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Calculating Project NPV Scott Investors, Inc., is considering the purchase of a \(\mathbf{\$ 4 5 0 , 0 0 0}\) computer with an economic life of five years. The computer will be fully depreciated over five years using the straight-line method. The market value of the computer will be \(\$ 80,000\) in five years. The computer will replace five office employees whose combined annual salaries are \(\$ 140,000\). The machine will also immediately lower the firm's required net working capital by \(\$ 90,000\). This amount of net working capital will need to be replaced once the machine is sold. The corporate tax rate is 34 percent. Is it worthwhile to buy the computer if the appropriate discount rate is 12 percent?

Step by step solution

01

Calculate Annual Cost Savings

The computer will replace five office employees whose combined annual salaries are $140,000, so we can calculate the annual cost savings as follows: Annual Cost Savings = Annual salaries of replaced employees = $140,000

02

Calculate Tax Shield on Depreciation

We need to calculate the annual depreciation expense using the straight-line method: Total Depreciation = Initial Cost - Market Value in 5 Years Total Depreciation = \(450,000 - \)80,000 = $370,000 Annual Depreciation = Total Depreciation / 5 years Annual Depreciation = \(370,000 / 5 = \)74,000 Now, we calculate the tax shield on depreciation: Tax Shield on Depreciation = Annual Depreciation × Corporate Tax Rate Tax Shield on Depreciation = \(74,000 × 0.34 = \)25,160

03

Calculate Annual After-Tax Cash Inflows

To calculate the annual after-tax cash inflows, we sum the annual cost savings and the tax shield on depreciation: Annual After-Tax Cash Inflows = Annual Cost Savings + Tax Shield on Depreciation Annual After-Tax Cash Inflows = \(140,000 + \)25,160 = $165,160

04

Estimate Terminal Value

The terminal value consists of the market value of the computer in 5 years and the required net working capital replacement: Terminal Value = Market Value in 5 Years + Required Net Working Capital Replacement Terminal Value = \(80,000 + \)90,000 = $170,000

05

Calculate the Project NPV

To calculate the Project NPV, we need to discount the annual after-tax cash inflows and terminal value: PV of Cash Inflows = \( \sum_{t=1}^{5} \frac{165,160}{(1 + 0.12)^t} \) PV of Terminal Value = \( \frac{170,000}{(1+0.12)^5}\) Project NPV = PV of Cash Inflows + PV of Terminal Value - Initial Investment After calculating the present value of the cash inflows and terminal value, if the Project NPV is greater than zero, it is worthwhile to buy the computer.

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Key Concepts

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

Capital Budgeting

Capital budgeting is the process of evaluating potential major projects or investments. A key part of this process is determining whether the future benefits (cash flows) from a project justify the initial investment. In the case of Scott Investors, Inc., they are deciding whether to purchase a computer to save on labor costs.
Capital budgeting helps companies make long-term decisions. It involves:

• Evaluating costs versus benefits
• Estimating future cash flows
• Using metrics like Net Present Value (NPV), Internal Rate of Return (IRR), and Payback Period

These methods help in determining if a project like buying a computer is financially worthwhile. If the project's NPV is positive, it often indicates a good investment.

Depreciation

Depreciation reflects the reduction in value of an asset over time, essential for capital budgeting. For Scott Investors, the computer's value diminishes over its five-year lifespan. This is calculated using the straight-line method.
In the straight-line method, the asset's initial cost is evenly spread over its useful life.

• Initial Cost: $450,000
• Market Value after 5 years: $80,000
• Total Depreciation: $450,000 - $80,000 = $370,000

Therefore, we allocate $74,000 annually as depreciation over 5 years. Depreciation provides a "non-cash" charge, reducing taxable income and offering a tax advantage known as a tax shield.

Tax Shield

A tax shield is a reduction in taxable income resulting from claiming allowable deductions such as depreciation. In capital budgeting, it increases a project's attractiveness by decreasing taxable income.
Scott Investors benefits from a tax shield through annual depreciation of their computer.

• Annual Depreciation: $74,000
• Corporate Tax Rate: 34%
• Annual Tax Shield on Depreciation: $74,000 × 0.34 = $25,160

This tax shield means less tax paid each year, enhancing the project's yearly cash flows. Tax shields play a vital role in increasing the net cash inflows of a project.

Discount Rate

The discount rate in capital budgeting is crucial for calculating present value of future cash flows. It reflects the project's cost of capital or required return. For Scott Investors, a 12% discount rate is used.
This rate helps determine the present value of both regular cash inflows and terminal values:

• Regular Cash Inflows: Discounted over the project's life
• Terminal Value: Discounted at the end of the project’s life

The importance of the discount rate lies in its reflection of risk and time value of money. A higher discount rate indicates higher project risk, reducing the present value of future cash flows. In this scenario, the discount rate is applied to evaluate if buying the computer is a sound investment choice.