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Best-Cost Foods is considering replacing all 10 of its old cash registers with new ones. The old registers are fully depreciated and have no disposal value. The new registers cost \(\$ 749,700\) (in total). Because the new registers are more efficient than the old registers, Best-Cost will have annual incremental cash savings from using the new registers in the amount of \(\$ 160,000\) per year. The registers have a seven-year useful life and no terminal disposal value, and are depreciated using the straightline method. Best-Cost requires an \(8 \%\) real rate of return. 1\. Given the preceding information, what is the net present value of the project? Ignore taxes. 2\. Assume the \(\$ 160,000\) cost savings are in current real dollars, and the inflation rate is \(5.5 \% .\) Recalculate the NPV of the project. 3\. Based on your answers to requirements 1 and 2 , should Best-Cost buy the new cash registers? 4\. Now assume that the company's tax rate is \(30 \% .\) Calculate the NPV of the project assuming no inflation. 5\. Again assuming that the company faces a \(30 \%\) tax rate, calculate the NPV of the project under an inflation rate of \(5.5 \%\) 6\. Based on your answers to requirements 4 and 5 , should Best-Cost buy the new cash registers?

Step by step solution

01

Calculate NPV without Inflation and Taxes

To find the NPV, we need to calculate the present value of the annual savings over 7 years, discounted at the required rate of return, and subtract the initial investment cost of the registers. The formula for NPV is: \[ NPV = \sum_{t=1}^{n} \frac{R}{(1 + r)^t} - C_0 \]where:- \( R = 160,000 \) (annual savings),- \( r = 0.08 \) (real rate of return),- \( C_0 = 749,700 \) (initial cost),- \( n = 7 \) (useful life).The present value of the savings is:\[ \text{PV} = 160,000 \times \left( \frac{1-(1+0.08)^{-7}}{0.08} \right) \approx 916,201.84 \]The NPV without inflation is:\[ NPV = 916,201.84 - 749,700 = 166,501.84 \]

02

Adjust for Inflation

With a nominal discount rate including inflation at 5.5%, the nominal rate becomes:\[ i = 0.08 + 0.055 + (0.08 \times 0.055) \approx 0.1384 \] Now, we'll recalculate the NPV using this nominal rate by adjusting the discount factor:\[ \text{PV} = 160,000 \times \left( \frac{1-(1+0.1384)^{-7}}{0.1384} \right) \approx 815,830.17 \]Thus, the NPV with inflation accounted is:\[ NPV = 815,830.17 - 749,700 = 66,130.17 \]

03

Evaluate Decision Without Taxes

Based on the NPVs calculated:- Without inflation, the NPV is \(166,501.84\).- With inflation, the NPV is \(66,130.17\).Since both NPVs are positive, Best-Cost should proceed with buying the new cash registers.

04

Calculate NPV with Taxes (No Inflation)

With a 30% tax rate, annual savings after taxes are \( 160,000 \times (1 - 0.3) = 112,000 \). Depreciation per year is \( 749,700 / 7 = 107,100 \). A tax shield from depreciation applies as \( 107,100 \times 0.3 = 32,130 \).Total yearly after-tax cash flow becomes \( 112,000 + 32,130 = 144,130 \). Recalculate NPV without inflation effects:\[ \text{PV after taxes} = 144,130 \times \left( \frac{1-(1+0.08)^{-7}}{0.08} \right) \approx 825,177.23 \]Thus, NPV becomes:\[ NPV = 825,177.23 - 749,700 = 75,477.23 \]

05

Adjust NPV for Taxes and Inflation

Now, with a tax rate and inflation, adjust the nominal discount rate as previously:\( i = 0.1384 \). Using the after-tax cash flow:\( 144,130 \) total yearly.Calculate NPV with taxes and inflation:\[ \text{PV} = 144,130 \times \left( \frac{1-(1+0.1384)^{-7}}{0.1384} \right) \approx 733,792.13 \]Thus, NPV becomes:\[ NPV = 733,792.13 - 749,700 = -15,907.87 \]

06

Evaluate Decision With Taxes

Based on the NPVs with taxes:- Without inflation, NPV is \(75,477.23\).- With inflation, NPV is \(-15,907.87\).With inflation, the NPV is negative, so Best-Cost should not buy the new registers if both taxes and inflation are considered.

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Key Concepts

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

Cost Accounting

Cost accounting is an essential aspect of evaluating business decisions like acquiring new equipment. It involves analyzing the costs associated with these decisions to help in budgeting and maximizing profits.
In the context of Best-Cost Foods' project, cost accounting helps determine the viability of replacing old cash registers by assessing both the initial investment of $749,700 and the anticipated cost savings.

• It provides critical insights into whether the capital outlay will lead to a net gain over time.
• By evaluating all costs, financial decision-makers can assess if future savings outweigh the initial expenses.
• This approach ensures that resources are allocated effectively and that investments lead to desired financial returns.

In summary, cost accounting offers a structured method for evaluating economic decisions and plays a crucial role in guiding businesses like Best-Cost Foods towards profitable strategic choices.

Depreciation

Depreciation is the process of allocating the cost of tangible assets over their useful lives. This allows businesses to spread the expense of an asset over the period it helps generate income. For Best-Cost Foods, each new cash register's cost is spread over 7 years.

• Using the straight-line method, the depreciation expense is constant for each year, calculated as the asset cost divided by its useful life.
• This method simplifies the recording of expenses and helps in planning and controlling cash flows.
• The depreciated amount is crucial in calculating the tax shield, which is the reduction in taxable income resulting from depreciation.

Understanding depreciation helps assess the actual burden of the investment over time, reflecting its impact on financial statements and cash flows. This makes it a vital consideration for evaluating the purchase of new equipment.

Inflation Rate

The inflation rate represents the rate at which prices for goods and services rise, eroding purchasing power over time. It is crucial in financial analysis as it affects both cost and revenue projections. In Best-Cost Foods' case, an inflation rate of 5.5% impacts the future value of cash savings.

• Adjusting for inflation involves using a nominal discount rate, which supplements real returns by accounting for expected inflation.
• This adjusted rate ensures future cash flows are accurately measured in terms of current purchasing power.
• Ignoring inflation could lead to overestimating the profitability of projects, as it affects both the nominal returns and the costs associated with investment.

When calculating NPV, considering inflation is essential to reflect the real economic value of the project over time. This ultimately impacts the decision-making process for investments.

Cash Flow Analysis

Cash flow analysis involves examining the inflows and outflows of cash to evaluate an investment's financial health. For Best-Cost Foods, analyzing cash flow provides insights into the benefits of replacing the old registers with new ones.

• The focus is on future cash savings generated by the new equipment as opposed to past transactions.
• This analysis calculates the net present value (NPV), which evaluates the profitability by discounting future cash flows back to their present value.
• Positive NPV indicates that the expected earnings (adjusted for present value) surpass the initial costs, justifying such an investment.

A thorough cash flow analysis offers quantitative data about the profitability and sustainability of an investment decision. It helps companies like Best-Cost Foods make informed decisions based on a comprehensive understanding of financial implications.