riaology
Learning path 5 · Topic 26 of 30

Compare dollars, returns, and liquidity carefully

Present worth, IRR, and payback are different measures. They can conflict because they express value creation, relative return, and recovery speed.

Change a scenario. Watch the consequence.
ProjectPW scoreIRR scorePBP scoreWeighted total
A10.40.20.6500
B0.610.60.7000
C0.30.610.5500
largest weighted project score · scoreSj=wPWsPW,j+wIRRsIRR,j+wPBPsPBP,j,Smax⁡=0.7S_j=w_{PW}s_{PW,j}+w_{IRR}s_{IRR,j}+w_{PBP}s_{PBP,j},\quad S_{\max}=0.7

Project B has the highest weighted score. Pre-normalized illustrative scores are benefit oriented; shorter payback was converted to a larger score.

Follow the reasoning

Define criteria, direction of preference, and comparable dimensionless scales.

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.

01

What the model means

For multiple criteria, define a scale for each attribute and its direction of preference. A benefit-oriented score increases when the attribute improves; payback usually needs reversal because shorter is preferred. Then assign weights that sum to one.

02

Build the calculation

A weighted score Σw_js_j is sensitive to normalization and preferences. It does not make an economically unacceptable project feasible or eliminate hard safety constraints. Use sensitivity analysis instead of claiming one set of subjective weights is uniquely correct.

Sk=∑jwjsjk,wj≥0,∑jwj=1S_k=\sum_j w_js_{jk},\quad w_j\ge0,\quad\sum_jw_j=1
Practice with feedback

Set up. Calculate. Explain.

Answer unit: score

Rebuild the starting scenario

Weight on present worth: 0.5 fraction; Weight on return (remaining weight shared): 0.5 fraction of remainder. Calculate the largest weighted project score.

Setup hint

Define criteria, direction of preference, and comparable dimensionless scales.

Open the visual solutionSj=wPWsPW,j+wIRRsIRR,j+wPBPsPBP,j,Smax⁡=0.7S_j=w_{PW}s_{PW,j}+w_{IRR}s_{IRR,j}+w_{PBP}s_{PBP,j},\quad S_{\max}=0.7
  1. Define criteria, direction of preference, and comparable dimensionless scales.
  2. Weights sum to one; change them to inspect preference sensitivity.
  3. This is a preference model, not a theorem that combines dollars, percentages, and years directly. Economic feasibility and hard constraints should be checked separately.
ProjectPW scoreIRR scorePBP scoreWeighted total
A10.40.20.6500
B0.610.60.7000
C0.30.610.5500
largest weighted project score · scoreSj=wPWsPW,j+wIRRsIRR,j+wPBPsPBP,j,Smax⁡=0.7S_j=w_{PW}s_{PW,j}+w_{IRR}s_{IRR,j}+w_{PBP}s_{PBP,j},\quad S_{\max}=0.7

Project B has the highest weighted score. Pre-normalized illustrative scores are benefit oriented; shorter payback was converted to a larger score.

Visual solution

Define criteria, direction of preference, and comparable dimensionless scales.

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.

Answer unit: score

Transfer the idea to a new scenario

Set weight on PW to 0.30. Give IRR 60% of the remaining weight and PBP the rest. Find the highest project score from the displayed normalized scores.

Setup hint

Define criteria, direction of preference, and comparable dimensionless scales.

Open the visual solutionSj=wPWsPW,j+wIRRsIRR,j+wPBPsPBP,j,Smax⁡=0.768S_j=w_{PW}s_{PW,j}+w_{IRR}s_{IRR,j}+w_{PBP}s_{PBP,j},\quad S_{\max}=0.768
  1. Define criteria, direction of preference, and comparable dimensionless scales.
  2. Weights sum to one; change them to inspect preference sensitivity.
  3. This is a preference model, not a theorem that combines dollars, percentages, and years directly. Economic feasibility and hard constraints should be checked separately.
ProjectPW scoreIRR scorePBP scoreWeighted total
A10.40.20.5240
B0.610.60.7680
C0.30.610.6220
largest weighted project score · scoreSj=wPWsPW,j+wIRRsIRR,j+wPBPsPBP,j,Smax⁡=0.768S_j=w_{PW}s_{PW,j}+w_{IRR}s_{IRR,j}+w_{PBP}s_{PBP,j},\quad S_{\max}=0.768

Project B has the highest weighted score. Pre-normalized illustrative scores are benefit oriented; shorter payback was converted to a larger score.

Visual solution

Define criteria, direction of preference, and comparable dimensionless scales.

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.

Explain the distinction

Why normalize criteria before weighting?

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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