Tax · super (composes 4 primitives)

Salary negotiation math

Two offers, side-by-side total comp. We chain base salary, target bonus, signing bonus amortized over expected tenure, RSU vesting present-valued, cost-of-living adjustment between cities, and after-tax cash delta.

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Inputs

Current base salaryCurrent target bonus %Current annual RSU vest valueOffer base salaryOffer target bonus %Offer signing bonusOffer RSU grant value (4-yr total)RSU vest yearsExpected tenure at new roleCost-of-living change (% increase = move to pricier city)Combined marginal tax rate

Result

Take it — $40,587/yr after-tax real (post-COL) gain. 4-yr total: +$292,400.

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Take it: After-tax real upside is meaningful. The 4-yr delta of $292,400 compounds — career-stage roles compound 10-15 yrs out.

1
Current total comp
$196,750
$145,000 base + 15% bonus + $30,000 RSU annual
2
Offer year-1 total comp
$288,600
$178,000 base + 20% bonus + $25,000 signing + $50,000 RSU
3
RSU annual vest (PV)
$50,000
$200,000 grant ÷ 4 years (assumes flat stock — most grants are net of equity-risk discount)
4
Signing amortized
$6,250/yr × 4 yrs
Most signing bonuses claw back if you leave inside year 1
5
Cost-of-living adjustment (+12%)
$235,357
Steady-state offer $263,600 ÷ (1 + COL)
6
After-tax annual delta
$45,458
Both at 32% marginal — flat-tax simplification
7
After-tax + COL adjusted
$40,587
Real purchasing power difference
8
4-year total compensation delta
$292,400
Captures full RSU vest + bonuses, ignores COL

Assumptions & notes

Signing bonuses usually claw back if you leave under 12 months. Read the offer letter carefully.
RSU value assumes flat stock — public-company grants are typically rated against the stock price at grant date.
COL adjustment is a single-number proxy. Specific cost categories (housing, childcare, state tax) deserve their own analysis if the move is between very different markets.

Multi-scenario comparison

What if — ±20% on one input

Vary

Scenario	Current base salary	Headline	Δ vs baseline
−20% (cautious)	$116,000	Take it — $60,836/yr after-tax real (post-COL) gain. 4-yr total: +$425,800.	$-33,350
Baseline	$145,000	Take it — $40,587/yr after-tax real (post-COL) gain. 4-yr total: +$292,400.	0
+20% (aggressive)	$174,000	Take it — $20,339/yr after-tax real (post-COL) gain. 4-yr total: +$159,000.	+$33,350

Try the input with the highest sensitivity (above). The Δ column shows the dollar swing from a 20% move — that's how much room you have for a counter, raise, or hedge.

Goal seek

Solve for an input value

Pick the input you want to vary and the output you care about. We'll find the input value that gets you to the target. Bisection-based; converges in < 50 iterations.

Vary inputTarget outputTarget value

Monte Carlo simulation

Distribution under input uncertainty (500 trials)

We perturb every numeric input with normal-distributed noise (10–25% sigma depending on input type) and run 500 compute trials. The output is a probability distribution, not a single number — closer to how finance actually works.

Most-leveraged inputs (sensitivity analysis)

Where to focus — what moves the answer most

Each input perturbed ±10%; measured impact on Current total comp. Higher elasticity = bigger lever.

1
Current base salary
Elasticity ↑ 0.85× — 10% change in this input increases Current total comp by 8.5%.
2
Current annual RSU vest value
Elasticity ↑ 0.15× — 10% change in this input increases Current total comp by 1.5%.
3
Current target bonus %
Elasticity ↑ 0.11× — 10% change in this input increases Current total comp by 1.1%.
4
Offer base salary
Elasticity ↕ 0.00× — 10% change in this input affects Current total comp by 0.0%.

ShowMath is the only calc site that surfaces this. Adjust the highest-leverage input first — that's where small moves create big results.

Chain payload (for the 3D constellation)

{
  "slug": "salary-negotiation-math",
  "depth": 1,
  "primitives": [
    "total-comp-calculator",
    "rsu-vesting-calculator",
    "cost-of-living-adjustment",
    "tax-bracket-calculator"
  ],
  "composes": [],
  "chain": [
    {
      "key": "current_comp",
      "label": "Current total comp",
      "primitive": "total-comp-calculator",
      "numeric": 196750
    },
    {
      "key": "offer_yr1",
      "label": "Offer year-1 total comp",
      "primitive": "total-comp-calculator",
      "numeric": 288600
    },
    {
      "key": "rsu_pv",
      "label": "RSU annual vest (PV)",
      "primitive": "rsu-vesting-calculator",
      "numeric": 50000
    },
    {
      "key": "signing_amort",
      "label": "Signing amortized",
      "numeric": 6250
    },
    {
      "key": "col_adjustment",
      "label": "Cost-of-living adjustment (+12%)",
      "primitive": "cost-of-living-adjustment",
      "numeric": 235357.14285714284
    },
    {
      "key": "after_tax_delta",
      "label": "After-tax annual delta",
      "primitive": "tax-bracket-calculator",
      "numeric": 45457.99999999997
    },
    {
      "key": "real_delta",
      "label": "After-tax + COL adjusted",
      "numeric": 40587.49999999997
    },
    {
      "key": "four_year",
      "label": "4-year total compensation delta",
      "numeric": 292400
    }
  ]
}

The chain explained

Each step above corresponds to a primitive calculator. Click any to see the stand-alone version with its own explainer + sources.

total comp calculatorshipping soon
rsu vesting calculatorshipping soon
cost of living adjustmentshipping soon
tax bracket calculatorshipping soon

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