Application Problems 6, Page 539: Brief Exercises 12.1

Application Problems 6page 539 Brief Exercises 12 1

Rihanna Company is considering purchasing new equipment for $450,000. It is expected that the equipment will produce net annual cash flows of $60,000 over its 10-year useful life. Annual depreciation will be $45,000. Compute the cash payback period.

Caine Bottling Corporation is considering the purchase of a new bottling machine. The machine would cost $200,000 and has an estimated useful life of 8 years with zero salvage value. Management estimates that the new bottling machine will provide net annual cash flows of $34,000. Management also believes that the new bottling machine will save the company money because it is expected to be more reliable than other machines, and thus will reduce downtime. How much would the reduction in downtime have to be worth in order for the project to be acceptable? Assume a discount rate of 9%. (Hint: Calculate the net present value.)

McKnight Company is considering two different, mutually exclusive capital expenditure proposals. Project A will cost $400,000, has an expected useful life of 10 years, a salvage value of zero, and is expected to increase net annual cash flows by $70,000. Project B will cost $310,000, has an expected useful life of 10 years, a salvage value of zero, and is expected to increase net annual cash flows by $55,000. A discount rate of 9% is appropriate for both projects. Compute the net present value and profitability index of each project. Which project should be accepted?

Quillen Company is performing a post-audit of a project completed one year ago. The initial estimates were that the project would cost $250,000, would have a useful life of 9 years, zero salvage value, and would result in net annual cash flows of $46,000 per year. Now that the investment has been in operation for 1 year, revised figures indicate that it actually cost $260,000, will have a total useful life of 11 years, and will produce net annual cash flows of $39,000 per year. Evaluate the success of the project. Assume a discount rate of 10%.

Bruno Corporation is involved in the business of injection molding of plastics. It is considering the purchase of a new computer-aided design and manufacturing machine for $430,000. The company believes that with this new machine it will improve productivity and increase quality, resulting in an increase in net annual cash flows of $101,000 for the next 6 years. Management requires a 10% rate of return on all new investments. Calculate the internal rate of return on this new machine. Should the investment be accepted?

Paper For Above instruction

In evaluating capital investment decisions, two primary methods are frequently used: the payback period and net present value (NPV). These methods assist companies in determining whether a project aligns with their financial goals and risk appetites. Each method offers unique insights; understanding their calculations and implications is essential for making informed investment choices.

Cash Payback Period

The payback period is a straightforward measure of investment liquidity, representing the amount of time required to recover the initial investment from net cash inflows. For Rihanna Company, the calculation involves dividing the initial investment by the annual net cash flows, assuming no consideration of the time value of money. Given the equipment cost of $450,000 and annual cash inflows of $60,000, the payback period calculations are as follows:

  • Payback Period = Initial Investment / Annual Cash Flows = $450,000 / $60,000 = 7.5 years.

Since the equipment's useful life is 10 years, Rihanna Company would recover its investment within the asset's lifespan, making the project acceptable based on this simple measure. However, this method ignores the time value of money and future cash flows beyond the payback period, which can be significant for comprehensive analysis.

Economic Value of Downtime Reduction and NPV

Caine Bottling Corporation's scenario introduces the concept of enhancing project acceptability through additional value creation. The initial investment is $200,000, with cash flows of $34,000 annually over 8 years, and zero salvage value. To determine how much the reduction in downtime must be worth, one calculates the net present value (NPV) of the project, considering the discount rate of 9%, and solves for the additional benefit that makes NPV zero.

The present value of future cash flows (PV) is computed as:

PV = Cash Flows * Annuity Factor

At a 9% discount rate over 8 years, the present value of cash flows ($34,000 per year) is:

PV = $34,000 Annuity Factor (8 years, 9%) ≈ $34,000 5.747

PV ≈ $195,398

Since the initial investment is $200,000, for the project to be acceptable (NPV ≥ 0), the value of reduced downtime savings must offset the difference:

Value of downtime reduction = Initial Investment - PV of cash flows ≈ $200,000 - $195,398 ≈ $4,602.

This indicates that if reducing downtime is worth at least $4,602 annually in present value terms, the investment becomes acceptable.

Net Present Value and Profitability Index

In comparing projects A and B for McKnight Company, the NPV and profitability index are vital indicators. NPV measures the absolute value added by the project, while the profitability index (PI) relates the NPV to the initial investment, useful for ranking mutually exclusive projects.

NPV is calculated as:

NPV = (Annual Cash Flows * Present Value of Annuity Factor) - Initial Investment.

Using a 9% discount rate over 10 years, the present value factor is approximately 6.418.

  • Project A: NPV = ($70,000 * 6.418) - $400,000 ≈ $449,260 - $400,000 = $49,260; PI ≈ $49,260 / $400,000 ≈ 0.123.
  • Project B: NPV = ($55,000 * 6.418) - $310,000 ≈ $352,990 - $310,000 = $42,990; PI ≈ $42,990 / $310,000 ≈ 0.139.

Since Project A has a higher NPV, but Project B has a higher profitability index, the decision depends on the company's priority. Generally, the project with the higher NPV provides greater absolute value addition and is often preferred.

Post-Audit Evaluation

Quillen Company's post-audit compares initial estimates with actual figures. The actual cost was $260,000 versus the estimated $250,000; the useful life increased from 9 to 11 years, and annual cash flows decreased from $46,000 to $39,000. The project’s success can be evaluated by calculating the actual ROI and comparing it to the required rate of return, considering the revised cash flows and lifespan.

The net present value of the project with the revised figures is:

NPV = (Annual Cash Flows * Present Value of Annuity for 11 years at 10%) - Actual Cost.

The present value factor for 11 years at 10% is approximately 6.858.

NPV = ($39,000 * 6.858) - $260,000 ≈ $267,462 - $260,000 = $7,462.

The positive NPV suggests the project still adds value, indicating acceptable performance despite increased costs and extended useful life. Nonetheless, the decreased annual cash flows reduce profitability, implying moderate success but not optimal.

Internal Rate of Return (IRR) Calculation

The IRR helps assess the profitability of Bruno Corporation’s potential investment. The cash flows are $101,000 annually over 6 years, with an initial investment of $430,000. Using iterative methods or financial calculators, the IRR can be approximated by solving:

0 = -$430,000 + $101,000 * (Present Value of Annuity factor at IRR).

Setting the equation, the IRR is roughly around 17.5%, exceeding the company's required 10%, suggesting the project is financially viable. The IRR surpassing the hurdle rate indicates investment acceptance.

Conclusion

These capital budgeting methods provide vital insights. The payback period offers quick liquidity information, while NPV and IRR provide comprehensive profitability indicators. The example scenarios demonstrate the importance of combining different methods to make well-rounded investment decisions aligned with strategic financial goals.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2019). Financial Management: Theory & Practice. Cengage Learning.
  • Gallo, A. (2018). The Complete Guide to Capital Budgeting. Harvard Business Review.
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  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley.
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