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Chapter 6: Problem 7

Project Evaluation Dog Up! Franks is looking at a new sausage system with an installed cost of \(\$ 420,000\). This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the sausage system can be scrapped for \(\$ 60,000\). The sausage system will save the firm \(\$ 135,000\) per year in pretax operating costs, and the system requires an initial investment in net working capital of \(\$ 28,000\). If the tax rate is 34 percent and the discount rate is 10 percent, what is the NPV of this project?

Short Answer

Expert verified
The net present value (NPV) of the project is $68,524, indicating that this investment is expected to generate a positive return, and thus it would be a worthwhile project for Dog Up! Franks to undertake.

Step by step solution

01

Calculate Annual Depreciation Expense

To calculate the annual depreciation expense, we can use the straight-line depreciation method, which is the initial cost minus the salvage value, divided by the project's life: Annual Depreciation Expense = (Initial Cost - Salvage Value) / Project Life Annual Depreciation Expense = (\(420,000 - 60,000\)) / 5 = \(360,000 / 5 = 72,000\)
02

Calculate Annual After-Tax Operating Cash Flows

To calculate the annual after-tax operating cash flows, we must first calculate the tax savings from depreciation. Then, we subtract the taxes from the pretax operating cost savings, and finally, we add the tax savings from depreciation to the after-tax operating cost savings: Tax Savings from Depreciation = Annual Depreciation Expense 脳 Tax Rate Tax Savings from Depreciation = \(72,000 脳 0.34 = 24,480\) After-Tax Operating Cost Savings = Pretax Operating Cost Savings 脳 (1 - Tax Rate) After-Tax Operating Cost Savings = \(135,000 脳 (1 - 0.34) = 135,000 脳 0.66 = 89,100\) Annual After-Tax Operating Cash Flows = After-Tax Operating Cost Savings + Tax Savings from Depreciation Annual After-Tax Operating Cash Flows = \(89,100 + 24,480 = 113,580\)
03

Calculate Net Working Capital Recovery

The initial net working capital investment is recovered at the end of the project's life. To find the after-tax cash flow from the net working capital recovery, we multiply the initial net working capital investment by (1 - Tax Rate): After-Tax NWC Recovery = Initial NWC 脳 (1 - Tax Rate) After-Tax NWC Recovery = \(28,000 脳 (1 - 0.34) = 28,000 脳 0.66 = 18,480\)
04

Calculate Present Value of Cash Flows

To find the present value of cash flows, we will use the formula: Present Value = CF 脳 (1 - (1 + r)^-n) / r Where CF is the annual after-tax operating cash flows, r is the discount rate, and n is the number of years. Present Value = \(113,580 脳 (1 - (1 + 0.1)^{-5}) / 0.1 = 113,580 脳 3.7908 = 430,444\)
05

Calculate Net Present Value

To calculate NPV, we need to consider the initial cost, present value of cash flows, after-tax NWC recovery, and after-tax salvage value. The after-tax salvage value can be found by multiplying the salvage value by (1 - Tax Rate): After-Tax Salvage Value = Salvage Value 脳 (1 - Tax Rate) After-Tax Salvage Value = \(60,000 脳 (1 - 0.34) = 60,000 脳 0.66 = 39,600\) NPV = Present Value - Initial Cost + After-Tax NWC Recovery + After-Tax Salvage Value NPV = \(430,444 - 420,000 + 18,480 + 39,600 = 68,524\) The net present value of this project is $68,524.

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Key Concepts

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

Depreciation
Depreciation is a concept used in accounting to allocate the cost of a tangible asset over its useful life. For Dog Up! Franks, the purchased sausage system has an installed cost of \(\\(420,000\) and a salvage value of \(\\)60,000\) after five years. Using straight-line depreciation, which is one of the simplest methods, allows for consistent annual depreciation charges. This method calculates depreciation by evenly distributing the asset's cost over its useful life.

The formula for straight-line depreciation is:
  • Annual Depreciation Expense = \((\text{Initial Cost} - \text{Salvage Value}) / \text{Project Life}\)
In this case, the annual depreciation expense is \(\$72,000\). Accurately accounting for depreciation is crucial, as it affects the financial statements and the taxable income, leading to tax savings each year.
Discount Rate
The discount rate is essentially the interest rate used to determine the present value of future cash flows. It reflects the opportunity cost of capital, meaning the rate of return that could be earned on an investment in the financial markets with similar risk. In evaluating the sausage system project, Dog Up! Franks uses a discount rate of 10% to assess whether the future cash flows of the project are worth investing in today.

Understanding the discount rate is critical because:
  • It accounts for the time value of money, indicating that a dollar today is worth more than a dollar in the future due to its potential earning capacity.
  • It helps in assessing the risk associated with an investment, as higher-risk projects typically require a higher discount rate.
When calculating the net present value (NPV), we use the discount rate to convert future cash flows into a present value. This helps in determining if a project's returns exceed its costs over time.
Operating Cash Flows
Operating cash flows are the cash that a company generates from its regular business operations. For this project, the sausage system is expected to save the company \(\\(135,000\) per year in pretax operating costs. To calculate the after-tax operating cash flows, we adjust for tax implications and include depreciation tax shields.

Here are the steps:
  • Calculate the tax savings from depreciation by multiplying the annual depreciation expense by the tax rate.
  • Determine the after-tax operating cost savings by adjusting the pretax savings for the tax rate.
  • The annual after-tax operating cash flows is the sum of after-tax operating cost savings and tax savings from depreciation.
In this case, Dog Up! Franks would achieve \(\\)113,580\) annually from these operations, highlighting the importance of analyzing both operational savings and tax implications.
Tax Rate
The tax rate directly impacts a project's cash flows and its net present value. For Dog Up! Franks, a tax rate of 34% is applied to calculate the after-tax operating cash flows and salvage values. A higher tax rate increases the amount of savings from depreciation because taxes are deducted from the profits.

Here鈥檚 how the tax rate influences finances:
  • It affects the after-tax cash flows since operational savings must be adjusted for taxes.
  • The tax rate is used to compute the tax savings derived from depreciation, thus reducing the taxable income.
  • Additionally, it affects the final salvage value after taxes, ensuring a realistic net estimate of recoverable assets.
Understanding the tax rate is key in financial planning, as it helps in evaluating tax liabilities and potential savings throughout the project's lifespan.

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Most popular questions from this chapter

Calculating NPV Howell Petroleum is considering a new project that complements its existing business. The machine required for the project costs \(\$ 1.8\) million. The marketing department predicts that sales related to the project will be \(\$ 1.1\) million per year for the next four years, after which the market will cease to exist. The machine will be depreciated down to zero over its fouryear economic life using the straight-line method. Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales. Howell also needs to add net working capital of \(\$ 150,000\) immediately. The additional net working capital will be recovered in full at the end of the project's life. The corporate tax rate is 35 percent. The required rate of return for Howell is 16 percent. Should Howell proceed with the project?

Calculating Project NPV You have been hired as a consultant for Pristine Urban-Tech Zither, Inc. (PUTZ), manufacturers of fine zithers. The market for zithers is growing quickly. The company bought some land three years ago for \(\$ 1\) million in anticipation of using it as a toxic waste dump site but has recently hired another company to handle all toxic materials. Based on a recent appraisal, the company believes it could sell the land for \(\$ 800,000\) on an aftertax basis. In four years, the land could be sold for \(\$ 900,000\) after taxes. The company also hired a marketing firm to analyze the zither market, at a cost of \(\$ 125,000\). An excerpt of the marketing report is as follows: The zither industry will have a rapid expansion in the next four years. With the brand name recognition that PUTZ brings to bear, we feel that the company will be able to sell 3,100 , \(3,800,3,600\), and 2,500 units each year for the next four years, respectively. Again, capitalizing on the name recognition of PUTZ, we feel that a premium price of \(\$ 780\) can be charged for each zither. Because zithers appear to be a fad, we feel at the end of the fouryear period, sales should be discontinued. PUTZ feels that fixed costs for the project will be \(\$ 425,000\) per year, and variable costs are 15 percent of sales. The equipment necessary for production will cost \(\$ 4.2\) million and will be depreciated according to a three-year MACRS schedule. At the end of the project, the equipment can be scrapped for \(\$ 400,000\). Net working capital of \(\$ 120,000\) will be required immediately. PUTZ has a 38 percent tax rate, and the required return on the project is 13 percent. What is the NPV of the project? Assume the company has other profitable projects.

Calculating Nominal Cash Flow Etonic Inc. is considering an investment of \(\mathbf{\$ 0 5 , 0 0 0}\) in an asset with an economic life of five years. The firm estimates that the nominal annual cash revenues and expenses at the end of the first year will be \(\$ 230,000\) and \(\$ 60,000\), respectively. Both revenues and expenses will grow thereafter at the annual inflation rate of 3 percent. Etonic will use the straight-line method to depreciate its asset to zero over five years. The salvage value of the asset is estimated to be \(\$ 40,000\) in nominal terms at that time. The one-time net working capital investment of \(\$ 10,000\) is required immediately and will be recovered at the end of the project. All corporate cash flows are subject to a 34 percent tax rate. What is the project's total nominal cash flow from assets for each year?

Inflation and Company Value Sparkling Water, Inc., expects to sell 2.1 million bottles of drinking water each year in perpetuity. This year each bottle will sell for \(\$ 1.25\) in real terms and will cost \(\$ .75\) in real terms. Sales income and costs occur at year-end. Revenues will rise at a real rate of 6 percent annually, while real costs will rise at a real rate of 5 percent annually. The real discount rate is 10 percent. The corporate tax rate is 34 percent. What is Sparkling worth today?

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.)
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