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Replacement Decisions Suppose we are thinking about replacing an old computer with a new one. The old one cost us \(\$ 650,000\); the new one will cost \(\$ 780,000\). The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about \(\$ 140,000\) after five years. The old computer is being depreciated at a rate of \(\$ 130,000\) per year. It will be completely written off in three years. If we don't replace it now, we will have to replace it in two years. We can sell it now for \(\$ 230,000\); in two years it will probably be worth \(\$ 90,000\). The new machine will save us \(\$ 125,000\) per year in operating costs. The tax rate is 38 percent, and the discount rate is 14 percent. 1\. Suppose we recognize that if we don't replace the computer now, we will be replacing it in two years. Should we replace now or should we wait? (Hint: What we effectively have here is a decision either to "invest" in the old computer-by not selling it-or to invest in the new one. Notice that the two investments have unequal lives.) 2\. Suppose we consider only whether we should replace the old computer now without worrying about what's going to happen in two years. What are the relevant cash flows? Should we replace it or not? (Hint: Consider the net change in the firm's aftertax cash flows if we do the replacement.)

Step by step solution

01

Calculate annual depreciation of the new machine

The new machine will be depreciated straight-line to zero over its five-year life. So, annual depreciation of the new machine will be: \(Depreciation = \frac{780000 - 140000}{5} = \$128,000\)

02

Calculate after tax cash flows for both old and new computers

We will calculate the cash flows for both the old and new computers for the first two years. After tax cash flow = (Cost Savings + Depreciation) x (1 - tax rate) + tax rate x Depreciation Old Computer cash flow: Year 1: \((0 + 130000) x (1 - 0.38) + 0.38 x 130000 = \$80,600\) Year 2: \((0 + 130000) x (1 - 0.38) + 0.38 x 130000 = \$80,600\) New Computer cash flow: Year 1: \((125000 + 128000) x (1 - 0.38) + 0.38 x 128000 = \$156,740\) Year 2: \((125000 + 128000) x (1 - 0.38) + 0.38 x 128000 = \$156,740\)

03

Calculate the net present value of the differences in cash flows

Now we will calculate the net present value of the difference in cash flows over the first two years. Difference in cash flows: Year 1: \(\$156,740 - \$80,600 = \$76,140\) Year 2: \(\$156,740 - \$80,600 = \$76,140\) Net Present Value (\(NPV = \frac{CF_1}{(1+r)^1} + \frac{CF_2}{(1+r)^2}\)): \(NPV = \frac{76140}{(1+0.14)^1} + \frac{76140}{(1+0.14)^2} \approx \$56,731 + \$49,608.77 = \$106,339.77\)

04

Compare the NPV with the initial investment and decide to replace or not

Now we will compare the NPV of the difference in cash flows to the difference in initial investments between the old computer and new one. Cost of keeping old computer: \(\$650,000 - \$230,000 = \$420,000\) Cost of buying new computer: \(\$780,000\) Difference in investments: \(\$780,000 - \$420,000 = \$360,000\) Since the NPV of the difference in cash flows (\$106,339.77) is less than the difference in investments (\$360,000), we should not replace the computer now. #Part 2: Considering only present situation and not worrying about the future#

05

Calculate the net change in after-tax cash flows

We already have calculated after-tax cash flows for old and new computers in the previous part. Let's calculate the net change in after-tax cash flows for the first year: Net change in after-tax cash flows = New computer cash flow (Year 1) - Old computer cash flow (Year 1) \(\$156,740 - \$80,600 = \$76,140\)

06

Check if net change in after-tax cash flows is greater than the difference in investments

If the net change in after-tax cash flows is greater than the difference in investments, we should replace the computer. Difference in investments: \(\$780,000 - \$420,000 = \$360,000\) Since the net change in after-tax cash flows (\$76,140) is less than the difference in investments (\$360,000), we should not replace the computer now even considering only the present situation.

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Key Concepts

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

Net Present Value

The net present value (NPV) is a core concept in capital budgeting. It evaluates the profitability of an investment by calculating the present values of expected future cash flows. To determine the NPV, subtract the initial investment from the sum of discounted cash flows. The formula used is: \[ NPV = \sum \frac{CF_t}{(1 + r)^t} - Initial\, Investment \] where \( CF_t \) refers to the cash flows in period \( t \), and \( r \) is the discount rate.
In the context of replacement decisions, calculating NPV helps us understand whether replacing equipment now will yield a higher return than sticking with the old one. A positive NPV indicates a profitable investment.
In our exercise, net cash flows from both computers were compared, and their NPVs helped guide the replacement decision by pinpointing whether the new machine's added value justifies its cost.

Replacement Decision

A replacement decision involves determining whether to substitute an existing asset with a new one. This type of decision can be complex due to differing asset lives, costs, and benefits. Key factors to consider include:

• The cost of acquiring a new asset versus maintaining the old one.
• The economic benefits provided by each option, like cost savings from the new machine.
• The residual value of old and new assets, as outlined by potential resale or scrap value.

In our case, the old computer still had some residual value and ongoing depreciation benefits. However, the potential cost savings from the new machine were taken into account to reach a sensible decision based on the analysis.

Cash Flow Analysis

Cash flow analysis breaks down the cash inflows and outflows associated with investment decisions, focusing on understanding the net cash impact of potential replacement. A few steps are involved:

• Calculate expected cash inflows and outflows for both the new and old assets.
• Account for differences in depreciation, operating costs, and tax impacts.
• Determine net cash flow differences to assess financial impact.

This analysis is essential because it puts all costs and benefits into present terms, allowing for more informed decision-making. In the exercise, the old and new computers' cash flows were calculated using the formula for after-tax cash flow, showing the benefits of replacing over retaining the old computer.

Depreciation

Depreciation refers to the systematic allocation of an asset's cost over its useful life. It reduces taxable income, providing a tax shield that effectively increases cash flow. There are various methods to calculate depreciation, but the straight-line method is commonly used for simplicity.

In our exercise, the new computer was depreciated using straight-line depreciation. This method involves equal annual depreciation expenses over the asset's five-year life span. Calculating these expenses helps in understanding the ongoing reductions in taxable income.

• It influences the cash flow, thus playing a major role in financial evaluations like our replacement exercise.
• The old computer's depreciation was continued from its existing schedule, affecting the decision process based on its comparatively larger rate than the new asset.

Investment Appraisal

Investment appraisal assesses whether it's worth investing in a new asset or keeping the existing one. It relies heavily on concepts like NPV, cash flow analysis, and the comparison of costs and benefits. The process includes:

• Evaluating the economic life and ongoing costs of old versus new assets.
• Factoring in savings, tax implications, and opportunity costs from different depreciation and residual value estimates.
• Analyzing quantitative data, but also considering qualitative aspects like strategic fit and operational benefits.

In our scenario, investment appraisal helped determine that despite potential savings from the new machine, the assessed net present value and cash flow differences were insufficient. Thus, the new investment wasn't justified on purely financial grounds, a decision supported by thorough appraisal of the available information.