Choose among alternatives, not only projects
An independent acceptance test and a mutually exclusive selection problem require different decision rules.
| Project | PW ($) | Individual IRR |
|---|---|---|
| A | 3,267.75 | 22.106% |
| B | 3,430.90 | 15.238% |
PW(A)=$3,267.75; PW(B)=$3,430.90. Among mutually exclusive optional investments, choose B.
Use one viewpoint, MARR, and common five-year study period.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
What the model means
Unconstrained independent investments can all be accepted if each meets MARR. Mutually exclusive investments compete for one role: select the greatest PW among feasible options on a common basis. Include do nothing when the investment is optional.
Build the calculation
For mandatory service with equal benefits, use cost-only analysis and choose minimum equivalent cost. For unequal lives establish a repeatability or study-period assumption before ranking. Benefits, constraints, taxes, and terminal values must be treated consistently across options.
Set up. Calculate. Explain.
Rebuild the starting scenario
MARR: 10 % per year; Additional annual benefit of B: 4000 $/year. Calculate the PW(B) minus PW(A).
Setup hint
Use one viewpoint, MARR, and common five-year study period.
Open the visual solution
- Use one viewpoint, MARR, and common five-year study period.
- For independent unconstrained projects, every PW ≥ 0 project can be accepted.
- For mutually exclusive projects, only one can be chosen: maximize PW including do nothing if optional. Mandatory cost alternatives instead minimize equivalent cost.
| Project | PW ($) | Individual IRR |
|---|---|---|
| A | 3,267.75 | 22.106% |
| B | 3,430.90 | 15.238% |
PW(A)=$3,267.75; PW(B)=$3,430.90. Among mutually exclusive optional investments, choose B.
Use one viewpoint, MARR, and common five-year study period.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Transfer the idea to a new scenario
At MARR 12%, A costs $10,000 and earns $3,500/year for five years. B costs $25,000 and earns $7,000/year. Calculate PW(B)−PW(A).
Setup hint
Use one viewpoint, MARR, and common five-year study period.
Open the visual solution
- Use one viewpoint, MARR, and common five-year study period.
- For independent unconstrained projects, every PW ≥ 0 project can be accepted.
- For mutually exclusive projects, only one can be chosen: maximize PW including do nothing if optional. Mandatory cost alternatives instead minimize equivalent cost.
| Project | PW ($) | Individual IRR |
|---|---|---|
| A | 2,616.72 | 22.106% |
| B | 233.43 | 12.376% |
PW(A)=$2,616.72; PW(B)=$233.43. Among mutually exclusive optional investments, choose A.
Use one viewpoint, MARR, and common five-year study period.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
For mutually exclusive optional investments, select:
Can you defend your setup?
Can you place each amount on the timeline, match the interest period, calculate the equivalent quantity, and state the decision or limitation?
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