ROI NPV Payback

NPV, IRR, and payback are the language of capital allocation. Every significant logistics investment — automation, systems, facility — is evaluated using them. If you can’t produce these numbers and explain what they mean, you won’t be in the room when the decision gets made.

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The Time Value of Money

A dollar today is worth more than a dollar in the future — due to opportunity cost, inflation, and risk. Net Present Value converts all future cash flows to their present value using a discount rate, then sums them. Positive NPV = investment creates value. Negative NPV = investment destroys value.

NPV formula:

NPV = Σ [CFt ÷ (1 + r)^t] − Initial Investment

Where CFt = cash flow in period t, r = discount rate, t = time period.

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Discount Rate Selection

WACC (Weighted Average Cost of Capital): The blended cost of a company’s debt and equity financing — the theoretically correct rate for most corporate investments.

WACC = (E/V × Re) + (D/V × Rd × (1 - T))

Hurdle rate: Many companies add a risk premium above WACC for specific project risk. A company with 8% WACC might require 12-15% returns on automation due to implementation risk.

Rule of thumb for logistics automation: 8-15% discount rates are common at mid-market companies. Always confirm with the client’s finance team — this is a critical assumption that can shift the NPV significantly.

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NPV: Worked Example

GTP automation scenario (simplified to 5 years):

• Initial investment: $4,500,000 (Year 0)
• Annual net benefit: $1,742,000 (Year 1) escalating 3%/year
• Discount rate: 10%
• Year 5 residual value: $450,000

Year	Net Benefit	Discount Factor	Present Value
0	($4,500,000)	1.000	($4,500,000)
1	$1,742,000	0.909	$1,583,478
2	$1,794,260	0.826	$1,482,059
3	$1,848,088	0.751	$1,388,514
4	$1,903,531	0.683	$1,299,711
5	$2,408,937*	0.621	$1,495,950
NPV			$2,749,712

*Year 5 includes $450,000 residual value

NPV = +$2.75M → Investment creates value. Proceed.

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Internal Rate of Return (IRR)

IRR is the discount rate at which NPV = 0. It’s the investment’s intrinsic return rate — what the investment actually generates.

For the scenario above: IRR ≈ 38%

Since 38% > 10% hurdle rate → approved.

Decision rule:

• IRR > hurdle rate: Invest
• IRR < hurdle rate: Do not invest (at this structure)
• IRR = hurdle rate: Breakeven

IRR Limitations

Multiple IRR problem: If cash flows change sign more than once, there can be multiple valid IRRs (e.g., major mid-life system overhaul cost).

Scale blindness: IRR doesn’t account for investment size. A 50% IRR on a $10K investment is often inferior to a 25% IRR on a $5M investment. Always evaluate IRR alongside NPV.

Reinvestment assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR rate — often unrealistic. Modified IRR (MIRR) uses a more realistic reinvestment rate.

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Payback Period

Simple payback: Time for cumulative cash inflows to equal initial investment. No discounting.

Payback = Initial Investment ÷ Annual Net Benefit Example: $4,500,000 ÷ $1,742,000 = 2.6 years

Discounted payback: Uses present value of cash flows — more conservative, more rigorous.

Year	PV of Net Benefit	Cumulative PV
1	$1,583,478	$1,583,478
2	$1,482,059	$3,065,537
3	$1,388,514	$4,454,051
4	$1,299,711	$5,753,762

Discounted payback: slightly over 3 years (initial $4.5M recovered between Year 3 and Year 4).

Use payback as a liquidity metric, not a value metric. Simple payback is the first number executives ask for — it’s intuitive. Don’t use it as the primary investment criterion; it ignores time value of money and doesn’t tell you total value created.

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Payback Benchmarks by System Type

System	Typical Payback	Key Driver
AMRs (picking assist, labor redeployment)	8-18 months	2-3× pick rate; labor redeployment
VLMs / Horizontal Carousels	6-18 months	Space recovery + targeted labor reduction
Packaging machines	1-2 years	Direct labor substitution
Palletizing robots (3 shifts)	10-18 months	Direct replacement; 24/7 capability
Conveyor/sortation	3-5 years	Throughput gain; sort accuracy
Mini-load AS/RS	4-6 years	Density + throughput; 15-20 year life
Unit-load AS/RS (crane)	5-7 years	20+ year life changes NPV fundamentally

The NPV reframe for CFOs: A 5-7 year payback on a unit-load AS/RS sounds long until you account for the 20+ year operating life. A $10M AS/RS at 6-year payback, generating $1.6M/year in savings, has an NPV at year 20 that dwarfs any conventional warehouse infrastructure investment. Always present NPV at full system life — not just payback in isolation.

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Sensitivity Analysis

Every NPV model has assumptions that can be wrong. Sensitivity analysis tests how much NPV changes when you vary a key assumption.

One-variable table — NPV vs. Discount Rate (same scenario):

Discount Rate	NPV
5%	$4,210,000
8%	$3,350,000
10%	$2,750,000
15%	$1,580,000
20%	$730,000
25%	$180,000
28%	~$0 (IRR)
30%	($220,000)

This investment creates value at any discount rate below 28% — a robust case.

Two-variable table — NPV vs. Discount Rate and Annual Savings:

	$1.4M/yr	$1.7M/yr	$2.0M/yr
8%	$1,850,000	$3,100,000	$4,400,000
10%	$1,200,000	$2,400,000	$3,600,000
12%	$680,000	$1,800,000	$2,900,000
15%	$80,000	$1,050,000	$2,000,000

At pessimistic savings ($1.4M/yr) and a high hurdle rate (15%), NPV is barely positive. Sensitivity analysis identifies the decision boundary — where the investment stops making financial sense. Always include it in investment presentations.

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Shift Utilization: The Most Sensitive Input

The same system achieves very different payback depending on shifts:

• AMR fleet: 8-12 month payback at 3 shifts → 20-30 months at 1 shift
• Palletizing robot: <1 year payback at 3 shifts → 4+ years at 1 shift

Nail down actual and projected shift utilization before building any ROI model. It’s the single assumption with the highest sensitivity in almost every automation business case.