FM - 6

A project requires an initial investment of $200,000 and expects to produce a cash flow before taxes of $120,000 per year for two years (i.e., cash flows will occur at t = 1 and t = 2). The corporate tax rate is 30 percent. The assets will depreciate using the MACRS 3-year schedule: (t = 1, 33%); (t = 2: 45%); (t = 3: 15%); (t = 4: 7%). The company's tax situation is such that it can use all applicable tax shields. The opportunity cost of capital is 12 percent. Assume that the asset can sell for book value at the end of the project. Calculate the NPV of the project (approximately).

$16,244 Book value at the end of year 2 = (.15 + .07) × $200,000 = $44,000. Year 1 cash flow: ($120,000 × (1 - .30)) + ($200,000 × .33 × .30) = $103,800. Year 2 cash flow: ($120,000 × (1 - .30)) + ($200,000 × .45 × .30) + $44,000 = $155,000. -$200,000 + ($103,800/1.12) + (($155,000)/(1.12^2)) = $16,244.

If depreciation is $600,000 and the marginal tax rate is 35 percent, then the tax shield due to depreciation is

$210,000.

A project requires an investment of $900 today. It can generate sales of $1,100 per year forever. Costs are $600 for the first year and will increase by 20 percent per year. (Assume all sales and costs occur at year-end [i.e., costs are $600 @ t = 1].) The project can be terminated at any time without cost. Ignore taxes and calculate the NPV of the project at a 12 percent discount rate.

$57.51

Using the technique of equivalent annual cash flows and a discount rate of 7 percent, what is the value of the following project?

3.61

Working capital is one of the most common sources of mistakes in estimating project cash flows.

True

Air conditioning for a college dormitory will cost $2.6 million to install and $145,000 per year to operate. The system should last 14 years. The real cost of capital is 6%, and the college pays no taxes. What is the equivalent annual cost? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Equivalent annual cost $424,720.76 Explanation: PV of costs = $2,600,000 + $145,000 × ((1 / .06) - {1 / [.06 × (1 + .06)14]}) PV of costs = $3,947,772.67 EAC = $3,947,773 / ((1 / .06) - {1 / [.06 × (1 + .06)14]}) EAC = $424,720.76

By undertaking an analysis in real terms, the financial manager avoids having to forecast inflation.

False

Low-energy lightbulbs typically cost $4.50, have a life of nine years, and use about $2.60 of electricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.70. On the other hand, they last only about a year and use about $7.60 of energy. a. If the real discount rate is 5%, what is the equivalent annual cost of the two products? (Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.)

Low-energy lightbulbs $3.23 Conventional lightbulbs $8.34 b. Which product is cheaper to use? Low-energy lightbulbs Explanation: a. PVLE = -$4.50 - $2.60 × ((1 / .05) - {1 / [.05 × (1 + .05)9]}) PVLE = -$22.98 EACLE = -$22.98 / ((1 / .05) - {1 / [.05 × (1 + .05)9]}) EACLE = $3.23 PVConventional = -$.70 - $7.60 / (1 + .05) PVConventional = -$7.94 EACConventional = -$7.94 / ((1 / .05) - {1 / [.05 × (1 + .05)1]}) EACConventional = $8.34 b. Select the low-energy lightbulb because it has the lower EAC

A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,800 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Company B pays corporate taxes at a rate of 35% and can depreciate the investment for tax purposes using the five-year MACRS tax depreciation schedule. Suppose the opportunity cost of capital is 10%. Ignore inflation. a. Calculate project NPV for each company. (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.) b-1. What is the IRR of the after-tax cash flows for each company? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) b-2. What does comparison of the IRRs suggest is the effective corporate tax rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

NPV Company A 1,593 Company B -6,900 IRR Company A 10.62% Company B 7.20% Effective Tax Rate 32.2 Explanation: a. NPVA = -$100,000 + $26,800 × ((1 / .10) - {1 / [.10 × (1 + .10)5]}) NPVA = $1,593 NPVB = -investment + PV(aftertax cash flow) + PV(depreciation tax shield) NPVB = -$100,000 + [$26,800 × (1 - .35)] × ((1 / .10) - {1 / [.10 × (1 + .10)5]}) + (.35 × $100,000) × [.20 / (1 + .10) + .32 / (1 + .10)2 + .192 / (1 + .10)3 + .1152 / (1 + .10)4 + .1152 / (1 + .10)5 + .0576 / (1 + .10)6] NPVB = -$6,900 b. To calculate the effective tax rate, first compute the project cash flows for each year. For years 1 and after, you can use this formula: Aftertax cash flowT = (pretax cash flowT × (1 - tax rate) + (initial investment × depreciation rateT × tax rate) Aftertax cash flows: Year:0123456Company A -100,000.0026,800.0026,800.0026,800.0026,800.0026,800.0035.00 Company B-100,000.0024,420.0028,620.0024,140.0021,452.0021,452.002,016.00 IRRA = 10.62% IRRB = 7.20% c. Effective tax rate = 1 - (.0720 / .1062) = .322, or 32.2%

As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $68,000. Its operating costs are $22,400 a year, but in five years the machine will require a $18,800 overhaul. Thereafter operating costs will be $31,200 until the machine is finally sold in year 10 for $6,800. The older machine could be sold today for $26,200. If it is kept, it will need an immediate $26,000 overhaul. Thereafter operating costs will be $35,000 a year until the machine is finally sold in year 5 for $6,800. Both machines are fully depreciated for tax purposes. The company pays tax at 35%. Cash flows have been forecasted in real terms. The real cost of capital is 14%. a. Calculate the equivalent annual costs for selling the new machine and for selling the old machine. (Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.) b. Which machine should United Automation sell?

Sell new machine $14,129.29 Sell old machine $14,238.57 Sell new machine Explanation: In order to solve this problem, we calculate the equivalent annual cost for each of the two alternatives. Alternative 1—Sell the new machine: If we sell the new machine, we receive the aftertax cash flow from the sale of the new machine, pay the costs associated with keeping the old machine, and receive the aftertax proceeds from the sale of the old machine at the end of year 5. PV1 = $68,000 × (1 - .35) - $26,000 × (1 - .35) - $35,000 × ((1 - .35) / .14) × (1 - {1 / (1 + .14)5}) + [$6,800 × (1 - .35)] / (1 + .14)5 PV1 = -$48,506.98 EAC1 = -$48,506.98 / (1 - {1 / [1 + .14]5} .14) EAC1 = -$14,129.29 Alternative 2—Sell the old machine: If we sell the old machine, we receive the aftertax cash flow from the sale of the old machine, pay the costs associated with keeping the new machine, and receive the aftertax proceeds from selling the new machine at the end of year 10. PV2 = $26,200 × (1 - .35) - $22,400 × ((1 - .35) / .14) × (1 - {1 / (1 + .14)5}) - $18,800 × (1 - .35)] / (1 + .14)5 - $31,200 × ((1 - .35) / .14) × (1 - {1 / (1 + .14)5}) / (1 + .14)5) + $6,800 × (1 - .35)) / (1 + .14)10 PV 2 = -$74,270.02 EAC2 = -$74,270.02 / (1 - {1 / [1 + .14]10} .14) EAC2 = -$14,238.57 Thus, the best alternative is to sell the new because this alternative has the lowest equivalent annual cost.

For the case of an electric car project, which of the following costs or cash flows should be categorized as incremental when analyzing whether to invest in the project?

Tax savings resulting from the depreciation charges

Most large U.S. corporations keep two separate sets of books, one for stockholders and one for the Internal Revenue Service.

True

The Important point(s) to remember while estimating the cash flows of a project

are cash flow is relevant, always estimate cash flows on an incremental basis, and be consistent in the treatment of inflation.

The principal short-term assets are

cash, accounts receivable, and inventories.

When Honda develops a new engine, the incidental effects might include the following:

demand for replacement parts, profits from the sale of repair services, and offer modified or improved versions of the new engine for other uses.

A reduction in the sales of existing products caused by the introduction of a new product is an example of

incidental effects.

Accountants do not depreciate investment in net working capital because

it is recovered during or at the end of the project; thus it is not a depreciating asset.

The cost of a resource that may be relevant to an investment decision even when no cash changes hand is called a(n)

opportunity cost

The NPV value obtained by discounting nominal cash flows using the nominal discount rate is the same as the NPV value obtained by discounting

real cash flows using the real discount rate only.

Net working capital is best represented as

short-term assets and short-term liabilities.

Germany allows firms to choose the depreciation method(s) of

straight-line method and declining-balance method.

Money that a firm has already spent, or committed to spend regardless of whether a project is taken, is called a(n)

sunk cost.

Costs incurred as a result of past irrevocable decisions and irrelevant to future decisions are called

sunk costs.

One should consider net working capital (NWC) in project cash flows because

typically firms must invest cash in short-term assets to produce finished goods.