Excess Return Model Calculator
The formula
What the excess return model tells you
Exactly what excess return model earned: total return, the annualised CAGR that makes it comparable, and the split between price gain and income.
Calculation: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. Enter your inputs and every substitution is shown below the result.
Reading the result
Compare with the boring alternative over the same window — the verdict bands anchor to long-run market returns; income-heavy gains are usually steadier than price-only ones.
Rules of thumb: Long-run real equity return sits near 6–7 % nominal CAGR plus inflation; bonds run 2–4 points lower.
Limitations and best practice
Ignoring the timing of income (reinvested vs spent) can overstate a CAGR by a few tenths; dividends spent as cash belong outside the ending value.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Why does CAGR differ from average yearly return?
Are taxes included?
Source & methodology
Time-weighted return arithmetic per CFA Institute conventions.
Excess Return Model: what this tool answers
Capital decisions deserve better than a gut feeling — this page gives you the arithmetic to defend one. Searchers land on an Excess Return Model page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
Like most useful measures, Excess Return Model is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
Every investing metric in Investing & Markets is a bet about the future priced in today’s language. Excess Return Model translates that bet: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. The translation is mechanical and reliable; the judgement is deciding whether the inputs you feed it are honest forecasts or wishful numbers.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here total return = 117.64%, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Buy price / invested first, at ≈20.6 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
The Excess Return Model formula, explained
One formula, published in full: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Buy price / invested ($) (example value 13,750) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Sell price / value now ($) (example value 28,750) is a measured number in the unit named by the label; the formula does not convert for you. If your source quotes a figure before and after some deduction, decide which one the formula wants and be consistent for every field.
Holding period (years) (example value 6) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. If the period is partial, decide whether you mean elapsed or planned time and keep that meaning across every field.
Income received over the hold ($) (example value 1,175) is a quantity rather than a category — precision here is cheap and worth having. If your source quotes a figure before and after some deduction, decide which one the formula wants and be consistent for every field.
A fully worked Excess Return Model example
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Buy price / invested ($), Sell price / value now ($), Holding period (years), Income received over the hold ($). Run to the end, the total return resolves to 117.64% — Strong annualised gain — well above broad-market history on the bands this tool uses.
- Ending value incl. income = $28,750.00 + $1,175.00 = $29,925.00
- Total return = (29,925.00 − 13,750.00) ÷ 13,750.00 = 117.64 %
- CAGR = (29,925.00 ÷ 13,750.00)^(1/6.0) − 1 = 13.84 % a year
Annualised (CAGR) — 13.84%. This is the number experienced users quote when the headline alone would mislead.
Net profit — $16,175.00. Read next to the headline, this is the figure that shows the shape of the trade-off.
Value multiple — 2.18 ×. Compare it against the main result of 117.64% before drawing conclusions.
Income share of gain — 7.3%. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Excess Return Model at ±10 % and ±20 % of the key input
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Excess Return Model, not an interpolation.
| Buy price / invested setting | Total return |
|---|---|
| 80 % of the example value | 172.05% |
| 90 % of the example value | 141.82% |
| example inputs | 117.64% |
| 110 % of the example value | 97.85% |
| 120 % of the example value | 81.36% |
The corridor runs from 81.36% to 172.05% across that band — which is the range worth planning inside rather than the single 117.64% point estimate. Reproduce it in the form above by editing Buy price / invested alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Excess Return Model the most
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the total return was recalculated from scratch. It is the fastest honest answer to “what matters most in Excess Return Model?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Buy price / invested +10 % → Excess Return Model = 97.85% · −10 % → 141.82% (the total return shifts ≈20.6 %)
- Nudge Sell price / value now by ±10 % and Excess Return Model lands between 96.73% and 138.55% (sensitivity ≈17.8 %)
- Income received over the hold +10 % → Excess Return Model = 118.49% · −10 % → 116.78% (the total return shifts ≈0.7 %)
Buy price / invested is the dominant lever here: ten percent either way moves the result by about 20.6 %, from 97.85% to 141.82%. Measure that input from a document rather than from memory, and treat Sell price / value now as the second priority (≈17.8 % per ten percent). The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
What an Excess Return Model of 117.64% means in practice
A number on its own is trivia; a number against a range is intelligence. On the example inputs the band reads “Strong annualised gain — well above broad-market history”; your own figures place you on a different rung of the same ladder. The sensitivity list shows how far a modest input error moves you along that ladder: for Buy price / invested, ±10 % covers 97.85% to 141.82%. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Where Excess Return Model sits next to similar measures: this tool answers “how much is the Excess Return Model”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
The errors that quietly break an Excess Return Model figure
Ignoring the timing of income (reinvested vs spent) can overstate a CAGR by a few tenths; dividends spent as cash belong outside the ending value. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Comparing an Excess Return Model computed here with a figure from another source that uses different conventions. Same name, different denominator — the disagreement is usually in the definitions, not the data.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Buy price / invested dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Excess Return Model to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Six things to confirm before acting on Excess Return Model
- Note the date and the inputs beside the number so the figure can be audited later.
- Confirm the example values are plausible for your own situation before replacing them.
- Check Buy price / invested before anything else: it is the measured dominant input, ≈20.6 % of Excess Return Model per ten percent.
- Verify each input against its original source document, not memory.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Confirm the answer against one independent method or published benchmark for Excess Return Model.
A routine for decision-grade Excess Return Model
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — one document, one pass. Open the statement, label or record that holds buy price / invested ($), sell price / value now ($), holding period (years), income received over the hold ($) and transcribe straight into the form. Transcription from a single source removes the mismatch errors that appear when figures are assembled from three different places. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. One decimal place more than your data supports is one decimal place of fiction.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. A result worth acting on survives having its two shakiest inputs halved.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Excess Return Model from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. The input you reach for first is usually the one you measured longest ago.
Step 5 — write the one-line memo. “Total return = 117.64% on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
The real-world conversations Excess Return Model settles
Numbers earn their keep in conversations, and Excess Return Model is no exception. In Investing & Markets discussions around Stocks & Equities, this figure decides whether an option stays on the table: it converts an opinionated debate into an arithmetic one, and arithmetic is the only referee both sides accept. Note the assumption you are least sure about; that is where the real risk lives.
The companion outputs — Annualised (CAGR) and Net profit — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. A figure with a date beside it becomes evidence; without one it stays an anecdote.
There is a personal-administration use people overlook: periodic self-checking. Excess Return Model quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. The inputs are the part of the work that nobody else can do for you.
The questions that come up most about Excess Return Model
What affects Excess Return Model the most?
The short answer: Buy price / invested. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the total return recalculated — Buy price / invested moved it furthest, by roughly 20.6 % (97.85% to 141.82%).
Which matters more: sell price / value now or buy price / invested?
For Excess Return Model, Buy price / invested wins the head-to-head (≈20.6 % against ≈17.8 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Excess Return Model?
With the example inputs on this page the result is 117.64%, labelled “Strong annualised gain — well above broad-market history”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Excess Return Model by hand?
Use the stated model — Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1 — and substitute in the order the tool prints (it starts from Ending value incl. income = $28,750.00 + $1,175.00 = $29,925.00). On the example inputs the hand route lands on 117.64%, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Excess Return Model if buy price / invested changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the total return goes across 97.85% to 141.82%, a swing of roughly 20.6 % around the 117.64% baseline. That ratio is the practical definition of how much this input matters.
Is the Excess Return Model result of 117.64% good or bad?
Neither, on its own — the label “Strong annualised gain — well above broad-market history” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Buy price / invested alone moves it by ≈20.6 %.
What is a good Excess Return Model?
Markets give away free benchmarks: anything that beats the relevant index after costs earns the label "good", and this tool’s verdict band translates Excess Return Model against experience ranges. Before that, check that the inputs are realistic — a great Excess Return Model built on optimistic inputs is just a nicer-looking error.
What affects Excess Return Model the most?
Sensitivity depends on where you start, but the inputs Buy price / invested ($) and Sell price / value now ($) typically move Excess Return Model further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
Why does CAGR differ from average yearly return?
CAGR compounds — it is the single steady rate that turns the start into the end, while arithmetic averages flatter volatile paths.
Are taxes included?
No, this is the pre-tax picture; subtract tax drag on gains and income before comparing with a tax-sheltered alternative.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
Glossary for Excess Return Model
- Annualised (CAGR)
- 13.84% in the default Excess Return Model calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Net profit
- $16,175.00 on the example inputs — a companion figure printed beside the headline of Excess Return Model so that no result is read in isolation.
- Value multiple
- 2.18 × on the example inputs — a companion figure printed beside the headline of Excess Return Model so that no result is read in isolation.
- Total return
- The primary output of this tool: 117.64% for the default inputs, computed exactly from Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Strong annualised gain — well above broad-market history”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Excess Return Model moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Excess Return Model calculation
Everything above runs on one stated formula, applied without hidden coefficients: Total return = (sell + income − buy) ÷ buy; CAGR = ((sell + income) ÷ buy)^(1/years) − 1. Source of record: Time-weighted return arithmetic per CFA Institute conventions. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
After the number: what to do with it
Pair this figure with the companion outputs above — the headline sizes the prize, the companions describe the risk.
This page was written for investors and founders comparing opportunities on equal terms, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.