Project Relationships

• Independent Projects: cash flows and decision for one project are unaffected by the others
  • You can choose to do any number of them, from none to all
• Mutually Exclusive Projects: Choosing one project means you cannot choose any of the others (i.e., three different machines for the same task)
  • Evaluation: rank all alternatives and choose the single best one
• Related but not Mutually Exclusive: profitability of one project depends on whether another is undertaken (i.e., building a hotel and a parking garage, the garage is more valuable if the hotel is built)
  • Evaluation: must combine them all into possible mutually exclusive sets including the “do-nothing” option, and evaluate each set as if it were a single, large project
  • For n related projects, there are 2^n possible combinations

Minimum Acceptable Rate of Return (MARR)

MARR is the hurdle rate an investment must clear to be considered acceptable

• Represents opportunity cost of capital— the return you could earn by investing your money elsewhere at similar risk level
• If a project’s return ≥ MARR, it is acceptable, else it is rejected
• Used as the interest rate i in all subsequent formulas

Present Worth and Annual Worth Methods

Present Worth Method

• Converts all future cash flows (costs and benefits of a project into their equivalent value today using the MARR)

• For a general project: $\text{PW = Sum of PW of all cash inflows and outflows}$

• For a standard project with a first cost P and annual income A and salvage value S:

  $$ PW = -P + A*(P/A, i, N) + S*(P/F, i, N) $$

Decision Rules

• Independent Project: if PW ≥ 0, accept the project. It means the project earns at least the MARR
• Mutually Exclusive Projects: choose the alternative with the highest PW

Annual Worth Method

• Convert all cash flows into an equivalent uniform annual series over the project’s life

  • Spreads the project’s net cost/benefit into equal yearly amounts

  $$ AW = PW * (A/P, i, N) $$