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Texas A&M University College of Engineering

Class 4

Posted on July 27, 2021 by Abigail Stason

Print out this page and bring it to class with you.
Learning Objectives – Class 4

After today’s lecture, and after working the homework problems, the student should be able to

  • Solve problems where an alternative choice is to be made between projects
  • Be able to chose between alternative projects on the basis of net present benefit/value/worth.
  • Be able to calculate the net present worth of a project
  • Be able to transform alternative projects onto an equivalent time basis
  • Be able to compare projects on the basis of net present worth
  • Be able to compare projects on the basis of annual cash flow analysis
  • Recognize that when a bank says 6% interest, they mean 6% nominal per year, not 6% per month, not 6% per day, not anything else! DOES THIS LOOK FAMILIAR?

Topics covered in today’s class

  1. Review how to move F, P, A, G under non-standard numbering conditions
  2. The “correct” answer – maximize Net Benefits, either present, future, or annual
  3. The “incorrect” answer – maximize benefit/cost ratio or internal rate of return
  4. Example of calculation of Net Present Value (or Worth) of Benefits = present value (or worth) of benefits – present value (or worth) of costs, for a single project
  5. Example of comparison of two projects using NPV
  6. Where did the project data in <Table 14.1 page 370 in 1st edition book> {Table 15.1 page 406 in 2nd edition} come from? From the NPV of expanded information found in <Table on page 384 in 1st edition> {Table on page 419 in 2nd edition}, and shown at the bottom of this page.
  7. How to compare two projects with equal life spans
  8. How to compare two projects with unequal life spans
    • Use multiple lifetimes for the projects until they have the same lifetime
    • Use Annual Worth Analysis rather than Net Present Value Analysis
    • Why it works
  9. Commonly used criteria:
    • NPV >= 0 (Net Present Value = Present Value (or Worth( of Benefits – Present Value (or Worth) of Costs)
    • NFV >= 0 (Net Future Value)
    • NAV >= 0 (Net Annual Value)
    • B/C Ratio >= 1 (Benefit/Cost Ratio)
    • IRR >= MARR (Internal Rate of Return >= Minimum Attractive Rate of Return)
    • Payback Period <= some time?

    Examples of non-standard cash flows:

EXAMPLE – Incremental Rates of Return Analysis – page 384 (1st edition) – page 419 (2nd edition) Revelle:

MARR = 8% Delta Delta Delta Delta

Added

Delta

Year Project E C A A-C D D-C F F-D B B-D M M-D
0 Cost -$5.000 -$7.000 -$10.000 -$3.000 -$12.000 -$5.000 -$16.000 -$4.000 -$19.000 -$7.000 -$24.000 -$12.000
1 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
2 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
3 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
4 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
5 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
6 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
7 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
8 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
9 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
10 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $0.300 $2.833 $0.300 $5.060 $2.527
 PVC -$5.00 -$7.00 -$10.00 -$3.00 -$12.00 -$5.00 -$16.00 -$4.00 -$19.00 -$7.00 -$24.00 -$12.00
PVB $3.00 $11.00 $12.00 $1.00 $17.00 $6.00 $19.01 $2.01 $19.01 $2.01 $33.95 $16.96
NPV ($2.00) $4.00 $2.00 ($2.00) $5.00 $1.00 $3.01 ($1.99) $0.01 ($4.99) $9.95 $4.96
B/C 0.60 1.57 1.20 0.33 1.42 1.20 1.19 0.50 1.00 0.29 1.41 1.41
IRR -1.987% 19.457% 12.250% -11.048% 16.541% 12.250% 12.011% -4.916% 8.011% -13.035% 16.509% 16.476%
MARR = 16%                                      Delta                        Delta                       Delta                      Delta     Added       Delta
Year Project E C A A-C D D-C F F-C B B-C M M-C
0 Cost -$5.000 -$7.000 -$10.000 -$3.000 -$12.000 -$5.000 -$16.000 -$9.000 -$19.000 -$12.000 -$24.000 -$17.000
1 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
2 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
3 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
4 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
5 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
6 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
7 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
8 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
9 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
10 Income $0.447 $1.639 $1.788 $0.149 $2.533 $0.894 $2.833 $1.194 $2.833 $1.194 $5.060 $3.421
PVC -$5.00 -$7.00 -$10.00 -$3.00 -$12.00 -$5.00 -$16.00 -$9.00 -$19.00 -$12.00 -$24.00 -$17.00
PVB $2.16 $7.92 $8.64 $0.72 $12.24 $4.32 $13.69 $5.77 $13.69 $5.77 $24.46 $16.53
NPV ($2.84) $0.92 ($1.36) ($2.28) $0.24 ($0.68) ($2.31) ($3.23) ($5.31) ($6.23) $0.46 ($0.47)
B/C 0.43 1.13 0.86 0.24 1.02 0.86 0.86 0.64 0.72 0.48 1.02 0.97
IRR -1.987% 19.457% 12.250% -11.048% 16.541% 12.250% 12.011% 5.500% 8.011% -0.091% 16.509% 15.261%

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