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Project Analysis and Inflation Sanders Enterprises, Inc., has been considering the purchase of a new manufacturing facility for \(\$ 150,000\). The facility is to be fully depreciated on a straightline basis over seven years. It is expected to have no resale value after the seven years. Operating revenues from the facility are expected to be \(\$ 70,000\), in nominal terms, at the end of the first year. The revenues are expected to increase at the inflation rate of 5 percent. Production costs at the end of the first year will be \(\$ 20,000\), in nominal terms, and they are expected to increase at 6 percent per year. The real discount rate is 8 percent. The corporate tax rate is 34 percent. Sanders has other ongoing profitable operations. Should the company accept the project?

Short Answer

Expert verified
The Net Present Value (NPV) of the project is calculated by first determining the Real Operating Cash Flow, which is adjusted for inflation, and then calculating the tax liability and net cash flows after tax. After calculating the present value of net cash flows using the real discount rate, the NPV is calculated by summing these present values and subtracting the initial investment. If the NPV is positive, Sanders Enterprises should accept the project.

Step by step solution

01

Calculating Operating Cash Flows

To calculate the operating cash flows, we first need to find the annual revenues and costs by adjusting for inflation. End of year, t = 1 to 7. Revenues: \( R_t = R_1 (1 + i_t)^{t-1} \) Costs: \( C_t = C_1 (1 + g_t)^{t-1} \) Where: - \(R_1 = \$ 70,000\) (initial revenues at the end of the first year) - \(i_t = 0.05\) (inflation rate) - \(C_1 = \$ 20,000\) (initial costs at the end of the first year) - \(g_t = 0.06\) (annual cost increase rate) To calculate operating cash flows, we need to subtract the annual costs from the annual revenues: \( OCF_t = R_t - C_t \)
02

Adjusting Operating Cash Flows for Inflation

Since the cash flows are given in nominal terms, we need to adjust them for inflation in order to calculate the real operating cash flows. Real Operating Cash Flow: \( ROCF_t = \frac{OCF_t}{(1+i_t)^{t-1}} \)
03

Calculating Annual Tax Liability

To calculate the tax liability, we need to first find the taxable income by subtracting the depreciation from the real operating cash flows. Depreciation: \( D_t = \frac{\$ 150,000}{7 \text{ years}} = \$ 21,428.57 \) Taxable Income: \( TI_t = ROCF_t - D_t \) Tax Liability: \( Tax_t = TI_t \times TaxRate \) Where the tax rate is 34%.
04

Determining Net Cash Flows After Tax

To determine the net cash flows after tax, we subtract the tax liability from the real operating cash flows and add back the depreciation. Net Cash Flows After Tax: \( NCF_t = ROCF_t - Tax_t + D_t \)
05

Calculating the Present Value of Net Cash Flows

To calculate the present value of the net cash flows, we will use the real discount rate. Present Value of Net Cash Flows: \( PV_t = \frac{NCF_t}{(1 + d)^t} \) Where the real discount rate, d = 8%.
06

Calculating the Net Present Value of the Project

Finally, we will calculate the net present value of the project by summing the present values of net cash flows and subtracting the initial investment. Net Present Value: \( NPV = -\$150,000 + \sum_{t=1}^{7} PV_t \) If NPV > 0, then the company should accept the project. By performing these calculations, we can determine whether Sanders Enterprises should accept this project based on the calculated net present value.

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Key Concepts

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

Operating Cash Flow Calculation
When calculating the operating cash flows for a project like Sanders Enterprises' manufacturing facility, we need to differentiate between revenues and costs and consider their growth over time. For instance, in this scenario, we account for the fact that while revenues start at \(70,000, they are expected to grow at the rate of inflation (5% in this case). Conversely, costs start at \)20,000 and grow at a rate of 6% per year. This gives us not only the initial cash flows but also their progression over the lifespan of the project.

The operating cash flow (OCF) for each year, therefore, is calculated by subtracting the projected costs from the revenues for that year:
\( OCF_t = R_t - C_t \)
This calculation provides us with a picture of what the facility will contribute to the company's cash flow before accounting for taxes and depreciation.
Real vs Nominal Cash Flows
Distinguishing between real and nominal cash flows is crucial in project analysis, particularly when dealing with inflation. Nominal cash flows represent the amount of money that will actually be received or paid out, without adjusting for the changing value of money over time. However, to evaluate the true earning power of a project, we need to look at real cash flows, which do take into account the impact of inflation.

To convert nominal operating cash flows to real operating cash flows, we adjust them by the inflation rate:
\( ROCF_t = \frac{OCF_t}{(1+i_t)^{t-1}} \)
The real cash flows allow us to see the facility's profitability in terms of today's dollars, which is necessary when making an informed decision on whether to proceed with the investment.
Net Present Value
The net present value (NPV) is a fundamental concept in capital budgeting and project analysis. It represents the total value of a series of cash flows over time, discounted back to their present value using a specific rate, known as the discount rate. In the case of Sanders Enterprises, the real discount rate is 8%, which reflects the company's cost of capital adjusted for inflation.

\( NPV = -Initial Investment + \sum_{t=1}^{7} \frac{NCF_t}{(1 + d)^t} \)
Here, if the NPV is greater than zero, it suggests that the project's returns exceed the cost of capital, implying that the project should be accepted. The NPV is a crucial indicator in decision-making as it directly considers the time value of money.
Capital Budgeting
Capital budgeting is the process of evaluating investment options and making decisions about long-term investments. It encompasses a variety of financial techniques, including the calculation of NPV, to determine which investments could yield the most favorable financial returns. Companies like Sanders Enterprises must consider several factors in capital budgeting, such as initial costs, projected revenue growth, cost escalation, tax implications, and their chosen discount rate.

Each of these components plays a part in the capital budgeting process, and together they align with the strategic goals of the company, ensuring that any investment made will be in the best interest of long-term growth and profitability.
Tax Depreciation Effects
In project analysis, considering the tax implications of depreciation is vital. Depreciation affects taxable income, which in turn affects tax liability. For the new facility being considered by Sanders Enterprises, the annual depreciation expense is calculated on a straight-line basis across seven years, resulting in an annual flat deduction from the real operating cash flows.

This annual deduction reduces taxable income, which means less tax is paid and higher net cash flows after tax. As we determine the net cash flows, we add back the depreciation since it is a non-cash expense:
\( NCF_t = ROCF_t - Tax_t + D_t \)
This highlights how tax depreciation not only serves as a tax shield but also critically impacts the net cash flows, significantly influencing the NPV calculation and the project's viability.

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Most popular questions from this chapter

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?

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?

Calculating Required Savings A proposed cost-saving device has an installed cost of \(\mathbf{\$ 5 4 0 , 0 0 0}\). The device will be used in a five-year project but is classified as three-year MACRS property for tax purposes. The required initial net working capital investment is \(\$ 45,000\), the marginal tax rate is 35 percent, and the project discount rate is 12 percent. The device has an estimated year 5 salvage value of \(\$ 50,000\). What level of pretax cost savings do we require for this project to be profitable?

EAC and Inflation Office Automation, Inc., must choose between two copiers, the XX40 or the RH45. The XX40 costs \(\$ 1,500\) and will last for three years. The copier will require a real aftertax cost of \(\$ 120\) per year after all relevant expenses. The RH45 costs \(\$ 2,300\) and will last five years. The real aftertax cost for the RH45 will be \(\$ 150\) per year. All cash flows occur at the end of the year. The inflation rate is expected to be 5 percent per year, and the nominal discount rate is 14 percent. Which copier should the company choose?

Calculating a Bid Price Another utilization of cash flow analysis is setting the bid price on a project. To calculate the bid price, we set the project NPV equal to zero and find the required price. Thus the bid price represents a financial break-even level for the project. Guthrie Enterprises needs someone to supply it with 130,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you've decided to bid on the contract. It will cost you \(\$ 830,000\) to install the equipment necessary to start production; you'll depreciate this cost straight-line to zero over the project's life. You estimate that in five years this equipment can be salvaged for \(\$ 60,000\). Your fixed production costs will be \(\$ 210,000\) per year, and your variable production costs should be \(\$ 8.50\) per carton. You also need an initial investment in net working capital of \(\$ 75,000\). If your tax rate is 35 percent and you require a 14 percent return on your investment, what bid price should you submit?

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