Engineering Economic Analysis 9th Edition

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CIE412 Lecture Notes Chapter 6, 7, 7A Prof.
Bryan Pearce Department of Civil and
Environmental Engineering University of Maine
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Annual Cash Flow CalculationsResolving a Present
Cost to an Annual Cost

• Simplest case is to convert the PV to a series of
  EUAW (equivalent uniform annual worth) cash
  flows previously A.
• AP(A/P,I,N)
• A is -PMT in Excel
• Where there is salvage value
• A will be reduced by
• A(reduction) F(salvage)(A/F,i,n)

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Annual Cash Flow Four Essential Points

• EUAW PW(A/P,i,n)
• EUAW is
• Decreased by a cost
• Increased by a benefit
• In Excel use -PMT to calculate EUAW
• (remember the minus sign)
• For an irregular cash flow over the analysis
  period, first determine the PW then convert to
  EUAW

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Annual Cash Flow Analysis
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Analysis Period Considerations

• Analysis period equal to alternative lives
• Analysis period a common multiple of alternative
  lives
• Analysis period for a continuing requirement
• Some other period such as project life

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Analysis Period Equal to Alternative Lives

• Base the comparison on the life of the
  alternatives
• This is the case we have most often considered in
  our examples
• This is rarely the case in real-life
  organizations

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Analysis Period a Common Multipleof Alternative
Lives

• When the lives of the equipment in the two
  alternatives varies, use a common multiple of the
  two lives.

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Analysis Period for a Continuing Requirement

• Where the project will last forever (nothing
  does) use an infinite time period.
• In most analyses, organizations often use a
  representatively long time period to get a
  reasonable estimate.

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Some Other Period Such AsProject Life

• Physical equipment usually has a useful life that
  is different from the project life.
• In this case, use the project life as the
  analysis period.
• This is the most common case in real-life
  organizations.

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Chapter 7 RATE OF RETURN ANALYSIS Prof. Bryan
Pearce Department of Civil and Environmental
Engineering University of Maine
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Three Major Methods of Economic Analysis

• PW - Present Worth
• AW - Annual Worth
• IRR - Internal Rate of Return

If PW A(P/A,i,n) Then (P/A,i,n) PW/A Solve
for (P/A,i,n) and look up interest in Compound
Interest Tables
IRR-The idea is what interest rate makes costs
and benefits equivalent????
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Internal Rate of Return Lenders Viewpoint

• The interest rate on the balance of a loan such
  that the unpaid loan balance equals zero when the
  final payment is made.
• Given a series of payments what is the equivalent
  rate????

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Internal Rate of Return InvestorsViewpoint

• The interest rate earned on the unrecovered
  investment such that the unrecovered investment
  equals zero at the end of the life of the
  investment.

IRR(B2B7,0.5)
After calculating IRR, use calculated value to
double check EXCELs function.
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Calculating Rate of Return

• The IRR is the interest rate at which the
  benefits equal the costs. IRR i
• PW Benefit - PW Cost 0
• PW Benefit/PW Cost 1
• NPW 0
• EUAB - EUAC 0
• PW Benefit PW Cost

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Calculating IRR Previous Example

• PWB/PWC 1
• 1252.28(P/A,i,5)/5000 1
• (P/A,i,5) 5000/1252.28 3.9927

Example 7-1
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Example 7-3
The iterations may be graphed and the true IRR
will be indicated at the point where the NPW
curve 0.
Note use of Excel Funtions IRR NPV
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Calculating IRR Bond - Example 7-4

• A new corporate bond was initially sold by a
  stockbroker to an investor for 1000. The
  issuing corporation promised to pay the
  bondholder 40 interest on the 1000 face value
  of the bond every 6 months, and to repay the
  1000 at the end of 10 years. After one year the
  bond was sold by the original buyer for 950.
• What rate of return did the original buyer
  receive on his investment?
• What rate of return did the new buyer (paying
  950) expect to receive if he keeps the bond for
  its remaining 9-year life?

7-4a 1000 40(P/A,i,2) 950(P/F,i,2) By lookup
and interpolation i 1.5 Nominal rate 2 x
1.5 3 Effective rate (1 1.5)2 - 1 3.02
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Rate of Return (ROR) Analysis

• Most frequently used measure of merit in industry
• More accurately called Internal Rate of Return
  (IRR)

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Calculating ROR

• Where two mutually exclusive alternatives will
  provide the same benefit, ROR is performed using
  an incremental rate of return-DROR-on the
  difference between the alternatives.

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ROR on Alternatives with Equivalent Benefits
Example 7-5
MARR 10
Since the ROR of the difference B-A is 8, which
is less than our MARR of 10, we reject B and
accept, project A _at_ 48.7
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Examples 7- 6, 7 8
Criterion Is to Maximize Return Not ROR
What happens to NPW when MARR is varied? Try 6,
30 35.
NPV (B-A) vs i
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Fixed Input and Differing Outputs
Choose the ranking so that the difference
represents an increment of investment goes from -
to over time.
Example 7-9
We see A is preferable.
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Analysis Period

• Just as in PW and AW analysis, the analysis
  period must be considered
• Useful life of the alternative equals the
  analysis period
• Alternatives have useful lives different from the
  analysis period
• The analysis period is infinite, n 8

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Engineering Economic Analysis9th Edition

• Chapter Appendix 7A
• Difficulties Solving for an Interest Rate

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• The Going Aircraft Company has an opportunity to
  supply a large airplane to Interair, a foreign
  airline.
• Interair will pay 19 million when the contract
  is signed and 10 million one year later.
• Going estimates its second- and third-year costs
  at 50 million each.
• Interair will take delivery of the airplane
  during Year 4 and agrees to pay 20 million at
  the end of that year and the 60 million balance
  at the end of Year 5.
• Compute the rate of return on this project.

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Multiple IRR
Example 7A-1
NPV(A14/100,B2B7)
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Cash Flow Rule of Signs

• May be converted to a polynomial
• Then, by Descartes rule

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Cash Flow Rule of Signs Expands on This Notion

• There may be as many positive values of i as
  there are sign changes in the cash flow.
• Sign changes are counted when
• to -
• - to
• A zero cash flow is ignored

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Ex 7 A-2 -- Adding an oil well to an existing
field costs 4 million (4M). It will increase
recovered oil by 3.5M, and it shifts 4.5M worth
of production for Years 5,6, and 7 to earlier
years. Thus, the cash flows for Years 1 through
4 total 8M and Years 5 through 7 total -4.5M.
If the well is justified, one reason is the oil
is recovered sooner. Take a look at the IRR of
this improvement.
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What are the IRRs??
What can we do to make better sense out of this?
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• When there are two or more sign changes in the
  cash flow, we know that there are several
  possibilities concerning the number of positive
  values of i.
• Probably the greatest danger in this situation is
  to fail to recognize the multiple possibilities
  and to solve for a value of i.
• The approach of constructing the PW plot both
  establishes whether there are multiple roots and
  what their values are.
• This may be tedious to do by hand but is very
  easy with a spreadsheet (or a graphing
  calculator).

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If there is a single positive value of i, we have
no problem. On the other hand, if there is no
positive value of i, or if there are multiple
positive values, the situation may be attractive,
unattractive, or confusing. Where there are
multiple positive values of i, none of them
should be considered a suitable measure of the
rate of return or attractiveness of the cash flow.
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• Modified Internal Rate of Return (MIRR)
• Two external rates of return can be used to
  ensure that the resulting equation is solvable
  for a unique rate of returnthe MIRR.
• The MIRR is a measure of the attractiveness of
  the cash flows, but it is also a function of the
  two external rates of return.
• The rates that are external to the projects cash
  flows are (1) the rate at which the organization
  normally invests and (2) the rate at which it
  normally borrows. These are external rates for
  investing, einv, and for financing, efin.
• Because profitable firms invest at higher rates
  than they borrow at, the rate for investing is
  generally higher than the rate for investing.
• Sometimes a single external rate is used for
  both, but this requires the questionable
  assumption that investing and financing happen at
  the same rate.

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• To use MIRR, the approach is
• Combine cash flows in each period into a single
  net receipt, R, or net expense, E,.
• 2. Find the present worth of the expenses with
  the financing rate.
• 3. Find the future worth of the receipts with the
  investing rate.
• 4. Find the MIRR which makes the present worth
  and future worth equivalent.

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This process of using the MIRR has reduced the
problem to one with a single solution. However,
the solution is no better than YOUR choice of
reasonable interest rates.