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Corcoran Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for \(\$ 20,000\), which will generate cash flows of \(\$ 6,000\) at the end of each of the next 6 years. Alternatively, the company can spend \(\$ 12,000\) for equipment that can be used for 3 years and will generate cash flows of \(\$ 6,000\) at the end of each year (System B). If the company's WACC is \(10 \%\) and both projects can be repeated indefinitely, which system should be chosen and what is its EAA?

Short Answer

Expert verified
Choose the system with the higher EAA, either System A or System B.

Step by step solution

01

Calculate Net Present Value (NPV) of System A

To calculate the NPV for System A, we need to discount the future cash flows back to their present value. System A has a cash flow of \(6,000 annually for 6 years, and it costs \)20,000. We use the formula for NPV: \( NPV = \sum \frac{C_t}{(1 + r)^t} - C_0 \), where \( C_t = \) cash flow in year \( t \), \( r = \) discount rate (WACC), and \( C_0 = \) initial investment. Here, \( r = 0.10 \) and the sum runs from \( t = 1 \) to \( t = 6 \).
02

Calculate NPV of System B

Similar to System A, calculate System B's NPV over 3 years, with cash flows of \(6,000 per year and an initial investment of \)12,000. The discount rate remains \( 10\% \). The NPV formula applies: \( NPV = \sum \frac{C_t}{(1 + r)^t} - C_0 \) from \( t = 1 \) to \( t = 3 \).
03

Calculate Equivalent Annual Annuity (EAA) for System A

The EAA for System A can be calculated using the formula: \( EAA = \frac{NPV}{\frac{(1 - (1 + r)^{-n})}{r}} \), where \( n = 6 \) years and \( r = 0.10 \). EAA evaluates the NPV as a series of equivalent annual payments."
04

Calculate EAA for System B

Similarly, calculate the EAA for System B using the formula: \( EAA = \frac{NPV}{\frac{(1 - (1 + r)^{-n})}{r}} \), where \( n = 3 \) years and \( r = 0.10 \).
05

Compare EAAs to Make a Decision

The system with the higher EAA should be chosen as it offers a higher value when repeated indefinitely. Compare the EAAs calculated for System A and System B and select the system with the greater EAA.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equivalent Annual Annuity (EAA)
The Equivalent Annual Annuity (EAA) is a financial concept used in capital budgeting to evaluate investments with different lifespans. It breaks down the net present value (NPV) of an investment into a series of identical annual payments over its life. This allows us to directly compare projects with unequal durations, effectively converting the value of cash flows into an easy-to-understand annual amount.

To calculate EAA, we first determine the NPV of the investment. Then we use the formula: \[ EAA = \frac{NPV}{\left(\frac{1 - (1 + r)^{-n}}{r}\right)} \] where _r_ is the discount rate, and _n_ is the number of periods (years). This formula takes into account the time value of money, converting the lump sum NPV into equal annual installments.

In the problem given, System A and System B have different lifespans. By calculating EAA for both, Corcoran Consulting can understand which system converted annually provides better financial performance over time.
Weighted Average Cost of Capital (WACC)
Weighted Average Cost of Capital (WACC) is the average rate of return a company is expected to pay its security holders to finance its assets. It represents the firm's cost of capital, which includes debt and equity. WACC is crucial in capital budgeting as it serves as the discount rate for calculating the NPV of potential projects.

The formula for WACC is: \[ WACC = \frac{E}{V} \times Re + \frac{D}{V} \times Rd \times (1-Tc) \] where _E_ is the market value of the equity, _D_ is the market value of the debt, _V_ is the total market value of the firm's financing (equity + debt), _Re_ is the cost of equity, _Rd_ is the cost of debt, and _Tc_ is the corporate tax rate.

In our original exercise, the WACC is given as 10%. This means that Corcoran Consulting expects the returns from the chosen computer system to be at least 10%, matching the company’s existing funding cost. Understanding the WACC helps in assessing whether the investments will generate sufficient returns to cover this cost.
Capital Budgeting Decision
A Capital Budgeting Decision is a process used by companies to evaluate and select long-term investments that align with their strategic objectives. Making these decisions involves analyzing the potential costs and benefits of prospective projects to determine their value to the company.

The key steps in a capital budgeting decision involve:
  • Estimating future cash flows
  • Determining the appropriate discount rate (like WACC)
  • Calculating the NPV or other metrics like EAA
  • Selecting the project with the best financial benefits
In the scenario provided, Corcoran Consulting is faced with choosing between two computer systems with different costs and cash flow patterns. By calculating the EAA of each system, the company can directly compare the options on an annual basis. The system with the higher EAA is chosen, as it indicates higher annualized benefits. This practical approach helps ensure capital is allocated effectively, maximizing shareholder value over the investment period.

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Most popular questions from this chapter

Kristin is evaluating a capital budgeting project that should last 4 years. The project requires \(\$ 800,000\) of equipment. She is unsure what depreciation method to use in her analysis, straight-line or the 3 -year MACRS accelerated method. Under straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life. (Ignore the half- year convention for the straight-line method.) The applicable MACRS depreciation rates are \(33 \%, 45 \%\), \(15 \%\), and \(7 \%\) as discussed in Appendix 12A. The company's WACC is \(10 \%\), and its tax rate is \(40 \%\) a. What would the depreciation expense be each year under each method? b. Which depreciation method would produce the higher NPV, and how much higher would it be?

A firm has two mutually exclusive investment projects to evaluate; both can be repeated indefinitely. The projects have the following cash flows: Projects \(X\) and \(Y\) are equally risky and may be repeated indefinitely. If the firm's WACC is \(12 \%,\) what is the EAA of the project that adds the most value to the firm? (Round your final answer to the nearest whole dollar.)

You must evaluate a proposed spectrometer for the R\&D Department. The base price is \(\$ 140,000\), and it would cost another \(\$ 30,000\) to modify the equipment for special use by the firm. The equipment falls into the MACRS 3 -year class and would be sold after 3 years for \(\$ 60,000\). The applicable depreciation rates are \(33 \%, 45 \%\) \(15 \%,\) and \(7 \%\) as discussed in Appendix 12 A. The equipment would require an \(\$ 8,000\) increase in working capital (spare parts inventory). The project would have no effect on revenues, but it should save the firm \(\$ 50,000\) per year in before-tax labor costs. The firm's marginal federal-plus-state tax rate is \(40 \%\) a. What is the net cost of the spectrometer; that is, what is the Year 0 project cash flow? b. What are the project's annual net cash flows in Years \(1,2,\) and \(3 ?\) c. If the WACC is \(12 \%\), should the spectrometer be purchased? Explain.

The Bigbee Bottling Company is contemplating the replacement of one of its bottling machines with a newer and more efficient one. The old machine has a book value of \(\$ 600,000\) and a remaining useful life of 5 years. The firm does not expect to realize any return from scrapping the old machine in 5 years, but it can sell it now to another firm in the industry for \(\$ 265,000\). The old machine is being depreciated by \(\$ 120,000\) per year using the straight-line method. The new machine has a purchase price of \(\$ 1,175,000,\) an estimated useful life and MACRS class life of 5 years, and an estimated salvage value of \(\$ 145,000\). The applicable depreciation rates are \(20 \%, 32 \%, 19 \%, 12 \%, 11 \%\), and \(6 \% .\) The machine is expected to economize on electric power usage, labor, and repair costs as well as to reduce the number of defective bottles. In total, an annual savings of \(\$ 255,000\) will be realized if the new machine is installed. The company's marginal tax rate is \(35 \%\), and it has a \(12 \%\) WACC. a. What initial cash outlay is required for the new machine? b. Calculate the annual depreciation allowances for both machines and compute the change in the annual depreciation expense if the replacement is made. c. What are the incremental net cash flows in Years 1 through 5? d. Should the firm purchase the new machine? Support your answer. e. In general, how would each of the following factors affect the investment decision, and how should each be treated? (1) The expected life of the existing machine decreases. (2) The WACC is not constant but is increasing as Bigbee adds more projects to its capital budget for the year.

The Chang Company is considering the purchase of a new machine to replace an obsolete one. The machine being used for the operation has a book value and a market value of zero. However, the machine is in good working order and will last at least another 10 years. The proposed replacement machine will perform the operation so much more efficiently that Chang's engineers estimate that it will produce after-tax cash flows (labor savings and depreciation) of \(\$ 9,000\) per year. The new machine will cost \(\$ 40,000\) delivered and installed, and its economic life is estimated to be 10 years. It has zero salvage value. The firm's WACC is \(10 \%\), and its marginal tax rate is \(35 \%\). Should Chang buy the new machine? Explain.

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