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Chapter 6: Problem 14

Comparing Mutually Exclusive Projects Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine \(A\) costs \(\$ \mathbf{\$ 2 , 4 0 0 , 0 0 0}\) and will last for six years. Variable costs are 35 percent of sales, and fixed costs are \(\$ 180,000\) per year. Machine B costs \(\mathbf{\$ 5 , 4 0 0 , 0 0 0}\) and will last for nine years. Variable costs for this machine are \(\mathbf{3 0}\) percent and fixed costs are \(\$ 110,000\) per year. The sales for each machine will be \(\$ 10.5\) million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. If the company plans to replace the machine when it wears out on a perpetual basis, which machine should you choose?

Short Answer

Expert verified
The company should choose Machine A, as it has a higher Net Present Value (NPV) of \(25,154,331\), compared to Machine B's NPV of \(18,367,856\).

Step by step solution

01

Calculate the Cash Flows for Machine A

1. Calculate the annual sales: \(10.5\) million. 2. Calculate the annual variable cost: \(35\%\) of sales. \(Variable\ cost\ = 0.35 \times 10,500,000 = 3,675,000\) 3. Calculate the annual fixed cost: \(180,000\). 4. Calculate the annual depreciation: \(Depreciation = \frac{Initial\ Cost}{Years} = \frac{2,400,000}{6} = 400,000\) 5. Calculate the annual operating income before tax: \(Operating\ Income = Sales - Variable\ Costs - Fixed\ Costs - Depreciation\) \(Operating\ Income = 10,500,000 - 3,675,000 - 180,000 - 400,000 = 6,245,000\) 6. Calculate the annual taxes: \(35\%\) of operating income. \(Taxes = 0.35 \times 6,245,000 = 2,185,750\) 7. Calculate the annual operating income after tax: \(Operating\ Income\ = 6,245,000 - 2,185,750 = 4,059,250\) 8. Calculate the cash flow for Machine A, considering the depreciation: \(Cash\ Flow = Operating\ Income + Depreciation\) \(Cash\ Flow = 4,059,250 + 400,000 = 4,459,250\)
02

Calculate the Present Value of Cash Flows for Machine A

1. Calculate the perpetual annuity for Machine A: \(Perpetual\ Annuity = \frac{Cash\ Flow}{Required\ Return}\) \(Perpetual\ Annuity = \frac{4,459,250}{0.1} = 44,592,500\) 2. Calculate the Present Value (PV) of the perpetual annuity for 6 years: \(PV = \frac{Perpetual\ Annuity}{(1 + Required\ Return)^6}\) \(PV = \frac{44,592,500}{(1 + 0.1)^6} = 27,554,331\)
03

Calculate the Cash Flows for Machine B

1. Calculate the annual variable cost: \(30\%\) of sales. \(Variable\ cost\ = 0.30 \times 10,500,000 = 3,150,000\) 2. Calculate the annual fixed cost: \(110,000\). 3. Calculate the annual depreciation: \(Depreciation = \frac{Initial\ Cost}{Years} = \frac{5,400,000}{9} = 600,000\) 4. Calculate the annual operating income before tax: \(Operating\ Income = 10,500,000 - 3,150,000 - 110,000 - 600,000 = 6,640,000\) 5. Calculate the annual taxes: \(35\%\) of operating income. \(Taxes = 0.35 \times 6,640,000 = 2,324,000\) 6. Calculate the annual operating income after tax: \(Operating\ Income\ = 6,640,000 - 2,324,000 = 4,316,000\) 7. Calculate the cash flow for Machine B, considering the depreciation: \(Cash\ Flow = Operating\ Income + Depreciation\) \(Cash\ Flow = 4,316,000 + 600,000 = 4,916,000\)
04

Calculate the Present Value of Cash Flows for Machine B

1. Calculate the perpetual annuity for Machine B: \(Perpetual\ Annuity = \frac{Cash\ Flow}{Required\ Return}\) \(Perpetual\ Annuity = \frac{4,916,000}{0.1} = 49,160,000\) 2. Calculate the Present Value (PV) of the perpetual annuity for 9 years: \(PV = \frac{Perpetual\ Annuity}{(1 + Required\ Return)^9}\) \(PV = \frac{49,160,000}{(1 + 0.1)^9} = 23,767,856\)
05

Calculate Net Present Value (NPV) for Machine A and Machine B

1. Calculate the NPV for Machine A: \(NPV_A = PV_A - Initial\ Cost_A\) \(NPV_A = 27,554,331 - 2,400,000 = 25,154,331\) 2. Calculate the NPV for Machine B: \(NPV_B = PV_B - Initial\ Cost_B\) \(NPV_B = 23,767,856 - 5,400,000 = 18,367,856\)
06

Determine which machine to choose

Compare the NPV of Machine A and Machine B: Machine A: NPV = \(25,154,331\) Machine B: NPV = \(18,367,856\) Since Machine A has a higher NPV, the company should choose Machine A.

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Key Concepts

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

Capital Budgeting
Capital budgeting is a crucial financial planning tool used by companies to evaluate the long-term profitability and risk of potential investment projects. It involves the analysis of future cash flows, investment costs, and the determination of the value such projects bring to the company.

When a business is faced with investment options鈥攍ike Vandalay Industries choosing between two machines鈥攊t uses capital budgeting techniques to decide which project will yield the most return over time. A common method is calculating the net present value (NPV) of each option, which discounts all cash flows back to their present value before comparing them. This allows the company to see how much value each project will add after considering the cost of the initial investment and the company's required rate of return.
Cash Flow Analysis
Cash flow analysis is the process of assessing the inflows and outflows of cash within a business. It's an integral part of capital budgeting as it provides the raw data required for calculating investment project values. Businesses must account for all cash transactions, including sales revenue, operating costs, tax payments, and investment expenditures.

In our example, Vandalay Industries must evaluate the variable costs, fixed costs, and depreciation associated with each machine to accurately calculate the annual cash flows. Understanding the cash flow is essential because it reveals the actual amount of cash generated by the investment, which can then be used to pay back the initial capital and ultimately contribute to the company's wealth.
Present Value
The concept of present value (PV) is at the heart of time value of money principles. It fundamentally implies that money available now is worth more than the same amount in the future because of its earning potential.

For instance, when we examine the perpetual annuity calculations for Vandalay Industries' machines, we apply the present value formula to determine what future cash flows are worth today. This is crucial because it allows the company to account for the erosion of value over time due to factors like inflation and opportunity cost. Present value calculations enable businesses to compare the profitability of projects with different time horizons and cash flow profiles on an equal basis.
Perpetual Annuity
A perpetual annuity refers to a series of equal cash flows that continue indefinitely. In the context of capital budgeting, companies sometimes assume that an investment project will last forever for simplification purposes.

The calculation of a perpetual annuity for Vandalay Industries' machines assumes that each machine will be replaced perpetually, providing a constant stream of cash flows. To determine the current worth of these endless payments, the company divides the annual cash flow by the required return. However, since the machine doesn't last forever, the present value is calculated only up to the end of its useful life. The ability to estimate these values is indispensable in comparing projects, as it quantifies expectations about profitability over an infinite period, adjusted for the time value of money.

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Most popular questions from this chapter

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.

Cash Flow Valuation Phillips Industries runs a small manufacturing operation. For this fiscal year, it expects real net cash flows of \(\$ 155,000\). Phillips is an ongoing operation, but it expects competitive pressures to erode its real net cash flows at 5 percent per year in perpetuity. The appropriate real discount rate for Phillips is 11 percent. All net cash flows are received at year-end. What is the present value of the net cash flows from Phillips's operations?

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?

Calculating Project NPV Raphael Restaurant is considering the purchase of a \(\$ \mathbf{1 2 , 0 0 0}\) souffl茅 maker. The souffl茅 maker has an economic life of five years and will be fully depreciated by the straight-line method. The machine will produce 1,900 souffl茅s per year, with each costing \(\$ 2.20\) to make and priced at \$5. Assume that the discount rate is 14 percent and the tax rate is 34 percent. Should Raphael make the purchase?
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