91Ó°ÊÓ

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.

Step by step solution

01

Calculate Initial Year 0 Cash Flow

The initial cash flow in Year 0 includes the base price of the spectrometer, the modification cost, and the change in working capital. The initial cost is the sum of these values: \[\text{Initial Investment} = \\(140,000 + \\)30,000 + \\(8,000 = \\)178,000\]The Year 0 project cash flow is therefore \$178,000.

02

Determine Depreciation Amounts

We will use the MACRS depreciation rates of 33%, 45%, and 15% to calculate the depreciation for each year:Year 1: \[\text{Depreciation} = 0.33 \times (\\(140,000 + \\)30,000) = \\(56,100\]Year 2: \[\text{Depreciation} = 0.45 \times (\\)140,000 + \\(30,000) = \\)76,500\]Year 3:\[\text{Depreciation} = 0.15 \times (\\(140,000 + \\)30,000) = \$25,500\]

03

Calculate Annual Operating Cash Flows

The operating cash flow is based on the savings from labor costs, after-tax savings, and the depreciation tax shield.Annual savings from labor cost:\[\text{Labor savings} = \\(50,000\]Tax savings on labor:\[\text{After-tax savings} = \\)50,000 \times (1 - 0.40) = \\(30,000\]Depreciation tax shield for each year:Year 1:\[\text{Tax shield} = \\)56,100 \times 0.40 = \\(22,440\]Year 2:\[\text{Tax shield} = \\)76,500 \times 0.40 = \\(30,600\]Year 3:\[\text{Tax shield} = \\)25,500 \times 0.40 = \\(10,200\]Annual net cash flows:Year 1:\[\text{Net cash flow} = \\)30,000 + \\(22,440 = \\)52,440\]Year 2:\[\text{Net cash flow} = \\(30,000 + \\)30,600 = \\(60,600\]Year 3:\[\text{Net cash flow} = \\)30,000 + \\(10,200 = \\)40,200\]

04

Calculate Terminal Year Cash Flow

In Year 3, consider the after-tax salvage value and recovery of working capital.Salvage value:\[\text{After-tax salvage} = \\(60,000 \times (1 - 0.40) = \\)36,000\]Recovery of working capital is \\(8,000. Thus, the terminal cash flow is:\[\text{Terminal cash flow} = \\)36,000 + \\(8,000 = \\)44,000\]Adding this to the Year 3 cash flow gives:\[\text{Total Year 3 cash flow} = \\(40,200 + \\)44,000 = \$84,200\]

05

Evaluate NPV and Decision

To decide if the purchase is justified, calculate the NPV using the formula for NPV and a WACC of 12%:\[NPV = \frac{-178,000}{1.12^0} + \frac{52,440}{1.12^1} + \frac{60,600}{1.12^2} + \frac{84,200}{1.12^3}\]Calculate each term:\[NPV = -178,000 + 46,786 + 48,319.64 + 59,977.44\]\[NPV = -22,916.92\]Since the NPV is negative, the spectrometer should not be purchased.

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Key Concepts

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

Net Present Value (NPV)

Net Present Value (NPV) is a vital tool in capital budgeting that helps determine the profitability of an investment. It compares the present value of cash inflows to the present value of cash outflows over the project's life. The formula for NPV is: \[ NPV = \sum \frac{R_t}{(1 + i)^t} - C_0 \]where:

• \( R_t \) is the net cash inflow during the period \( t \)
• \( i \) is the discount rate (in this case, the WACC)
• \( t \) is the number of time periods
• \( C_0 \) is the initial investment

A positive NPV indicates that the projected earnings, adjusted for time and risk, exceed the costs, suggesting a good investment opportunity. Conversely, a negative NPV, as in the spectrometer's case, suggests that the expected profits do not justify the expense, leading to the advice not to purchase.

Depreciation

Depreciation reflects the reduction in value of an asset over time due to wear and tear. It allows firms to allocate the cost of an asset over its useful life. In our exercise, the spectrometer is subjected to Modified Accelerated Cost Recovery System (MACRS) depreciation, which is a method used in the United States:

• Year 1: 33% depreciation.
• Year 2: 45% depreciation.
• Year 3: 15% depreciation.

Using these rates, the company can save on taxes through what's known as the depreciation tax shield. This shield reduces taxable income, thereby leading to tax savings. The depreciation tax shield is calculated by multiplying the depreciation expense by the tax rate. This was an important part of the spectrometer analysis, as it contributed to the yearly cash flows.

Working Capital Management

Working capital management involves handling a firm's short-term assets and liabilities efficiently to ensure ongoing operation and financial health. In capital budgeting, any change in working capital directly impacts cash flows. With the spectrometer project, there was an additional working capital requirement of $8,000 for spare parts inventory, affecting the initial cash outflow in Year 0. However, this working capital is typically recovered at the end of the project, contributing to the final cash flows, as seen in Year 3 in our exercise. Proper management ensures that a company retains enough liquid assets to meet its short-term obligations without unnecessary excess.

Weighted Average Cost of Capital (WACC)

WACC represents the average rate that a company is expected to pay to finance its assets, weighing each category of capital by its proportion in the overall capital structure. It acts as the discount rate in NPV calculations, reflecting the opportunity cost of investing in a specific project instead of alternative scenarios. WACC is calculated as follows:\[ WACC = \frac{E}{V} \times Re + \frac{D}{V} \times Rd \times (1 - Tc) \] 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 our exercise, a WACC of 12% was crucial to discount future cash flows to their present value. Measuring against WACC, the NPV helps determine if the spectrometer should be a viable purchase, which in this case, was not recommended due to a negative NPV.