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The Fernandez Company has an opportunity to invest in one of two mutually exclusive machines that will produce a product the company will need for the next 8 years. Machine \(A\) costs \(\$ 10\) million but will provide after-tax inflows of \(\$ 4\) million per year for 4 years. If Machine \(A\) was replaced, its cost would be \(\$ 12\) million due to inflation and its cash inflows would increase to \(\$ 4.2\) million due to production efficiencies. Machine B costs \(\$ 15\) million and will provide after-tax inflows of \(\$ 3.5\) million per year for 8 years. If the \(\mathrm{WACC}\) is \(10 \%,\) which machine should be acquired? Explain.

Short Answer

Expert verified
Choose the machine with the higher total NPV.

Step by step solution

01

Calculate NPV of Machine A for First 4 Years

For Machine A, we first need to calculate the Net Present Value (NPV) for the first 4 years. The cost is \\(10 million and the after-tax cash inflows are \\)4 million per year. The formula for NPV is \( NPV = \sum \frac{C_t}{(1+r)^t} - C_0 \), where \( C_t \) is the cash inflow at time \( t \), \( r \) is the WACC, and \( C_0 \) is the initial investment. For the first 4 years:\[NPV_1 = \frac{4}{(1.1)^1} + \frac{4}{(1.1)^2} + \frac{4}{(1.1)^3} + \frac{4}{(1.1)^4} - 10\]Calculate this value.
02

Calculate NPV of Machine A for Next 4 Years if Replaced

Since Machine A can be replaced after 4 years at a cost of \\(12 million, with cash inflows increasing to \\)4.2 million per year, calculate the NPV for the next 4 years.\[NPV_2 = \frac{4.2}{(1.1)^1} + \frac{4.2}{(1.1)^2} + \frac{4.2}{(1.1)^3} + \frac{4.2}{(1.1)^4} - 12\]This NPV is computed as if the replacement happens, essentially at year 4. Add this value to the previously computed NPV from Step 1, considering discounting. Total the NPVs appropriately by translating these 4 additional years in terms of the original timeline.
03

Calculate NPV of Machine B for 8 Years

Machine B has a cost of \\(15 million and provides \\)3.5 million per year for 8 years. Calculate the NPV over the 8-year period using the formula:\[NPV_B = \frac{3.5}{(1.1)^1} + \frac{3.5}{(1.1)^2} + \ldots + \frac{3.5}{(1.1)^8} - 15\]Calculate this full 8-years inflow and subtract the initial investment to find the NPV for Machine B.
04

Compare NPVs of Machines A and B

After calculating the total NPV for Machine A (including both intervals with replacement) and the NPV for Machine B, compare these values. The machine with the higher NPV is the preferable investment, since it offers a greater expected gain over cost when discounted at the company's WACC.

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Key Concepts

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

Investment Decision Making
Investment decision making involves evaluating various investment opportunities to determine which ones align best with a company's financial goals. The objective is to enhance shareholder value by selecting projects or assets that are likely to generate the most benefit. In the exercise given, the decision revolves around acquiring either Machine A or Machine B. This evaluation often uses financial metrics such as Net Present Value (NPV) to compare the expected profitability of each investment
and ensure that the choice made will suit both current and future organizational needs.
Key steps in investment decision making include:
  • Identifying potential projects or assets to invest in.
  • Carefully analyzing the cash inflows and outflows over time.
  • Applying financial metrics such as NPV to assess value.
  • Considering the overall risk and return of each option.
  • Estimating the effect of these investments on the company's strategic direction.
The calculation of NPV here aids in determining which machine yields a better return once adjusted for present value, enabling Fernandez Company to make a comprehensive decision.
Weighted Average Cost of Capital (WACC)
The Weighted Average Cost of Capital (WACC) is a crucial metric in the world of corporate finance, acting as the required rate of return a company must achieve on its projects to maintain its current value. WACC represents the average rate that a company is expected to pay to finance its assets, accounting for the cost of both equity and debt.
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 equity.
  • \(V\) is the total market value of equity and debt.
  • \(Re\) is the cost of equity.
  • \(D\) is the market value of debt.
  • \(Rd\) is the cost of debt.
  • \(Tc\) is the corporate tax rate.
In the exercise, a WACC of 10% was used. This percentage reflects the minimum return required to justify the investment in either Machine A or Machine B. It is an integral part of the NPV calculation and influences the final investment decision, as a lower WACC can increase the NPV, making an investment more attractive.
Mutually Exclusive Projects
Mutually exclusive projects are a scenario where choosing one investment opportunity precludes the selection of another. This often arises when resources—whether financial, operational, or strategic—are limited and thus require a choice between alternatives. In the case of Fernandez Company, selecting either Machine A or Machine B means that the company cannot pursue both investments simultaneously.
To decide between these projects, Fernandez Company evaluates:
  • The initial cost of each machine and corresponding cash inflows.
  • The expected lifespan and performance of each alternative.
  • The calculated NPV to reveal which project provides the larger net gain.
  • Other qualitative factors such as ease of integration and potential market impacts.
By prioritizing one machine over the other based on NPV, Fernandez Company can ensure that it allocates its capital in the most efficient manner, ultimately choosing the investment that maximizes returns while fitting within its operational capacity and strategic goals.

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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?

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.

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 Erley Equipment Company purchased a machine 5 years ago at a cost of \(\$ 90,000 .\) The machine had an expected life of 10 years at the time of purchase, and it is being depreciated by the straight-line method by \(\$ 9,000\) per year. If the machine is not replaced, it can be sold for \(\$ 10,000\) at the end of its useful life. A new machine can be purchased for \(\$ 150,000\), including installation costs. During its 5-year life, it will reduce cash operating expenses by \(\$ 50,000\) per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless. MACRS depreciation will be used. The machine will be depreciated over its 3 -year class life rather than its 5 -year economic life; so the applicable depreciation rates are \(33 \%, 45 \%, 15 \%,\) and \(7 \%\) The old machine can be sold today for \(\$ 55,000\). The firm's tax rate is \(35 \%\). The appropriate WACC is \(16 \%\) a. If the new machine is purchased, what is the amount of the initial cash flow at Year \(0 ?\) b. What are the incremental net cash flows that will occur at the end of Years 1 through 5? c. What is the NPV of this project? Should Erley replace the old machine? Explain.

Zappe Airlines is considering two alternative planes. Plane A has an expected life of 5 years, will cost \(\$ 100\) million, and will produce after-tax cash flows of \(\$ 30\) million per year. Plane \(B\) has a life of 10 years, will cost \(\$ 132\) million, and will produce after-tax cash flows of \(\$ 25\) million per year. Zappe plans to serve the route for 10 years. The company's WACC is \(12 \%\). If Zappe needs to purchase a new Plane \(A\), the cost will be \(\$ 105\) million, but cash inflows will remain the same. Should Zappe acquire Plane \(\mathrm{A}\) or Plane B? Explain your answer.

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