400,000 = $17,102.60

Project B

  • Initial investment: $160,000
  • Annual cash inflow: $52,800
  • Present value of inflows: $52,800 × 3.3121 ≈ $175,867.08
  • NPV: $175,867.08 – $160,000 = $15,867.08

Based on the NPV approach, both projects are financially viable since both exhibit positive NPVs. However, Project A has a slightly higher NPV, indicating it adds more value to the company and thus should be preferred if NPV is the sole criterion.

Calculating Internal Rate of Return

The IRR is the discount rate at which the present value of cash inflows equals the initial investment, rendering the NPV zero. To approximate IRR, financial calculators or iterative trial-and-error methods are used. Alternatively, the following formula applies for a simple annuity, rearranged to solve for the discount rate (r):

Initial Investment = Cash Flows × Present Value of Annuity Factor at r

Since this is an iterative process, approximate IRRs are calculated as follows:

Project A

Using trial discount rates, the IRR for Project A is approximately 10.27%. This indicates that at about 10.27%, the present value of the inflows equals the initial investment.

Project B

Similarly, the IRR for Project B is approximately 11.65%. This suggests Project B's cash inflows are slightly more efficient relative to its initial outlay.

Both IRRs exceed the company’s desired rate of return of 8%, reinforcing that both investments are attractive. Nonetheless, Project B exhibits a higher IRR, suggesting it provides a higher return relative to its cost.

Comparing NPV and IRR Approaches

The NPV and IRR methodologies are both popular among financial analysts, yet they can occasionally produce conflicting signals, especially when projects differ significantly in scale or duration. In this scenario, the NPV approach indicates that Project A is marginally more valuable, whereas the IRR approach favors Project B due to its higher rate of return.

NPV is generally considered superior for decision-making because it directly measures the expected increase in value to the firm, accounting for the magnitude of project benefits. Conversely, IRR can sometimes be misleading, particularly with mutually exclusive projects, because it does not consider the scale of investments and may produce multiple values in unconventional cash flow patterns.

Given the circumstances, the company's primary goal should be to maximize value. Therefore, NPV should be preferred in this context, as it objectively quantifies the expected contribution of each project to shareholder wealth.

Nevertheless, considering the higher IRR of Project B, if the firm’s decision criterion is to choose projects based on return rate alone, Project B remains attractive. To make an optimal decision, integrating both metrics along with strategic considerations is advisable.

In conclusion, while both projects are financially viable, the NPV approach suggests selecting Project A for its higher contribution to value, aligning with the goal of wealth maximization. Practitioners should employ both methods and consider other qualitative factors for comprehensive investment decisions.

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