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Chapter 6: Problem 1

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?

Short Answer

Expert verified
The Net Present Value (NPV) of the souffl茅 maker purchase for Raphael Restaurant is calculated to be $3,091.37, using a 14% discount rate and a 34% tax rate. As the NPV is positive, it is a good investment opportunity, so Raphael Restaurant should proceed with the purchase.

Step by step solution

01

Calculate the annual operating cash flow (OCF)

First, we need to find the annual operating cash flow (OCF). This can be calculated by multiplying the total number of souffles produced per year by the profit per souffle, which is the selling price minus the cost to make. Then, we will deduct the taxes from the annual operating cash flow before depreciation. Number of souffles per year = 1,900 Selling price per souffle = $5 Cost to make per souffle = $2.20 \[ \text{Profit per souffle} = \$5 - \$2.20 = \$2.80 \] \[ \text{Annual OCF before depreciation} = 1,900 \times \$2.80 = \$5,320 \] Now, calculate the taxes on the annual OCF before depreciation: \[ \text{Taxes} = \$5,320 \times 34\% = \$1,808.80 \] Finally, calculate the annual operating cash flow (OCF) after taxes: \[ \text{Annual OCF after taxes} = \$5,320 - \$1,808.80 = \$3,511.20 \]
02

Calculate the annual depreciation and the after-tax salvage value

Next, we need to calculate the annual depreciation using the straight-line method: \[ \text{Annual depreciation} = \frac{\text{Initial cost}}{\text{Economic life}} = \frac{\$12,000}{5\text{ years}} = \$2,400\text{ per year} \] Now, find the after-tax salvage value: \[ \text{After-tax salvage value} = \text{Initial cost} - (\text{Annual depreciation} \times \text{Economic life}) \times (1 - \text{Tax Rate}) \] \[ = \$12,000 - (\$2,400 \times 5) \times (1 - 34\% ) = \$2,280 \]
03

Calculate the NPV of the investment opportunity

Finally, we will calculate the NPV using the 14% discount rate: \[ \text{NPV} = \sum_{t=1}^5 \frac{\text{OCF}_t - \text{Depreciation}_t}{(1 + \text{Discount Rate})^t} + \frac{\text{After-tax Salvage Value}}{(1 + \text{Discount Rate})^5} \] We already know the OCF, Depreciation, After-tax Salvage Value, and Discount Rate. We can plug those values into the formula: \[ \text{NPV} = \sum_{t=1}^5 \frac{\$3,511.20 - \$2,400}{(1 + 14\%)^t} + \frac{\$2,280}{(1 + 14\%)^5} = \$3,091.37 \] Since the NPV is positive (\(3,091.37 > 0\)), it is a good investment for Raphael Restaurant, and they should proceed with the purchase of the souffl茅 maker.

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Key Concepts

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

Operating Cash Flow
Understanding the operating cash flow (OCF) is key to evaluating a project's profitability. It represents the cash generated from a company's normal business operations. Calculating the OCF involves estimating the revenue produced by an asset and subtracting the operating expenses and taxes.

In the context of Raphael Restaurant's potential purchase of a souffl茅 maker, the annual OCF is the net income from selling souffl茅s minus the cost to make them and the taxes paid. The calculation shows that the souffl茅 maker will contribute positive cash flow after tax, which is a crucial factor in deciding whether to proceed with the investment.
Straight-Line Depreciation
Straight-line depreciation is the most straightforward way to allocate the cost of an asset over its useful life. It assumes the asset's value will decrease equally each year. The formula is simply the initial cost of the asset divided by its estimated economic life.

For Raphael's souffl茅 maker, with a cost of \(12,000 and an economic life of five years, the annual depreciation is \)2,400. This depreciation is an accounting expense that reduces taxable income, thereby affecting the operating cash flow and the investment's overall profitability.
Discount Rate
The discount rate is the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows. It reflects the opportunity cost of using funds for a specific investment rather than an alternative. The rate can be influenced by factors such as risk, inflation, and cost of capital.

In the exercise, a 14% discount rate is applied to evaluate the desirability of investing in the souffl茅 maker. This high rate suggests that the investment carries a substantial level of risk or that the restaurant has high standards for investing its money, as future cash flows must be considerable to justify the investment when discounted back to the present.
Tax Rate
Taxes significantly impact business decisions, as they reduce the net profits a company keeps. The tax rate is the percentage levied by government authorities on profits earned. In our scenario, the 34% tax rate applied to Raphael Restaurant's operational profits influences the effective gain from the investment.

When calculating cash flows, taxes are deducted from operating income to determine how much cash will actually be available to meet other financial obligations, reinvest in the business, or distribute to shareholders. The tax rate is also used to calculate the after-tax salvage value of an asset.
After-Tax Salvage Value
The after-tax salvage value represents the net amount a company expects to receive from disposing of an asset after its useful life, once taxes on the salvage are considered. This value adds to the total return of the investment.

For the calculation of the souffl茅 maker's NPV, we considered its potential after-tax salvage value after full depreciation. Despite the asset being fully depreciated, it will have some residual value. For Raphael Restaurant, this value diminished by the tax effect still contributes positively to the NPV of the investment, providing an additional cash flow at the end of the asset's life that boosts the project's overall attractiveness.

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Most popular questions from this chapter

Project Analysis and Inflation Dickinson Brothers, Inc., is considering investing in a machine to produce computer keyboards. The price of the machine will be \(\$ 530,000\), and its economic life is five years. The machine will be fully depreciated by the straight-line method. The machine will produce 15,000 keyboards each year. The price of each keyboard will be \(\$ 40\) in the first year and will increase by 5 percent per year. The production cost per keyboard will be \(\$ 20\) in the first year and will increase by 6 percent per year. The project will have an annual fixed cost of \(\$ 75,000\) and require an immediate investment of \(\$ \mathbf{2 5 , 0 0 0}\) in net working capital. The corporate tax rate for the company is 34 percent. If the appropriate discount rate is 15 percent, what is the NPV of the investment?

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?

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 Pilot Plus Pens is deciding when to replace its old machine. The machine's current salvage value is \(\$ 1.8\) million. Its current book value is \(\$ 1.2\) million. If not sold, the old machine will require maintenance costs of \(\$ 520,000\) at the end of the year for the next five years. Depreciation on the old machine is \(\$ 240,000\) per year. At the end of five years, it will have a salvage value of \(\$ \mathbf{2 0 0 , 0 0 0}\) and a book value of \(\$ \mathbf{0}\). A replacement machine costs \(\$ 3\) million now and requires maintenance costs of \(\$ 350,000\) at the end of each year during its economic life of five years. At the end of the five years, the new machine will have a salvage value of \(\$ 500,000\). It will be fully depreciated by the straight-line method. In five years a replacement machine will cost \(\$ 3,500,000\). Pilot will need to purchase this machine regardless of what choice it makes today. The corporate tax rate is 34 percent and the appropriate discount rate is 12 percent. The company is assumed to earn sufficient revenues to generate tax shields from depreciation. Should Pilot Plus Pens replace the old machine now or at the end of five years?

Project Analysis Benson Enterprises is evaluating alternative uses for a three-story manufacturing and warehousing building that it has purchased for \(\$ 850,000\). The company can continue to rent the building to the present occupants for \(\$ 36,000\) per year. The present occupants have indicated an interest in staying in the building for at least another 15 years. Alternatively, the company could modify the existing structure to use for its own manufacturing and warehousing needs. Benson's production engineer feels the building could be adapted to handle one of two new product lines. The cost and revenue data for the two product alternatives are as follows: The building will be used for only 15 years for either product \(A\) or product \(B\). After 15 years the building will be too small for efficient production of either product line. At that time, Benson plans to rent the building to firms similar to the current occupants. To rent the building again, Benson will need to restore the building to its present layout. The estimated cash cost of restoring the building if product \(A\) has been undertaken is \(\$ \mathbf{2 9}, 000\). If product \(B\) has been manufactured, the cash cost will be \(\$ 35,000\). These cash costs can be deducted for tax purposes in the year the expenditures occur. Benson will depreciate the original building shell (purchased for \(\$ \mathbf{8 5 0 , 0 0 0}\) ) over a 30 -year life to zero, regardless of which alternative it chooses. The building modifications and equipment purchases for either product are estimated to have a 15-year life. They will be depreciated by the straight-line method. The firm's tax rate is 34 percent, and its required rate of return on such investments is 12 percent. For simplicity, assume all cash flows occur at the end of the year. The initial outlays for modifications and equipment will occur today (year 0 ), and the restoration outlays will occur at the end of year 15. Benson has other profitable ongoing operations that are sufficient to cover any losses. Which use of the building would you recommend to management?
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