Chapter 8 Capital Budgeting Decision Criteria：8章资本预算决策标准

Accounting Rate of Return Criterion
What is the straight-line method annual depreciation? ($70,000 – $10,000) ÷5 = $12,000 What is the increased annual income? $20,000 – $12,000 = $8,000 What is the average investment? ($70,000 + $10,000) ÷2 = $40,000
Long-Term (Capital) Assets
Organizations have developed specific tools to control the acquisition and use of longterm assets for three reasons: 1 Organizations commit to long-term assets for extended periods of time. 2 The amount of capital committed is usually very large. 3 The long-term nature of capital assets creates technological risk for organizations.
Year 4: $1.2155 Year 3: $1.1576 Year 2: $1.1025 Year 1: $1.05 Year 0: $1.00
Present Value
What is the present value of money? It is the current monetary worth of an amount to be paid in the future under stated conditions of interest and compounding. Analysts call a future cash flow’s value at time zero its present value. The process of computing present value is called disconey

Use the basic tools and concepts of financial analysis:
investment, return, future value, present value, annuities, and required rate
of return.
Investment and Return
Present Value
What is the present value of $127.63 to be received 5 years from now when the rate of return is 5% per year? $100.00
PV = FV ÷(1 + r)n

Time Value of Money
The future value of money is the value that an amount invested today will be after a stated number of periods at a given rate of return. How much would an initial amount of $100 accumulate over five years when the rate of return is 5% per year?
Time Value of Money
A central concept in capital budgeting is the time value of money. Because money can earn a return, its value depends on the time period in which it is received. Amounts of money received at different periods of time must be converted to their value on a common date to be compared.

Copyright © 2018 by the McGraw-Hill Companies, Inc. All rights reserved. 18-10
-$1,000
$125
$250
$375
$500
0
1
2
3
4
The APV of the project under leverage is:
ST
APV
T t 1
StOCFt (1 τ) (1 Kud )t
T t 1
St τDt (1 id )t
T t 1
St τIt (1 id )t
STTVT (1 Kud )T
S0C0 S0RF0
S0CL0
T t 1
St LPt (1 id )t
Copyright © 2018 by the McGraw-Hill Companies, Inc. All rights reserved. 18-13
International Capital Budgeting
Chapter Eighteen
Copyright © 2018 by the McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
• Review of Domestic Capital Budgeting • The Adjusted Present Value Model • Capital Budgeting from the Parent Firm’s
It is incremental interest
expense is the marginal tax rate

investment, return, future value, present value, annuities, and required rate
of return.
2001 Prentice Hall Business Publishing Management Accounting, 3/E, Atkinson, Banker, Kappter 8
2001 Prentice Hall Business Publishing Management Accounting, 3/E, Atkinson, Banker, Kaplan, and Young
8- 1
Learning Objective 1
u Organizations commit to long-term assets for extended periods of time.
u The amount of capital committed is usually very large.
u The long-term nature of capital assets creates technological risk for organizations.
2001 Prentice Hall Business Publishing Management Accounting, 3/E, Atkinson, Banker, Kaplan, and Young
8- 3
Long-Term (Capital) Assets
Organizations have developed specific tools to control the acquisition and use of longterm assets for three reasons:

Performance report
Static budget Flexible budget Static budget variance
Sales volume variance Flexible budget variance
Favorable variance and unfavorable variance Management by exception
16
Types of Problems
A. Equipment Replacement
Sunk Costs & Depreciation
B. Special Order
Fixed Cost & Opportunity Costs
C. Outsourcing: Make or Buy Decision
Comparison of traditional and ABC overhead allocation
6
Major Points of Cost Allocation
1 2 3
4
Why allocate? How much to allocate?
Allocate to whom? How to allocate?
7
Chapter 5 : Cost Behavior
Common cost behavior patterns
Fixed costs : think as total Variable costs : think on a per-unit basis Relevant range
Mixed costs and its separation
2
Chapter 2 :Classifying Costs

Step 2: Compute the payback period. Using the annual net cash inflow from above, the payback period can be determined as follows: Cost of the new equipment . . . . . . . . . . . . . . $80,000 Less salvage value of old equipment . . . . . . 5,000 Investment required . . . . . . . . . . . . . . . . . . . . . $75,000 Payback period = = Investment required Annual net cash inflow $75,000 = 2.5 years $30,000
Evaluation of the Payback Method
To illustrate, refer back to Example A on the previous page. Machine B has a shorter payback period than machine A, but it has a useful life of only 5 years rather than 10 years for machine A. Machine B would have to be purchased twice—once immediately and then again after the fifth year—to provide the same service as just one machine A.

Chapter 8: Risk Analysis, Real Options, and Capital Budgeting 8.1Calculate the NPV of the expected payoff for the option of going directly to market.NPV(Go Directly) = C Success (Prob. of Success) + C Failure (Prob. of Failure)= $20,000,000 (0.50) + $5,000,000 (0.50)= $12,500,000The expected payoff of going directly to market is $12,500,000.The test marketing requires a $2 million cash outlay. Choosing the test marketing option will also delay the launch of the product by one year. Thus, the expected payoff is delayed by one year and must be discounted back to year 0.NPV(Test Market) = -C0 + [C Success (Prob. of Success)] / (1+r)T +[C Failure (Prob. of Failure)] / (1+r)T= -$2,000,000 + [$20,000,000 (0.75)] / (1.15) +[$5,000,000 (0.25)] / (1.15)= $12,130,434.78The expected payoff of test marketing the product is $12,130,434.78.Sony should go directly to market with the product since that option has the highestexpected payoff.8.2Calculate the NPV of each option. The manager should pursue the option with the highest NPV.NPV(Go Directly) = C Success (Prob. of Success)= $1,200,000 (0.50)= $600,000The NPV of going directly to market is $600,000.NPV(Focus Group) = C0 + C Success (Prob. of Success)= -$120,000 + $1,200,000 (0.70)= $720,000The NPV when conducting a focus group is $720,000.NPV(Consulting Firm) = C0 + C Success (Prob. of Success)= -$400,000 + $1,200,000 (0.90)= $680,000The NPV when hiring a consulting firm is $680,000.The firm should conduct a focus group since that option has the highest NPV.8.3Recommend the strategy that has the highest NPV.NPV(Lower Prices) = C Success (Prob. of Success) + C Failure (Prob. of Failure)= -$1,300,000 (0.55) - $1,850,000 (0.45)= -$1,547,500NPV(Lobbyist) = C0 + C Success (Prob. of Success) + C Failure (Prob. of Failure)= -$800,000 - $0 (0.75) - $2,000,000 (0.25)= -$1,300,000The CFO should hire the lobbyist since that option has the highest NPV.8.4Since the NPV of Research is greater than that of no research, based on expected outcomes, B&Bshould go directly to market.$3 million at t = 0Note: Research = –1 million investment + 0.7 * (26.087) if successful + 0.3 * (2.6087) if unsuccessful No Research = 0.55 * (30) if successful + 0.45 * (3) if unsuccessful8.5Carl should have taken the $5,000.Expected return for 1% of movie profits is $3,000. Since only good scripts are made into movies and only a good movie would make a profit: (10% x 30% x $10 mil x 1%)Movie studio decision tree:B-1648.6 Apply the accounting profit break-even point (BEP) formula and solve for the sales price, x, thatallows the firm to break even when producing 20,000 calculators. In order for the firm to breakeven, the revenues from the calculator sales (number of calculators sold sales price per unit)must equal the total annual cost of producing the calculators. Remember to include taxes in theanalysis.Variable costs = $15 per calculatorFixed costs = $900,000 per yearDepreciation = (Initial Investment / Economic Life)= ($600,000 / 5)= $120,000 per yearDivide the after-tax sum of the depreciation expense and the fixed costs by the calculator’s after-tax contribution margin (selling price, x, minus variable cost). The after-tax contribution margin is the amount that each additional calculator contributes to the firm’s profit. Before the firm canrealize a positive profit, it must have earned enough to cover its fixed costs and depreciationexpense. Solve for x.[(Fixed Costs + Depr.) (1–T c)] / [(Sales Price - Variable Cost) (1-T c)] = BEP[($900,000 + $120,000) (1 – 0.30)] / [(x - $150) (1 – 0.30)] = 20,000x= $66 The break-even sales price of the calculator is $66.8.7 Apply the accounting profit break-even point formula. Divide the after-tax sum of the annualdepreciation expense and the annual fixed costs by the television’s after-tax contribution margin(selling price minus variable cost).[(Fixed Costs + Depr.) (1–T c)] / [(Sales Price - Variable Cost) (1-T c)] = BEP[($120,000 + $20,000) (1 -0.35)] / [($1,500 - $1,100) (1 - 0.35)] = 350 The distributor must sell 350 televisions per year to break even.8.8 a. Apply the accounting profit break-even point formula. Divide the after-tax sum of thefixed costs and depreciation charge by the abalone’s after-tax contribution margin(selling price minus variable cost). The number of abalones that the proprietor must sellin order for you to receive any profit is the break-even point (BEP).[(Fixed Costs + Depr.) (1–T c)] / [(Sales Price – Variable Cost) (1-T c)] = BEP[($340,000 + $20,000) (1 – 0.35)] / [($2.00 - $0.72) (1 – 0.35)]= 281,250The proprietor must sell at least 281,250 abalones per year in order for you toreceive any profit.b. To calculate the amount of profit you will receive if the proprietor sells 300,000 abalones,subtract the total cost incurred from the total revenue received. Remember to includetaxes.Total Revenue Per Year = (Sales Price) (Number Sold) (1 – T c)= ($2.00) (300,000) (1 – 0.35)= $390,000Total Cost Per Year = [Fixed Cost + Deprc. + (Variable Cost) (Number Sold)] (1-T c)= [$340,000 + $20,000 +($0.72) (300,000)] (1 – 0.35)= $374,400Total Profit = Total Revenue – Total Cost= $390,000 - $374,400= $15,600You will receive $15,600 if the proprietor sells 300,000 abalones.8.9 Played 2187.5 = CEILING ((1000 + 50)/(0.5-0.02),1)8.10 a) ()()()()()()()()shirts-T10003.18103.1000,2Tc-1costVariable-priceSalesTc-1onDepreciatiCostFixed=-⨯--⨯+=⨯⨯+b) ()()()()()()()()shirts-T29743.18104018.2/000,10Tc-1costVariable-priceSalesTconDepreciatiTc1costFixedEAC=-⨯-++=⨯⨯+-⨯+8.11 When calculating the present value break-even point, express the initial investment of $140,000 asan equivalent annual cost (EAC). Divide the initial investment by the seven-year annuity factor,discounted at 15 percent. The EAC incorporates the opportunity cost of the investment.EAC = Initial Investment / A T r= $140,000 / A70.15= $33,650.45Calculate the annual depreciation expense.Depreciation = $140,000 / 7= $20,000Calculate the present-value break-even point. The fixed costs are $340,000. Remember toincorporate taxes into the calculation. Remember to include the depreciation tax shield, whichlowers the firm’s tax bill.[EAC+(Annual Fixed Costs) (1 - T c) – (Annual Depr.) (T c)] / [(Sales Price – Variable Cost) (1 – T c)]= BEP[$33,650.45 + $340,000 (0.65) - $20,000 (0.35)] / [($2 - $0.72) (0.65)] =297,656.79≅ 297,657 units The present value break-even point is 297,657 abalones.8.12 When calculating the present value break-even point, express the initial investment of $200,000 asan equivalent annual cost (EAC). Divide the initial investment by the five-year annuity factor,discounted at 12 percent.EAC = Initial Investment / A T r= $200,000 / A50.12= $55,481.95Calculate the annual depreciation expense.Depreciation = $200,000 / 5= $40,000Calculate the present-value break-even point.[EAC+(Fixed Costs) (1 - T c) – (Depr.) (T c)] / [(Sales Price – Variable Cost) (1 – T c)]= BEP[$55,481.95 + ($350,000) (0.75) – ($40,000) (0.25)] / [($25 - $5) (0.75)] = 20,532.13 The present value break-even point is 20,532 units.8.13 The following represents a different approach to solving present-value break-even problems,unlike the EAC method used in problems 8.8 and 8.7.Both the EAC approach and this approach will yield the same answer.First, determine the cash flow from selling the old harvester. When calculating the salvage value, remember that tax liabilities or credits are generated on the difference between the resale value and the book value of the asset.Use the original purchase price of the old harvester to determine annual depreciation.Depreciation Per Period = $45,000 / 15= $3,000Since the machine is five years old, the firm has accumulated five annual depreciation charges,reducing the book value of the machine. The current book value of the machine is equal to theinitial purchase price minus the accumulated depreciation.Book Value = Initial Purchase Price – Accumulated Depreciation= $45,000 – ($3,000 ⨯ 5 years)= $30,000Since the firm is able to resell the old harvester for $20,000, which is less than the $30,000 bookvalue of the machine, the firm will generate a tax credit on the sale.PV(Resale Value) = C - T C (Resale Value – Book Value)= $20,000 – 0.34 ($20,000 - $30,000)= $23,400Calculate the incremental depreciation. Calculate the depreciation tax shield generated by the new harvester less the forgone depreciation tax shield from the old harvester. Let P be the break-even purchase price.Depreciation Tax Shield, New Harvester = (Initial Investment / Economic Life) ⨯ T c= (P / 10) (0.34)Depreciation Tax Shield, Old Harvester = ($45,000 / 15) (0.34)= ($3,000) (0.34)Incremental Depreciation Tax Shield = (P / 10 - $3,000) (0.34)Apply the 10-year annuity formula, discounted at 15 percent, to calculate the PV of theincremental depreciation tax shield.PV(Depreciation Tax Shield) = (P / 10 - $3,000) (0.34) A100.15 The new harvester will generate year-end pre-tax cash flow savings of $10,000 per year for 10years. Apply the 10-year annuity formula, discounted at 15 percent, to find the PV of thosesavings. Remember to include taxes.PV(Savings) = (1 – T c) C1 A T r= (1 - 0.34) $10,000 A100.15= $33,123.87The break-even purchase price of the new harvester is the price, P, which makes the NPV of themachine equal to zero.NPV = -P + PV(Resale Value) + PV(Depreciation Tax Shield) + PV(Savings)$0 = -P + $23,400 + (P / 10 - $3,000) (0.34) A100.15 + $33,123.87P= $61,981.06The break-even purchase price is $61,981.06.8.14 A 5,0.08 3.993EAC 75,136,936Depreciation 60,000PVBreak-Even 3,5188.15 a. Pessimistic:Calculate the NPV of the pessimistic scenario. First, determine the yearly cash flow.Cash Flow = [Revenue - Variable Costs – Fixed Costs] (1 – T c) + Depr. Tax Shield= [($38 ⨯ 23,000) – ($21 ⨯ 23,000) - $320,000] (1- 0.35) +($420,000 / 7) (0.35)= $67,150Apply the seven-year annuity formula to calculate the NPV of the machine. Subtract theinitial investment.NPV = C0 + C1 A T r= -$420,000 + $67,150 A70.13= -$123,021.71The NPV of the pessimistic scenario is -$123,021.71.Expected:Calculate the NPV of the expected scenario. First, determine the yearly cash flow.Cash Flow = [Revenue - Variable Costs – Fixed Costs] (1 – T c) + Depr. Tax Shield= [($40 ⨯ 25,000) – ($20 ⨯ 25,000) - $300,000] (1- 0.35)+ ($420,000 / 7) (0.35)= $151,000Apply the seven-year annuity formula to calculate the NPV of the machine. Subtract theinitial investment.NPV = C0 + C1 A T r= -$420,000 + $151,000 A70.13= $247,814.18The NPV of the expected scenario is $247,814.18.Optimistic:Calculate the NPV of the optimistic scenario. First, determine the yearly cash flow.Cash Flow = [Revenue – Variable Costs – Fixed Costs] (1 – T c)+ Depreciation Tax Shield= [($42 ⨯ 27,000) – ($19 ⨯ 27,000) - $280,000] (1- 0.35)+ ($420,000 / 7) (0.35)= $242,650Apply the seven-year annuity formula to calculate the NPV of the machine. Subtract theinitial investment.NPV = C0 + C1 A T r= -$420,000 + $242,650 A70.13= $653,146.42The NPV of the optimistic scenario is $653,146.42.b. Calculate the expected NPV of the project to form your conclusion about the project.Remember that, since each scenario is equally likely, the expected NPV is the average ofthe three scenarios.NPV = [NPV(Pessimistic) + NPV(Expected) + NPV(Optimistic)] / (3)= [-$123,021.71 + $247,814.18 + $653,146.42] / 3= $259,312.96The expected NPV of the project is $259,312.96. You should conclude that theproject is worthwhile.8.16 Pessimistic:Calculate the NPV of the pessimistic scenario. First, determine the yearly cash flow. Todetermine the number of rackets sold, multiply the market size by the market share.Number of Rackets = Market Size ⨯ Market Share= 110,000 ⨯ 0.22= 24,200Cash Flow = [Revenue – Variable Costs – Fixed Costs] (1 – T c)+ Depreciation Tax Shield= [$115 ⨯ 24,200 - $72 ⨯ 24,200 - $850,000] (1 – 0.4)+ ($1,500,000 / 5) (0.4)= $234,360Apply the five-year annuity formula to calculate the NPV of the racket project. Subtract the initial investment.NPV = C0 + C1 A T r= -$1,500,000 + $234,360 A50.13= -$675,701.68Expected:Calculate the NPV of the expected scenario. First, determine the yearly cash flow. To determine the number of rackets sold, multiply the market size by the market share.Number of Rackets = Market Size ⨯ Market Share= 120,000 ⨯ 0.25= 30,000Cash Flow = [Revenue – Variable Costs – Fixed Costs] (1 – T c)+ Depreciation Tax Shield= [$120 ⨯ 30,000 - $70 ⨯ 30,000 - $800,000] (1 – 0.4)+ ($1,500,000 / 5) (0.4)= $540,000Apply the five-year annuity formula to calculate the NPV of the racket project. Subtract the initial investment.NPV = C0 + C1 A T r= -$1,500,000 + $540,000 A50.13= $399,304.88Optimistic:Calculate the NPV of the optimistic scenario. First, determine the yearly cash flow. To determine the number of rackets sold, multiply the market size by the market share.Number of Rackets = Market Size ⨯ Market Share= 130,000 ⨯ 0.27= 35,100Cash Flow = [Revenue – Variable Costs – Fixed Costs] (1 – T c)+ Depreciation Tax Shield= [$125 ⨯ 35,100 - $68 ⨯ 35,100 - $750,000] (1 – 0.4)+ ($1,500,000 / 5) (0.4)= $870,420Apply the five-year annuity formula to calculate the NPV of the racket project. Subtract the initial investment.NPV = C0 + C1 A T r= -$1,500,000 + $870,420 A50.13= $1,561,468.43Calculate the expected NPV of the project. Since each scenario is equally likely, the expectedNPV is the average of the three scenarios.NPV = [NPV(Pessimistic) + NPV(Expected) + NPV(Optimistic)] / (3)= [-$675,701.68 + $399,304.88 + $1,561,468.43] / (3)= $428,357.21The expected NPV of the project is $428,357.21. You should accept the project.8.17 Holding all variables as expected, except a single sensitivity analysis variable that is held atpessimistic or optimistic.Since under all scenarios NPVs come out positive, the project should be taken.8.18B-172Optimistic8.19 a. Apply the 10-year annuity formula, discounted at 10 percent, to calculate the NPV of thevideo game.NPV = C0 + C1 A T r= -$4,000,000 + $750,000 A100.1= $608,425.33The NPV of the video game is $608,425.33.b.Calculate the revised NPV of the project. The firm expects to receive net cash flow of$750,000 at the end of the first year of operations. Discount that value back one period toyear 0.PV(Year 1 Cash Flow) = C1 / (1+r)T= $750,000 / (1.1)= $681,818.18For the next nine years, the firm has a 50 percent chance of receiving annual cash flowsof $1,500,000 and a 50 percent chance of receiving annual cash flows of $0. Should thefirm receive cash flows of $0, the firm should exercise the option of abandonment andreceive the $200,000 cash flow. The probability of exercising that option is 50 percent.Calculate the expected PV of the revised cash flows by applying the nine-year annuityformula. To calculate the expected PV as of year 0, discount that value back one periodto year 0. The option is exercised in year 1 and must also be discounted back one periodto year 0.PV(Revised) = (Prob. ⨯ C2⨯ A T r + Prob. ⨯ Salvage) / (1+r)T= (0.5 ⨯ $1,500,000 ⨯ A90.1 + 0.5 ⨯ $200,000) / (1.1)= $4,017,516.23After including the initial investment, the revised NPV of the project is equal to the sumof the first year’s cash flow, the PV of the expected cash flows for the next nine years,and the expected value of abandoning the project.Revised NPV = C0 + C1 / (1+r)T +[(Prob. ⨯ C2⨯ A T r) + (Prob. ⨯ C2)] / (1+r)T= -$4,000,000 + $750,000 / (1.1) +(0.5 ⨯ $1,500,000 ⨯ A90.1 + 0.5 ⨯ $200,000) / (1.1)= $699,334.42The revised NPV is $699,334.42.c. The market value of the project, M, is the NPV of the project without an option toabandon plus the value of the option, Opt. The NPV of the project without the option toabandon was calculated in part (a). The difference between the NPV as calculated in part(a) and the revised NPV is equal to the option value of abandonment, Opt.M= NPV + Opt$699,334.42 = $608,425.33+ Opt$90,909.09 = OptThe option value of abandonment is $90,909.09.8.20 a. Apply the 10-year annuity formula, discounted at 20 percent to calculate the NPV of theproject. Total annual net cash flow is $200,000,000.NPV = C0 + C1 A T r= -$100,000,000 + $200,000,000 A100.2= $738,494,417.11The NPV of the project is $738,494,417.11.b.Allied Products should abandon the project if the PV of the revised cash flows for thenext nine years is less than the project’s scrap value. Since the option to abandon theproject occurs in year 1, discount the revised cash flows to year 1 as well. To determinethe level of expected cash flows below which Allied should abandon the project,calculate the equivalent annual cash flows the project must earn to equal the scrap value,$50 million. Set the scrap value equal to a nine-year annuity, discounted at 20 percent.Solve for C1.Scrap Value = C1 A T r$50,000,000 = C1 A90.2$50,000,000 / A90.2= C1$12,403,973.08 = C1The firm should abandon the project after the first year if the revised expectedannual cash flows are below $12,403,973.08. Below that level, the firm is better offabandoning the project and receiving the $50 million scrap value of the project.8.21 a. NPV (1.932) = –10 + 10*0.3*(1/0.25-1/0.25*(1/1.25)5)b. Option Value 2.000 = 0.5*9/1.25New NPV 0.068 = –10 + 10*0.3/1.25 + 0.5*15*0.3*(1/0.25 –1/0.25*(1/1.25)4)/(1.25) + 0.5*9/1.25B-175。

Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision. Example: A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow. Assume an opportunity cost of capital of 10%. Year 0 1 2 3 4 5 Cost 50 55 60 64 68 70 Sales 70 80 88 95 102 105 Value 20 25 28 31 34 35 NPV 20.0 22.7 23.1 23.3 23.2 21.7
Cash Flows Project Project 1 Project 2 Project 3 C0 - $1,000 - $1,000 - $1,000 C1 $700 $500 $500 C2 $500 $700 $700 $700 C3
Payback Period 1.6 years 1.7 years 1.7 years
8-2
Net Present Value
Opportunity Cost of Capital - Expected rate of
return given up by investing in a project
Net Present Value - Present value of cash flows

12-13
Internal Rate of Return - Uneven
Cash-Flows (cont’d)
• Using the trial and error approach, we use both 10% and 12% to arrive at the answer: Year 10% 1…….$5,000 X 0.909 = $4,545 2…….$5,000 X 0.826 = 4,130 3…….$2,000 X 0.751 = 1,502 $10,177
• At 10%, the present value of the inflows exceeds $10,000 – we therefore use a higher discount rate
Year 12% 1…….$5,000 X 0.893 = $4,464 2…….$5,000 X 0.797 = 3,986 3…….$2,000 X 0.712 = 1,424
• Averaging would either understate or overstate the IRR by moving the cash-flows either to the end or beginning of the project
• Cash flows in early years are worth more and increase the return
(Annuity)
$244
• The present value of an annuity (given in Appendix D) shows that the factor of 4.1 for five years indicates a yield of 7%

Example of Investment Rules
Payback Period:
Time 0 1 2 3 CF -200 200 800 -800 Project A Cum. CF -200 0 800 0 CF -150 50 100 150 Project B Cum. CF -150 -100 0 150
Opportunity Costs
Consider the case of an MBA student who pays $30,000 per year
in tuition and fees at a private university. For a two year MBA program, the cost of tuition and fees would be $60,000, this is the monetary cost of the education. However, when making the decision to go back to school, one should consider the opportunity cost, which includes the income in his or her job had been made. If the student had been earning $50,000 per year and was expecting a 10% salary increase in one year,$105,000 in salary would be foregone as a result of the decision to return to school. Adding this amount to the educational expenses results in a cost of $165,000 for the degree.

–10.00
–6.32 –8.65 3.75 21.22
(7) Total cash flow of
–260.00
–6.32 –8.65 3.75 192.98
investment
[(1) + (4) + (6)]
At the end of the project, the warehouse is unencumbered, so we can sell it if we want to.
(5,000, 8,000, 12,000, 10,000, 6,000).
Price during the first year is $20 and increases 2% per year thereafter. Sales revenue in year 3 = 12,000×[$20×(1.02)2] = 12,000×$20.81 = $249,720.
cash flows. Inflation matters.
Cash Flows—Not Accounting
Consider depreciation expense.
You never write a check made out to “depreciation.”
Much of the work in evaluating a project lies in taking accounting numbers and generating cash flows.
Be able to compute depreciation expense for tax purposes
Incorporate inflation into capital budgeting Understand the various methods for computing

Chapter 8Fundamentals of Capital BudgetingNote:All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems with a higher level of difficulty.1.Plan: We can compute the total capitalization of the machine by adding the total cost oftransporting and installing the machine to the initial cost of purchasing the machine, and thiswill provide us with the total cost of the machine that we must appreciate over the 5 years of themachine’s life. In order to compute the annual depreciation expense of the machine we can thentake the total capitalization of the machine and divide it by the depreciable life of the machine.Execute:Capitalization of machine: $10,050,000Annual depreciation expense: 10,050,000/5 = $2,010,000Evaluate: Rather than expensing the $10,050,000 it costs to buy, ship, and install the machinein the year it was bought, accounting principles require you to depreciate the $10,050,000 overthe depreciable life of the equipment. Assuming the equipment has a 5-year depreciable life andthat we use the straight-line method, we would expense $10,050,000/5 = $2,010,000 per year for five years. The idea is to match the cost of acquiring the machine to the timing of the revenuesit generates.2.Plan: We need four items to calculate incremental earnings: (1) incremental revenues,(2) incremental costs, (3) depreciation, and (4) the marginal tax rate.Execute:= (Revenues − Costs − Depreciation) × (1 − tax rate)earningsAnnualincrementalearningsincrementalAnnual=−−×−=(4 1.2 2.01)(10.35)$513,500Evaluate: These incremental earnings are an intermediate step on the way to calculating theincremental cash flows that would form the basis of any analysis of the project. The cost of theequipment does not affect earnings in the year it is purchased, but does so through the depreciation expense in the following five years. Note that the depreciable life, which is based on accountingrules, does not have to be the same as the economic life of the asset—the period over which itwill have value.90 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance3. Plan: We can compute the incremental revenues by taking the percentage increase in sales ofthe 100,000 units multiplied by the $20 sales price per unit.Execute: Incremental revenues =××=(0.20100,000)$20$400,000.Evaluate: A new product typically has lower sales initially, as customers gradually becomeaware of the product. Sales will then accelerate, plateau, and ultimately decline as the productnears obsolescence or faces increased competition. Similarly, the average selling price of aproduct and its cost of production will generally change over time. Prices and costs tend to risewith the general level of inflation in the economy.4.Plan: We can compute the level of incremental sales associated with introducing the new pizzaassuming that customers will spend the same amount on either version by using the sales of the new pizza and the lost sales of the original pizza (40% of customers who switched to the newpizza multiplied by the $20 million in new sales).We can compute the level of incremental sales associated with introducing the new pizzaassuming that 50% of the customers will switch to another brand by using the sales of the newpizza and the lost sales of the original pizza from the customers who would not have switchedbrands.Execute:a. Sales of new pizza − lost sales of original = 20 − 0.40(20) = $12 million.b. Sales of new pizza − lost sales of original pizza from customers who would not have switchedbrands = 20 − 0.50(0.40)(20) = $16 million.Evaluate: More incremental sales are generated if 50% of the customers who will switch fromPisa Pizza’s original pizza to its healthier pizza will switch to another brand if Pisa Pizza doesnot introduce a healthier pizza than just the incremental sales associated with introducing thenew pizza. A new product typically has lower sales initially, as customers gradually becomeaware of the product. Sales will then accelerate, plateau, and ultimately decline as the productnears obsolescence or faces increased competition. Similarly, the average selling price of aproduct and its cost of production will generally change over time. Prices and costs tend to risewith the general level of inflation in the economy.5. Plan: We need four items to calculate incremental earnings: (1) incremental revenues,(2) incremental costs, (3) depreciation, and (4) the marginal tax rate.Execute:Year 1 2 Incremental Earnings Forecast ($000s)1 Sales of Mini Mochi Munch 9,000 7,000Sales 2,000 2,0002 Other3 Cost of Goods Sold (7,350) (6,050)2,9504 Gross Profit 3,6505 Selling, General & Admin. (5,000) —6 Depreciation — —2,9507 EBIT (1,350)8 Income tax at 35% 473 (1,033)9 Unlevered Net Income (878) 1,918Chapter 8 Fundamentals of Capital Budgeting 91 Evaluate: These incremental earnings are an intermediate step on the way to calculating the incremental cash flows that would form the basis of any analysis of the project. The cost of the equipment does not affect earnings in the year it is purchased, but does so through thedepreciation expense in the following five years. Note that the depreciable life, which is based on accounting rules, does not have to be the same as the economic life of the asset—the period over which it will have value. Net income is negative in the first year because the additional selling, general, and administrative costs occurred only in the first year.6. Plan: We can compute the incremental impact on this year’s EBIT of the drop in price bysubtracting the gross profit without the price drop from the gross profit with the price drop.We can compute the incremental impact on EBIT for the next three years of a price drop in the first year from the additional sales on ink cartridges by finding the change in EBIT from ink cartridge sales, which will be the incremental impact on EBIT for years 2 and 3. Note that for year one, we must remember to subtract the incremental impact on EBIT from the price drop in year one.Execute:a. Change in EB I T = Gross profit with price drop − Gross profit without price drop= 25,000 × (300 − 200) − 20,000 × (350 − 200)=−$500,000b. Change in EBIT from ink cartridge sales = 25,000 × $75 × 0.70 − 20,000 × $75 × 0.70= $262,500T herefore, incremental change in EBIT for the next three years is− 500,000 =−$237,500Year1: $262,5002: $262,500Year3: $262,500YearEvaluate: A new product typically has lower sales initially, as customers gradually become aware of the product. Sales will then accelerate, plateau, and ultimately decline as the product nears obsolescence or faces increased competition. Similarly, the average selling price of a product and its cost of production will generally change over time. Prices and costs tend to rise with the general level of inflation in the economy.7. Plan: The difference between incremental earnings and incremental free cash flows is driven bythe equipment purchased. We need to recognize the cash outflow associated with the purchase in year 0 and add back the depreciation expenses from years 1 to 5, as they are not actually cash outflows.Execute:Free cash flows = After-tax earnings + depreciation − capital expenditures − changes in NWC FCF (this year) =−$10,050,000FCF (for each of the next five years) = 513,500 + 2,010,000 = $2,523,500Evaluate: By recognizing the outflow from purchasing the equipment in year 0, we account for the fact that $10,050,000 left the firm at that time. By adding back the depreciation expenses in years 1 to 5, we adjust the incremental earnings to reflect the fact that the depreciation expense is not a cash outflow.92 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance8. Plan: We can project the net working capital needed for this operation by adding cash, inventory,and receivables and subtracting payables.Execute: Net working capital in this problem is the sum of Cash, Accounts Receivable, and Inventory (Lines 1, 2, and 3 below) less Accounts Payable (Line 4). Line 5 is net workingcapital and Line 6 is the changes in working capital from year to year. For example, net working capital in year 1 was 14 and in year 2 it grew to 19, so the increase in NWC, as computed on Line 6 for year 2, is 5. The firm must add 5 to working capital in year 2, so it represents a reduction in cash flow available to investors.Year 0Year 1Year 2 Year 3 Year 4 Year 51 Cash 6 12 15 15 15 2 Accounts Receivable 21 22 24 24 24 3 I nventory 5 7 10 12 13 4 Accounts Payable18 22 24 25 30 5 Net working capital (1 + 2 + 3 − 4) 0 14 19 25 26 226 Increase in NWC−14−5−6−1 4Evaluate: Most projects will require the firm to invest in net working capital. We care about networking capital because it reflects a short-term investment that ties up cash flow that could be used elsewhere. Note that whenever net working capital increases, reflecting additional investment in net working capital, it represents a reduction in cash flow that year.9. Plan: In order to compute the net working capital for each year we need to compute the receivables and payables for each year as a percentage of sales and COGS (receivables are 15% of sales, and payables are 15% of COGS).Execute:0 1 2 3 4 Sales $23,500 $26,438 $23,794 $8,566COGS $ 9,500 $10,688 $ 9,619 $3,463 Receivables: $0 $ 3,525 $ 3,966 $ 3,569 $1,285Payables: $0 $ 1,425 $ 1,603 $ 1,443 $ 519 NWC: $0 $ 2,100 $ 2,363 $ 2,126 $ 765Δ NWC (Required Investment): $ 2,100$ 263−$ 236 −$1,364Evaluate: Most projects will require the firm to invest in net working capital. We care about networking capital because it reflects a short-term investment that ties up cash flow that could be used elsewhere. Note that whenever net working capital increases, reflecting additional investmentin net working capital, it represents a reduction in cash flow that year.Chapter 8 Fundamentals of Capital Budgeting 9310. Plan: We need four items to calculate incremental earnings: (1) incremental revenues,(2) incremental costs, (3) depreciation, and (4) the marginal tax rate.Earnings include non-cash charges, such as depreciation, but do not include the cost of capital investment. To determine the project’s free cash flow from its incremental earnings, we mustadjust for these differences. We need to add back depreciation to the incremental earnings torecognize the fact that we still have the cash flow associated with it.Execute:Solution: Note—we have assumed any incremental cost of goods sold is included as part ofoperating expenses.a.Year 1 2 Incremental Earnings Forecast ($000s)1 Sales 125.0 160.02 Operating Expenses (40.0) (60.0)3 Depreciation (25.0) (36.0)64.04 EBIT 60.05 Income tax at 35% (21.0) (22.4)6 Unlevered Net Income 39.0 41.6b.Free Cash Flow ($000s) 1 27 Plus: Depreciation 25.0 36.08 Less: Capital Expenditures (30.0) (40.0)9 Less: Increases in NWC (5.0) (8.0)10 Free Cash Flow32.0 29.6Evaluate: These incremental earnings are an intermediate step on the way to calculating theincremental cash flows that would form the basis of any analysis of the project. Earnings are an accounting measure of the firm’s performance. They do not represent real profits, and a firmneeds cash. Thus, to evaluate a capital budgeting decision, we must determine its consequences for the firm’s available cash.11. Plan: Earnings include non-cash charges, such as depreciation, but do not include the cost ofcapital investment. To determine the project’s free cash flow from its incremental earnings, we must adjust for these differences. We need to add back depreciation to the incremental earnings to recognize the fact that we still have the cash flow associated with it.Execute: FCF = Unlevered Net Income + Depreciation − CapEx − Increase in NWC = 250 +100 − 200 − 10 = $140 million.Evaluate: Earnings are an accounting measure of the firm’s performance. They do not represent real profits, and a firm needs cash. Thus, to evaluate a capital budgeting decision, we mustdetermine its consequences for the firm’s available cash.94 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance12. This opportunity cost lowers the incremental earnings of Home net by the after-tax earnings thatthey would have otherwise earned had they rented out the space instead. This would be a decrease in incremental earnings of 200,000 × (1 − 0.40) = $120,000 per year for the 4 years.*13. Plan: Incremental revenues: 0 I ncremental costs: −150,000 Depreciation: $10,000 per year Capital Gain on Salvage: $50,000 − $0 = $50,000 Cash flow from salvage value: +50,000 − (50,000)(0.45) = 27,500Execute: Replacing the machine increases EBITDA by 40,000 − 20,000 = 20,000. Depreciationexpenses rises by $15,000 − $10,000 = $5,000. Therefore, FCF will increase by (20,000) × (1 − 0.45) + (0.45)(5,000) = $13,250 in years 1 through 10.In year 0, the initial cost of the machine is $150,000. Because the current machine has a book value of $110,000 − 10,000 (one year of depreciation) = $100,000, selling it for $50,000generates a capital gain of 50,000 − 100,000 = −50,000. This loss produces tax savings of 0.45 × 50,000 = $22,500, so that the after-tax proceeds from the sales including this tax savings is $72,500. Thus, the FCF in year 0 from replacement is −150,000 + 72,500 = −$77,500. NPV of replacement = −77,500 + 13,250 × (1/0.10)(1 − 1/1.1010) = $3,916. There is a small profit from replacing the machine.Evaluate: Even though the decision has no impact on revenues, it still matters for cash flows because it reduces costs. Further, both selling the old machine and buying the new machine involve cash flows with tax implication.*14. Plan: We can use Eq. (8.5) to evaluate the free cash flows associated with each alternative. Notethat we only need to include the components of free cash flows that vary across each alternative. For example, since NWC is the same for each alternative, we can ignore it.Execute: The spreadsheet below computes the relevant FCF from each alternative. Note that each alternative has a negative NPV—this represents the PV of the costs of each alternative. We should choose the one with the highest NPV (lowest cost), which in this case is purchasing the existing machine. a. See spreadsheet.12345678910Rent Machine1 Rent (50,000) (50,000)(50,000)(50,000)(50,000)(50,000)(50,000)(50,000) (50,000) (50,000)2 FCF (rent) (32,500) (32,500)(32,500)(32,500)(32,500)(32,500)(32,500)(32,500) (32,500) (32,500)3 NPV at 8%(218,078)Purchase Current Machine4 Maintenance (20,000) (20,000)(20,000)(20,000)(20,000)(20,000)(20,000)(20,000) (20,000) (20,000)5 Depreciation 21,429 21,42921,429 21,429 21,429 21,429 21,429 — — —6 Capital Expenditures (150,000)7 FCF (purchase current)(150,000) (5,500) (5,500)(5,500)(5,500)(5,500)(5,500)(5,500)(13,000) (13,000) (13,000)8 NPV at 8%(198,183)ContinuedChapter 8 Fundamentals of Capital Budgeting 950 1 2 3 4 5 6 7 8 9 10 Purchase Advanced Machine9 Maintenance (15,000)(15,000)(15,000)(15,000)(15,000)(15,000) (15,000) (15,000) (15,000)(15,000)10 Other Costs (35,000) 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,00011 Depreciation 35,714 35,714 35,714 35,714 35,714 35,714 35,714 — — —12 Capital Expenditures (250,000)13 FCF (purchase advanced) (272,750) 9,250 9,250 9,250 9,250 9,250 9,250 9,250 (3,250) (3,250)(3,250)14 NPV at 8%(229,478)b. See spreadsheet.Evaluate: When evaluating a capital budgeting project, financial managers should make thedecision that maximizes NPV. In this case Beryl’s Iced Tea should purchase the current machine because it has the lowest negative NPV.Plan: Compute the depreciation charges and the book value of the asset during each of the five 15.years of its life. Then compute the after tax proceeds if the asset is sold after three years.Execute:a. The MACRS 5-year schedule, along with the book value:Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 MACRS schedule: 20.00%32.00%19.20%11.52% 11.52% 5.76%Depreciation charge: $ 60,000 $ 96,000 $57,600 $34,560 $34,560 $17,280Remaining book value: $240,000 $144,000 $86,400 $51,840 $17,280 $ 0b. The profits on the sale would be $180,000 − 51,840 = 128,160. The taxes on this profitwould be 128,160 × 0.35 = 44,856. Thus, the total after tax proceeds from the sale are180,000 − 44,856 = 135,144.Evaluate: The book value of the asset after three years would be $51,840. If the asset were soldafter three years for $180,000 the firm would receive $135,144 net of taxes.Plan: If the company accepts the order and does not sell the machine, determine the cost to the 16.company.Execute: Yes, the cost of taking the order is the lost $135,144 in after tax cash flow that itwould have otherwise received by selling the equipment.Evaluate: By taking the order and not selling the machine the company is foregoing the$135,144 it would have received from the sale of the machine. This is therefore a cost of takingthe order.17. a. No, this is a sunk cost and will not be included directly. (But see part (f) below.)b. Yes, this is a cost of opening the new store.c. Yes, this loss of sales at the existing store should be deducted from the sales at the newstore to determine the incremental increase in sales that opening the new store will generatefor HBS.d. No, this is a sunk cost.96 Berk/DeMarzo/Harford • Fundamentals of Corporate Financee. This is a capital expenditure associated with opening the new store. These costs willtherefore increase HBS’s depreciation expenses.f. Yes, this is an opportunity cost of opening the new store. (By opening the new store, HBSforgoes the after-tax proceeds it could have earned by selling the property. This loss is equalto the sale price less the taxes owed on the capital gain from the sale, which is the differencebetween the sale price and the book value of the property. The book value equals the initialcost of the property less accumulated depreciation.)g. While these financing costs will affect HBS’s actual earnings, for capital budgeting purposeswe calculate the incremental earnings without including financing costs to determine theproject’s unlevered net income.18. The incremental cash flows would increase in years 0 and 1, as the accelerated depreciationschedule would give Daily Enterprises a higher tax shield during those two years. In years 2through 5, the incremental free cash flows would be lower, since the depreciation expenses inthese years is lower than 20%. Overall, the present value of the free cash flows would increaseunder a MACRS depreciation schedule.19. a. $15 million/5 years = $3 million per year.b. $3 million × 35% = $1.05 million per year.c.Year0 1 2 3 4 5 MACRS DepreciationEquipment Cost 15,000MACRS Depreciation Rate 20.00%32.00% 19.20% 11.52% 11.52% 5.76%Depreciation Expense 3,000 4,800 2,880 1,728 1,728 864Depreciation Tax Shield1,050 1,680 1,008 605 605 302(at 35% tax rate)d. In both cases, its total depreciation tax shield is the same. But with MACRS, it receives thedepreciation tax shields sooner—thus, MACRS depreciation leads to a higher NPV ofMarkov’s FCF.e. If the tax rate will increase substantially, then Markov may be better off claiming higherdepreciation expenses in later years, since the tax benefit at that time will be greater.20. Plan: Under MACRS, we take the percentage in the table for each year and multiply it by theoriginal purchase price of the equipment to calculate the depreciation for that year.Execute:a. Free Cash Flows are:9…1021= Net income 4,875 4,875 4,875 4,875+ Overhead (after tax at 35%) 650 650 650 650+ Depreciation 2,500 2,500 2,500 2,500− Capex 25,000− Inc. in NWC 10,000–10000FCF −35,0008,025 8,025 …8,025 18,025Chapter 8 Fundamentals of Capital Budgeting 97b. NPV 9101118.025358.02519.5570.14 1.14 1.14⎛⎞=−+×−+=⎜⎟⎝⎠Evaluate: Compared with straight-line depreciation, the MACRS method allows for largerdepreciation deductions earlier in the asset’s life, which increases the present value of the depreciation tax shield and so will raise the project’s NPV.21. Plan: Compute the Free Cash Flow forecast for the next 10 years. Compute the NPV of the projectbased on the forecasted Free Cash Flows. Then compute the NPV under different assumptions about Initial Sales and Growth. Then compute the NPV of the project under a range of discount rates.Year 0 1 2 3 4 5 6 7 8 9 10Free Cash Flow Forecast($ millions)1 Sales — 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.02 Manufacturing — (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0)3 Marketing Expenses — (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0)4 Depreciation — (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0)5 EB I T — 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.06 Income tax at 35% —(14.0)(14.0) (14.0) (14.0)(14.0)(14.0) (14.0) (14.0) (14.0) (14.0)7 Unlevered Net Income— 26.0 26.0 26.0 26.0 26.0 26.0 26.0 26.0 26.0 26.0 8 Depreciation — 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 9 Inc. in NWC — (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0)10 Capital Expenditures(150.0) — — — — — — — — — — 11 Continuation value ——————————12.012 Free Cash Flow(150.0) 36.0 36.0 36.0 36.0 36.0 36.0 36.0 36.0 36.0 48.0 13 NPV at 12%57.3 — — — — — — — — — —Execute:a. The NPV of the estimate free cash flow is9101148NPV 1503610.12 1.12 1.12$57.3 million⎛⎞=−+×−+⎜⎟⎝⎠=b. I nitial Sales 90 100 110 NPV 20.5 57.3 94.0c. Growth Rate 0% 2% 5% NPV57.3 72.5 98.198 Berk/DeMarzo/Harford • Fundamentals of Corporate Financed. NPV is positive for discount rates below the IRR of 20.6%.Evaluate: Under the forecast assumptions the project has an NPV of $57.3 million and thereforeshould be accepted. Under various scenarios of assumed initial sales and growth the projectcontinues to have a positive NPV meaning that even if the forecast assumption proves toooptimistic or pessimistic, the project will still create firm value. Finally the discount rate used inthe forecast assumptions is 12%, but the project would have a positive NPV using any discountrate below 20.6%. The project is positive and the results are robust.*22. a. See spreadsheet.b. See spreadsheet.c. See spreadsheet.d. See data tables in spreadsheet.e. See data tables in spreadsheet.f. See spreadsheet—need additional sales of $11.384 million in years 3 to 10 for larger machineto have a higher NPV than XC-750.Incremental Effects(with vs. without XC-750)Year 0 1 2 3 4 5 6 7 8 9 10 11 Sales Revenues −5,000 10,000 10,00010,00010,00010,00010,00010,00010,000 10,000 10,000Cost of Goods Sold 3,500 −7,000 −7,000−7,000−7,000−7,000−7,000−7,000−7,000 −7,000 −7,000S, G, & A Expenses −2,000 −2,000−2,000−2,000−2,000−2,000−2,000−2,000 −2,000 −2,000 Depreciation −275 −275−275−275−275−275−275−275 −275 −275 EBIT −1,500 725 725725725725725725725 725 725 Taxes at 35% 525 −254 −254−254−254−254−254−254−254 −254 −254 Unlevered Net Income −975 471 471471471471471471471 471 471ContinuedChapter 8 Fundamentals of Capital Budgeting 99Incremental Effects(with vs. without XC-750)Year 0 1 2 3 4 5 6 7 8 9 10 11Depreciation 275275275275275275275 275 275 275Capital Expenditures −2,7501,000800Add. to Net Work. Cap. −600 −1,200000000 0 0FCF −4,325 −454746746746746746746 746 746 1,746800Cost of Capital 10.00% PV(FCF) −4,325 −413617561510463421383 348 316 673280NPV −164.6Net Working Capital Calculation810119 Year 01234567Receivables at 15% −750 1500150015001500150015001500 1500 1500 15000Payables at 10% 350 −700−700−700−700−700−700−700 −700 −700 −7000Inventory 1000 1000100010001000100010001000 1000 1000 00NWC 600 1800180018001800180018001800 1800 1800 8000Sensitivity Analysis: New SalesNew Sales (000s) 8 9 10 10.143 11 122142NPV −2472 −1318 −165 0 989Sensitivity Analysis: Cost of Goods Sold69.545%69% 70%71%COGS 67% 68%NPV 921 559 0 197 −165−526Incremental Effects(with vs. without XC-900)Year 0 1 2 3 4 5 6 7 8 9 10 11Sales Revenues −5,00010,00010,00011,38411,38411,38411,38411,38411,38411,38411,384Cost of Goods Sold 3,500−7,000−7,000−7,969−7,969−7,969−7,969−7,969−7,969−7,969−7,969S, G, & A Expenses −2,000−2,000−2,000−2,000−2,000−2,000−2,000−2,000−2,000−2,000Depreciation −400−400−400−400−400−400−400−400−400−400EBIT −1,5006006001,0151,0151,0151,0151,0151,0151,0151,015Taxes at 35% 525−210−210−355−355−355−355−355−355−355−355Unlevered Net Income −975390390660660660660660660660660Depreciation 400400400400400400400400400400Capital Expenditures −4,000Add. to Net Work. Cap. −600−1,2000−1110000001,000911FCF −5,575−4107909491,0601,0601,0601,0601,0601,0602,060911Continued100 Berk/DeMarzo/Harford • Fundamentals of Corporate FinanceIncremental Effects(with vs. without XC-900)Year 0 1 2 3 4 5 6 7 8 9 10 11Cost of Capital 10.00%PV(FCF) −5,575−373 653713724658598544494450 794319NPV 0.0Net Working Capital Calculation234567891011Year 0 1Receivables at 15% −7501500 15001708170817081708170817081708 17080Payables at 10% 350−700 −700−797−797−797−797−797−797−797 −7970Inventory 10001000 10001000100010001000100010001000 00NWC 6001800 18001911191119111911191119111911 9110New Sales8 9 10 10.40 11 12NPV −652 −326 0 129 326 652Cost of Goods Sold67% 68% 68.76% 69.00% 70% 71%NPV 1203 802 498 401 0 −40123.Real options must have positive value because they are only exercised when doing so wouldincrease the value of the investment. If exercising the real option would reduce value, managerscan allow the option to go unexercised. Thus, having the option but not the obligation to act isvaluable.24. The XC-900 allows Billingham the option to expand production starting in year 3. If it would bebeneficial to expand production, Billingham will increase production with the XC-900. If itwould be better if production remains the same, Billingham is under no obligation to utilize allof the XC-900 production capacity.25. This provides Billingham the option to abandon the investment.。

NPV
=
∑
n
t=0
NCF (1 + K
t
)
t
2010-12-11
Chap8 Capital Budgeting
16
Example used in following analysis: Expected After-tax Net Cash Flow: CFt Year Project S Project L 0 ($1,000) ($1,000) 1 500 100 2 400 300 3 300 400 4 100 600
If it has not spent enough on fixed asset, two problems may arise.
Firstly, the firm’s equipment may not be sufficiently modern to enable it to produce competitively. Secondly, if it has inadequate capacity, it may lose a portion of its market share to rival firms. And regaining customers typically requires heavy selling expenses, pricing reductions, and product improvements. All of which are costly.
Some Criteria related to NPV
2010-12-11
Chap8 Capital Budgeting
7
Capital Budgeting Decision Criteria

Normal Projects -only one sign change in sequence of cash flows
N sign changes in cash flow series.
Our Case Study
We want to help Marge Simpson, Inc. analyze the following business opportunities by using the following cash flow information. Assume Marge's opportunity cost of capital is 12%.
Think about this as we cover Chapter 7 Investment Criteria.
Which of the following investment opportunities would you prefer?
#1) Give me $1 now and I’ll give you $2 at the end of class.
NPV

C0

C1 (1 r)1

C2 (1 r)2
...
Ct (1 r)t
Net Present Value
Terminology C = Cash Flow t = time period of the investment r = “opportunity cost of capital”
Understand the advantages and disadvantages of each technique.
Understand which project to select when there is a ranking conflict between NPV and IRR.

Ignores cash flows after the payback period.
McGraw-Hill/Irwin
Copyright © 2008, The McGraw-Hill Companies, Inc.
Evaluation of the Payback Method
Serves as screening tool. Strengths of the payback period. Identifies investments that recoup cash investments quickly.
Capital Budgeting Decisions
McGraw-Hill/Irwin
Copyright © 2008, The McGraw-Hill Companies, Inc.
Typical Capital Budgeting Decisions
Plant expansion
Equipment selection Equipment replacement
What is the payback period for the espresso bar?
McGraw-Hill/Irwin Copyright © 2008, The McGraw-Hill Companies, Inc.
The Payback Method
Payback period = Investment required Annual net cash inflow $140,000 $35,000 4.0 years
1. Cost $140,000 and has a 10-year life. 2. Will generate incremental revenues of

表12.6 還本期間的計算：每年現金流量不同
表12.7 還本期間的計算：考慮現值
12.3.2 會計報酬率法
會計報酬率法(Accounting Rate of Return, ARR)也稱為投資報酬率。所採用的公 式是每年的淨收益除以投資額，或是年平均收 益除以平均經營資產，其公式如下：
假如公司要每年分別計算其投資計畫的會計報酬率， 要注意採用每年投資資產的帳面價值之平均數所 產生的結果。由於資產的帳面價值會隨時間的增 加而減少，因而造成每年的會計報酬率增加。
資本預算決策
第十二章
審慎評估長期投資 -環球購物中心
環球購物中心Global Mall，導入日本 AEON Mall 營運管理，透過中日跨國合作與經 營管理的技術轉移及成功經驗，讓台灣Global Mall 產品選擇和服務品質媲美日本水準。
學習目標
1.辨別資本預算決策種類 2.分析資本預算的現金流量 3.認識貨幣的時間價值 4.討論投資方案的評估方法 5.考量投資計畫的風險 6.研究通貨膨脹的影響 7.敘述策略性價值 8.瞭解放棄價值
投資計畫的再評估(續)
為避免發生一些人為的失誤，許多組織系統性地 追蹤進行中之專案計畫的成效，找出差異之處，以便 予以修正。此種查核的程序稱為事後稽核(post-audit or re-appraisal)。 進行事後稽核時，管理會計人員應蒐集與專案計畫實 際現金流量相關的資料，並且重新計算淨現值(net present value)，再把原來預估的數據和實際發生者 相比，若相去太遠，則需謹慎的分析其原因。
產生較多的應收帳款時，而使現金積壓的金額。 5.償付到期的應付帳款。
至於現金流入量方面，包括以下五項所造成增加現金 的方式：
1.由該項投資所增加的收入。 2.因該項投資提高生產效率所降低的生產成本。 3.折舊費用所導致的所得稅減少數。 4.投資計畫結束後，廠房設備出售的殘值收入。 5.結束投資計畫時，現金的餘額會因存貨出售和應收

Group Assignment 2Capital Budgeting DecisionDec.19.2013BE1108Group Members: 刘茹冰蔡熤A/Q1：Payback period in capital budgeting refers to the period of time required torecoup the funds expended in an investment, or to reach the break-even point. For example, a $1000 investment which returned $500 per year would have a two-year payback period. Payback period intuitively measures how long something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback periods. Payback period is popular due to its ease of use.Net present value In finance, the net present value (NPV) or net presentworth (NPW)of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows of the same entity.In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV).NPV can be described as the “difference amount” between the sums of disco unted: cash inflows and cash outflows. It compares the present value of money today to the present value of money in the future, taking inflation and returns into account.Profitability index (PI), also known as profit investment ratio (PIR) and valueinvestment ratio (VIR), is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects because it allows you to quantify the amount of value created per unit of investment.The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero. It can also be defined as the discount rate at which the present value of all future cash flow is equal to the initial investment or in other words the rate at which an investment breaks even.In more specific terms, the IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment.IRR calculations are commonly used to evaluate the desirability of investments orprojects. The higher a project's IRR, the more desirable it is to undertake the project.Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital. Investment may be limited by availability of funds to the firm and/or by the firm's capacity or ability to manage numerous projects.The Modified Internal Rate of Return (MIRR) is a financial measure of an investment's attractiveness.[1][2] It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.While there are several problems with the IRR, MIRR resolves two of them.Firstly, IRR assumes that interim positive cash flows are reinvested at the same rate of return as that of the project that generated them.[3] This is usually an unrealistic scenario and a more likely situation is that the funds will be reinvested at a rate closer to the firm's cost of capital. The IRR therefore often gives an unduly optimistic picture of the projects under study. Generally for comparing projects more fairly, the weighted average cost of capital should be used for reinvesting the interim cash flows.Secondly, more than one IRR can be found for projects with alternating positive and negative cash flows, which leads to confusion and ambiguity. MIRR finds only one value.A/Q2：Payback period as a tool of analysis is often used because it is easy to apply and easy to understand for most individuals, regardless of academic training or field of endeavor. When used carefully or to compare similar investments, it can be quite useful. As a stand-alone tool to compare an investment to "doing nothing," payback period has no explicit criteria for decision-making (except, perhaps, that the payback period should be less than infinity). The time value of money is not taken into account.The payback period is considered a method of analysis with serious limitations and qualifications for its use, because it does not account for the time value of money, risk, financing, or other important considerations, such as the opportunity cost. Whilst the time value of money can be rectified by applying a weighted average cost of capital discount, it is generally agreed that this tool for investment decisions should not be used in isolation. Alternative measures of "return" preferred by economists are net present value and internal rate of return. An implicit assumption in the use of payback period is that returns to the investment continue after the payback period. Payback period does not specify any required comparison to other investments or even to not making an investment.NPV is a central tool in discounted cash flow (DCF) analysis and is a standardmethod for using the time value of money to appraise long-term projects. Used for capital budgeting and widely used throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, above the cost of funds.If... It means...Then...NPV > 0 the investment wouldadd value to the firmthe project may be acceptedNPV < 0 the investment wouldsubtract value fromthe firmthe project should be rejectedNPV = 0 the investment wouldneither gain nor losevalue for the firmWe should be indifferent in the decision whether to accept orreject the project. This project adds no monetary value.Decision should be based on other criteria, e.g., strategicpositioning or other factors not explicitly included in thecalculation.Rules for selection or rejection of a project:If PI > 1 then accept the projectIf PI < 1 then reject the projectBecause the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment. This is in contrast with the net present value, which is an indicator of the value or magnitude of an investment.An investment is considered acceptable if its internal rate of return is greater than an established minimum acceptable rate of return or cost of capital. In a scenario where an investment is considered by a firm that has equity holders, this minimum rate is the cost of capital of the investment (which may be determined by the risk-adjusted cost of capital of alternative investments). This ensures that the investment is supported by equity holders since, in general, an investment whose IRR exceeds its cost of capital adds value for the company (i.e., it is economically profitable).The rate of return that equates the present value of a project’s cash inflows with the present value of its cash outflows i.e. it sets out the net present value equal to zero. Internal rate of return is basically used to measure the efficiency of capital investment. Internal rate of return is generally required low cost of capital to accept the project.Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return.A rate of return for which this function is zero is an internal rate of return.The period is usually given in years, but the calculation may be made simplerif is calculated using the period in which the majority of the problem is defined(e.g., using months if most of the cash flows occur at monthly intervals) andconverted to a yearly period thereafter.Any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value obtained is zero if and only if the NPV is zero.In the case that the cash flows are random variables, such as in the case of a life annuity, the expected values are put into the above formula.Often, the value of cannot be found analytically. In this case, numericalmethods or graphical methods must be used.Like the internal rate of return, the modified internal rate of return cannot be validly used to rank-order projects of different sizes, because a larger project with a smaller modified internal rate of return may have a higher present value.However, there exist variants of the modified internal rate of return which can be used for such comparisons.Page 299Q1:Construct a spreadsheet to calculate the payback period, internal rate of return, modified internal rate of return, and net present value of the proposed mine. A:year 1=-500000000+6000000=-440000000Year 2=-440000000++90000000=-350000000Year 3=-350000000+170000000=-180000000Year 4=-180000000+230000000=500000005000000-80000000=-30000000Year 5=-30000000+205000000=175000000Payback period is 4.15 years.Internal rate of return :-500000000+60000000/(1+r)+90000000/(1+r)^2+170000000/ (1+r)^3+230000000/(1+r)^4+205000000/(1+r)^5+140000000/(1+r)^6+110000000/(1 +r)^7+70000000/(1+r)^8-80000000/(1+r)^9=0Irr=18.87percentModified internal rate of return=14.748％,Finance rate=.12Reinvest rate=.12Npv=115109801.56Q2:Based on your analysis, should the company open the mine? A:payback period=4.85Irr=.1887>.12Mirr=.14748Npv is positiveIt should open the mine.。