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62/3335–8FE Reference Handbook 10.4 · Engineering Economics · Risk
1. Simple Interest2. Single-Payment Compound Amount (F/P)3. Single-Payment Present Worth (P/F)4. Uniform-Series Compound Amount (F/A)5. Sinking-Fund Factor (A/F)6. Capital-Recovery Factor (A/P)7. Uniform-Series Present Worth (P/A)8. Effective Interest Rate9. Arithmetic Gradient Present Worth (P/G)10. Net Present Worth11. Benefit–Cost Ratio12. Straight-Line Depreciation13. Geometric Gradient Present Worth14. Capitalized Cost (Perpetual PW)15. Payback Period16. Break-Even Quantity17. Equivalent Uniform Annual Worth18. Internal Rate of Return vs MARR19. MACRS Depreciation20. Declining-Balance Depreciation21. Inflation and Real Interest22. Expected Value of Alternatives

Handbook formula

Expected Value of Alternatives

Under risk with given probabilities, pick the alternative with the best expected NPW (or AW). Variance is a second tie-breaker if the problem asks for risk attitude.

Probability of outcome i
Payoff (NPW) of outcome i

Step-by-step solved example

Project: 0.3 chance of NPW=$40k, 0.7 of $10k. E[NPW]?

E[X]12345An
Two (or more) possible NPW outcomes weighted by probability.

  1. 1. Compute

    0.3×40+0.7×10=12+7=19 k$.

  2. 2. Decision

    Compare with do-nothing (0) or other E[NPW].

Answer: E[NPW]=$19,000

10 practice questions

0/10 correct

1.Probabilities of a complete set of outcomes must sum to

2.A risk-neutral decision maker maximizes

3.E[aX+b] =

4.If two outcomes 20 and 0 are equally likely, E =

5.Variance is

6.A sure $10 vs 50% of $20: risk-neutral is

7.Decision trees fold back by

8.p=0.2, x=100; p=0.8, x=−10; E =

9.If probabilities are unknown, FE problems may use

10.Correlation between two projects matters when