Chapter 7 Problem

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Chapter 7 Problem 4

• Problem 4
• FastTrack Bikes, Inc. is thinking of developing a
  new composite road bike. Development will take
  six years and the cost is 200,000 per year.
  Once in production, the bike is expected to make
  300,000 per year for 10 years. Assume the cost
  of capital is 10.
• Calculate the NPV of this investment opportunity.
  Should the company make the investment?
• Calculate the IRR and use it to determine the
  maximum deviation allowable in the cost of
  capital estimate to leave the decision unchanged.
• How long must development last to change the
  decision?

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Chapter 7 Problem 4

• Cost is a 6 year annuity. Revenue is a 10 year
  annuity starting at the end of the 7th year.
• PV(Cost)
• 6N200000PMT10I/YR
• PV-871,052
• PV(Revenue)
• 10N300000PMT10I/YR
• PV-1,843,370
• Remember to discount back 6 periods
• 6N1,843,370FV10I/YRPV
• -1,040,534
• NPV-871,0521,040,534169,482

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Chapter 7 Problem 4
4
Chapter 7 Problem 4

• IRR
• -200000CF-200000CF
• 300000CF..300000CF
• IRR12.66
• If the cost of capital estimate is off by 2.66,
  then the decision might change from accept to
  reject.

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Chapter 7 Problem 16

• You are considering investing in a new gold mine
  in South Africa. Gold in South Africa is buried
  very deep, so the mine will require an initial
  investment of 250 million. Once this investment
  is made, the mine is expected to produce revenues
  of 30 million per year for the next 20 years.
  It will cost 10 million per year to operate the
  mine. After 20 years, the gold will be depleted.
  The mine must then be stabilized on an ongoing
  basis, which will cost 5 million per year in
  perpetuity. Calculate the IRR of this investment.

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Chapter 7 Problem 16

• Initial Cost 250
• Income
• Revenue 30 for 20 years
• Cost 10 for 20 years
• Stabilization
• Cost 5/year in perpetuity
• NPV-250PVbenefits-PVstabilization

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Chapter 7 Problem 16

• What is the IRR?
• No IRR!

8
Finance 350 Business FinanceNPV and
Fundamentals of Capital Budgeting (Slide 8)

• Instructor Yen-cheng Chang

9
Review

• Investment Decision Rules
• NPV
• Payback Period
• No discounting
• Subjective cut-off period
• IRR
• Unconventional CFs

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Preview

• IRR
• Mutually exclusive projects scale and timing
• Projects with different lives
• Equivalent Annual Annuity
• Choosing among projects when resources are
  limited
• Chapter 8 Fundamentals of Capital Budgeting

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Mutually Exclusive Investment Decisions

• The problem of Scale
• Earning 100 over 1 is not as good as earning
  10 over 1,000,000.
• Compare two business ventures with the same
  scale, r12
• (1) Joint venture with your girlfriend
• -10000, 6000, 6000, 6000
• NPV4,411
• IRR36.3
• (2) Solo venture in Internet café
• -10000, 5000, 5000, 5000
• NPV2,009
• IRR23.4

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Mutually Exclusive Investment Decisions
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Mutually Exclusive Investment Decisions

• What happens if I can scale up my solo venture by
  5 times?
• (1) Joint venture with your girlfriend
• -10000, 6000, 6000, 6000
• NPV4,411
• IRR36.3
• (2) Solo venture in Internet café
• -50000, 25000, 25000, 25000
• NPV10,046
• IRR23.4

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Mutually Exclusive Investment Decisions

• Choose Internet Café whenever the cost of capital
  is lower than 20.
• IRR always favors girlfriends business.

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Mutually Exclusive Investment Decisions

• The problem of CF timing

• Project As revenue concentrated in later periods
• Project Bs revenue concentrated in earlier
  periods

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Crossover Point

• Crossover rate The discount rate that makes the
  NPVs of two projects equal.
• To find the crossover rate, take the difference
  in cash flows first
• Year 0 1 2 3 4
• CF -100 -75 0 75 150
• Then find the IRR using the differenceCrossover
  rate 8.07Check NPV 47.36

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IRR

• Why use this rule?
• Consider time value of money
• Easier to talk about the rate of return for a
  project than to talk about the dollar value of
  the project.
• Disadvantages
• Can not deal with nonconventional cash flows
  multiple answers
• May lead to incorrect decisions in comparing
  mutually exclusive investments
• The bottom line Only invest in the project if
  the IRR is greater than the opportunity cost of
  capital.

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Projects with Different Lives

• Scenario (1) Comparing solutions to the same
  problem. (2) Solutions have different lives
  before it can be renewed. (3) Our business
  requires this solution for long term.
• Internal network servers, assembly line
  equipments, office building contracts, etc.

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Projects with Different Lives

• Example Compare two internal accounting
  software
• Option A (2 years)
• -100, -10, -10
• Option B (3 years)
• -140, -8, -8, -8
• Discount rate 10
• NPVA-117
• NPVB-159
• Can we use NPV to compare Option A Option B?

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Projects with Different Lives

• Compute a per year cost for the two alternatives
  Equivalent Annual Annuity (annuity payment)
• Find the constant annual payment that gives the
  project NPVs (annuity PV).
• Project A
• PV117 r10 N2
• C67.41
• Project B
• PV159 r10 N3
• C63.94
• Which is cheaper?

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Projects with Different Lives

• We assumed both solutions would be required for
  long term.
• What if we only require the service for only 2
  years?
• Option A (assuming we could resell the license
  for a price at the end of the 2nd year)
• -100, -8, -2
• Option B
• -140, -8, -8
• Use NPV

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Projects with Limited Resources

• What happens when we have limited resources to
  devote to multiple NPVgt0 projects?
• Limited resources human capital, budget, office
  space, etc.
• Goal Exhaust available resource to create the
  highest total NPV.
• Compute the
• Profitability Index
• NPV/Resource Consumed

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Projects with Limited Resources

• Example 26
• Orchid Biotech Company is evaluation several RD
  projects for drugs.
• Suppose Orchid has a budget of 60 million. How
  should it prioritize projects?
• Suppose Orchid has 12 scientists. How should it
  prioritize projects?

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Projects with Limited Resources

• What are the PIs of the projects based on initial
  capital?
• What are the PIs of the projects based on
  research scientists?
• Use PI to rank projects until the total required
  resource is exhausted.

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Chapter 8 Fundamentals of Capital Budgeting

• Capital Budgeting the decision making process
  for investment decisions, i.e., deciding how much
  and what to invest in.
• We measure the incremental cash flows associated
  with investment proposals and compare the PV of
  future cash flows to the projects initial
  investment amount.
• NPVCF0PV(future incremental free cash flow)
• The two primary tasks in evaluating investment
  proposals are
• Measuring the relevant, or incremental free CFs,
  and
• Determining the appropriate discount rate.

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Incremental Earnings

• Earning is an accounting concept.
• Consider an investment in a new equipment
  (operational for 5 years).
• Equipment 1,020,000
• Cost 1,000,000
• Shipping Installation 20,000
• Plant redesign 50,000
• Revenue 500,000/year
• Cost 150,000/year
• Cost of Goods Sold
• Operational Expenses
• Accounting reminder To compute earnings,
  investment expenses in plant, property, and
  equipment are computed as depreciation for each
  period.
• Not a real CF outflow

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Incremental Earnings

• Incremental earnings before interest and taxes
  (EBIT)
• Incremental revenue Incremental cost
  Depreciation
• Depreciation (per period)
• 1,020,000/5
• 204,000
• Incremental earnings
• EBIT X (1 Corporate Tax Rate)
• Ignore interest payments unlevered net income,
  unlevered earnings

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Incremental Earnings
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Cash is King

• How can I adjust (unlevered) earnings to reflect
  incremental cash flows?
• Depreciation is not a cash outflow add back
• Depreciation is still important because it
  affects tax (cash flow)
• Capital expenditure is a cash outflow subtract
• Changes in Net Working Capital subtract
• NWCCash Inventory Receivables - Payables

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Cash is King

• Compute the project incremental free cash flows

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Cash is King

• Example 8.4
• Assume receivables are 15 of sales payables are
  15 of COGS.
• New equipment costs 7.5m upfront.
• Compute the incremental FCFs.

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Cash is King

• Compute NWC

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Cash is King

• Compute the project FCF

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NPV

• To compute the NPV, we should use FCFs in the
  numerator.
• If we assume the yield curve is flat
• Well learn about how to estimate the denominator
  (cost of capital) later.