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Class 5

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Print out this page and bring it to class with you.   <—NOTE!!!
Learning Objectives – Class 5

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

  • Use incremental benefit-cost ratio analysis to determine the relative value of competing projects
  • Use incremental rate of return analysis to determine the relative value of competing projects
  • Be able to define and explain how a company would set their Minimum Attractive Rate of Return
  • Be able to compute the Internal Rate of Return on an project
  • Be able to compute the payback period for a project
  • Be able to perform a break-even analysis for two competing projects

Topics covered in today’s class

  1. Review of Capitalized Costs
  2. Review of Present Worth Analysis
  3. Importance of drawing a Cash Flow Diagram for all problems
  4. Why Future Worth Analysis, Present Worth Analysis, and Annual Worth Analysis always give the same results when selecting a project
  5. Why Future Worth Analysis is not normally used
  6. When Annual Worth Analysis SHOULD be used
  7. Benefit/Cost Ratio analysis
  8. Internal Rate of Return analysis
  9. Incremental Benefit/Cost Ratio analysis
  10. Incremental Internal Rate of Return analysis
  11. Minimum Attractive Rate of Return
  12. Payback period
  13. Breakeven Analysis
  14. Example showing why you cannot use NPV to compare two projects with different lives

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

Note: See below for example on how to calculate IRR

MARR = 8%
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%
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%

Excel spreadsheet to easily calculate Internal Rate of Return

Example of how to calculate the IRR by hand (like you must be prepared to do on an exam):

To calculate the Internal Rate of Return (istar) for the cash flow of Project D, 8% (see table above) you have an initial cost of $12.000, and an annual income of $2.533.

– P + A [ P/A, istar, n ] = 0
– $12.000 + $2.533 [ P/A , istar, 10 ] = 0
[ P/A, istar, 10 ] = 12.000 / 2.533 = 4.737

so you need to find an interest page on which the [ P/A, istar, 10 ] = 4.737, which is between the 16% and 17% page, or by interpolation = 16.5%.