91Ó°ÊÓ

Mississippi River Shipyards is considering replacing an 8-year-old riveting machine with a new one that will increase earnings before depreciation from \(\$ 27,000\) to \(\$ 54,000\) per year. The new machine will cost \(\$ 82,500,\) and it will have an estimated life of 8 years and no salvage value. The new machine will be depreciated over its 5 -year MACRS recovery period; so the applicable depreciation rates are \(20 \%, 32 \%\) \(19 \%, 12 \%, 11 \%,\) and \(6 \% .\) The applicable corporate tax rate is \(40 \%,\) and the firm's WACC is \(12 \% .\) The old machine has been fully depreciated and has no salvage value. Should the old riveting machine be replaced by the new one? Explain your answer.

Step by step solution

01

Calculate Initial Investment

The initial investment is the cost of the new machine, which is \( \$82,500 \). The old machine has no salvage value and has been fully depreciated.

02

Determine Depreciation

Use the 5-year MACRS recovery period to calculate the annual depreciation for the new machine:- Year 1: \( 82,500 \times 0.20 = 16,500 \)- Year 2: \( 82,500 \times 0.32 = 26,400 \)- Year 3: \( 82,500 \times 0.19 = 15,675 \)- Year 4: \( 82,500 \times 0.12 = 9,900 \)- Year 5: \( 82,500 \times 0.11 = 9,075 \)- Year 6: \( 82,500 \times 0.06 = 4,950 \)

03

Calculate Incremental Earnings After Tax

Calculate the incremental earnings before and after tax:- Incremental Before-tax Earnings: \( 54,000 - 27,000 = 27,000 \)- Tax on Incremental Earnings: \( 27,000 \times 0.40 = 10,800 \)- Incremental Earnings After Tax: \( 27,000 - 10,800 = 16,200 \)

04

Calculate Cash Flow for Each Year

Add back the tax savings from depreciation to the incremental earnings after tax:- Year 1 Cash Flow: \( 16,200 + 16,500 \times 0.40 = 22,800 \)- Year 2 Cash Flow: \( 16,200 + 26,400 \times 0.40 = 26,760 \)- Year 3 Cash Flow: \( 16,200 + 15,675 \times 0.40 = 22,470 \)- Year 4 Cash Flow: \( 16,200 + 9,900 \times 0.40 = 20,160 \)- Year 5 Cash Flow: \( 16,200 + 9,075 \times 0.40 = 19,830 \)- Year 6 Cash Flow: \( 16,200 + 4,950 \times 0.40 = 18,180 \) (Note the new machine only has 5 useful years).

05

Compute Net Present Value (NPV)

Discount the cash flows at the firm's WACC of \(12\%\):- Year 1 Cash Flow: \( \frac{22,800}{(1+0.12)^1} \approx 20,357.14 \)- Year 2 Cash Flow: \( \frac{26,760}{(1+0.12)^2} \approx 21,352.23 \)- Year 3 Cash Flow: \( \frac{22,470}{(1+0.12)^3} \approx 17,916.60 \)- Year 4 Cash Flow: \( \frac{20,160}{(1+0.12)^4} \approx 12,785.71 \)- Year 5 Cash Flow: \( \frac{19,830}{(1+0.12)^5} \approx 11,290.48 \)Sum these values and subtract the initial investment to get the NPV:Total Present Value = \( 20,357.14 + 21,352.23 + 17,916.60 + 12,785.71 + 11,290.48 = 83,702.16 \)NPV = \( 83,702.16 - 82,500 = 1,202.16 \)

06

Make the Decision

The NPV is positive \( (1,202.16) \), indicating that the investment in the new machine will add value to the firm. Therefore, Mississippi River Shipyards should replace the old riveting machine with the new one.

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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 critical concept in capital budgeting. It helps companies make informed decisions about where to invest their money. NPV compares the value of a project's anticipated cash flows, discounted back to the present using the firm's Weighted Average Cost of Capital (WACC), to the initial investment outlay. The formula for NPV is:\[ NPV = \sum \left( \frac{CF_t}{(1 + r)^t} \right) - I \]where:

• CF_t is the cash flow in year t
• r is the WACC or discount rate
• I is the initial investment

A positive NPV indicates that the project's returns exceed the required rate of return, meaning it's a good investment. In this exercise, we calculated an NPV of $1,202.16, suggesting that replacing the machine is profitable for the firm.

Depreciation

Depreciation is an accounting method that spreads the cost of a tangible asset over its useful life. This approach recognizes that assets decrease in value over time due to wear and tear or obsolescence. In this scenario, the new machine's depreciation follows the MACRS 5-year recovery period, giving specific percentages each year that affect tax calculations and cash flow.

• Year 1: 20%
• Year 2: 32%
• Year 3: 19%
• Year 4: 12%
• Year 5: 11%
• Year 6: 6% (even though the machine's life is 5 years, this accounts for residual value)

Depreciation reduces taxable income because it is considered an expense. This, in turn, generates tax savings, contributing to the incremental cash flows of the new machine.

Incremental Cash Flows

Incremental cash flows are the additional cash that a company expects from making a specific change in its operations. Here, the change involves replacing an old machine with a new one. Incremental cash flows are critical for analyzing the viability of capital investments. In this exercise:

• The incremental earnings before depreciation changed from $27,000 to $54,000 per year, providing a difference of $27,000.
• These earnings undergo taxation, resulting in after-tax incremental earnings.
• Adding tax savings from depreciation to these after-tax earnings gives the annual incremental cash flow.

These cash flows are then discounted to present value to decide if the new machine is more beneficial than the existing one.

Weighted Average Cost of Capital (WACC)

The Weighted Average Cost of Capital (WACC) is a vital metric in capital budgeting as it serves as the discount rate for evaluating investments' present value. WACC represents the average return that the company must pay to finance its assets, weighing each financing component proportionately. To calculate WACC, companies consider:

• Cost of Equity: the return required by equity investors.
• Cost of Debt: the effective rate that the company pays to lenders.
• The proportions of equity and debt financing in the company's capital structure.

In this exercise, we use a WACC of 12% to discount future cash flows to their present value. It helps determine the profitability of the new machine investment, ensuring the discount reflects the firm's average financing cost.