Ten investing calculations worth doing yourself

Most investing advice is delivered as adjectives. Fees are "low", a dividend is "safe", a portfolio is "diversified". The arithmetic behind those words is usually simple, and running it yourself changes what you do more reliably than reading another opinion. Below are ten calculations worth doing, each with the answer our own free calculators produce on a realistic set of inputs, so you can see what the number looks like before you open anything.

The ten, at a glance

Every figure in this table comes from the linked calculator on its default inputs. Nothing here is rounded for effect.

Four calculations about reaching retirement

These are the same journey seen from four angles, and they are worth doing in order rather than picking the one that sounds most relevant.

Your FIRE number is the destination: annual spending divided by a withdrawal rate, which at 4% is 25 times what you spend. A thirty-year-old spending $40,000 a year, with $50,000 saved and $1,500 a month going in at a 6% real return, reaches $1 million at 52. Of that, $446,000 is money they put in; the rest is growth. The FIRE calculator gives the number and the age on your own figures.

Coast FIRE is the earliest milestone and the one most people underestimate. It is the point where what you have already saved will compound to your target on its own, with no further contributions. The formula is a single division: your target divided by growth over the years remaining. On a $1.5 million target at a 7% real return, a forty-year-old needs $276,400 to coast to 65. Reach that and saving becomes optional, which usually arrives more than a decade before independence does. The Coast FIRE calculator shows the crossover point on your own numbers.

Barista FIRE asks the same question assuming you keep earning something. Subtract your part-time income from your annual spending and apply a withdrawal rate to what is left. Spending $50,000 with $20,000 of part-time income leaves a $30,000 gap, needing $750,000 rather than the $1.25 million full independence would take. The exchange rate is exactly linear and it is striking: at 4%, every $10,000 of annual income removes $250,000 from the target.

The safe withdrawal rate question comes next, and the honest answer is not 4%. On a $1 million portfolio earning 4% after inflation over 30 years, the highest rate that survives is 5.5%. Stretch the horizon to 40 years and lower the return to 3%, which is what an early retirement actually looks like, and the ceiling falls to 4.2%. The famous rule still passes, but the margin has nearly gone.

Four calculations about growing and keeping it

Compound interest is the baseline everything else is measured against. Five thousand dollars plus $300 a month for twenty-five years at 7% becomes $271,649, of which $95,000 is money you put in. Seeing the split between contributions and growth is usually more persuasive than the total.

Dividend income is one multiplication, and the useful version runs it backwards. Twenty-five thousand dollars at a 4% yield pays $1,000 a year, or $250 a quarter. Turned around, $1,000 a month needs $300,000 at 4% and $400,000 at 3%, which shows how much a single point of yield is worth and why the highest yields deserve the most suspicion. The dividend calculator does both directions.

Dividend reinvestment adds a second compounding on top. Ten thousand dollars at a 3% yield, with the dividend growing 6% a year and the price 5%, finishes twenty years later at $49,154 with the payments reinvested against $37,569 without. The decomposition is the interesting part: annual income grows 5.9 times, which is the dividend per share growing 3.2 times multiplied by the share count growing 1.85 times. The company did roughly half the work and reinvestment did the rest. If you are choosing what to hold, our guide to the best dividend growth stocks ranks 25 of them, and how to tell if a dividend is safe covers the checks worth doing first.

The expense ratio calculation is the one that changes behaviour most often. A 1% annual fee on $10,000 plus $500 a month over thirty years takes $132,555, which is 19% of the balance you would otherwise have finished with. The reason a 1% fee costs a fifth of the pot rather than a fiftieth is that it is charged every year on a growing balance, and every dollar it takes would have compounded for the rest of your investing life.

Two calculations about individual stocks

A discounted cash flow estimates what a business is worth from the cash it will produce. One billion dollars of free cash flow growing 10% a year for five years and 6% for the next five, discounted at 9%, with $2 billion of net debt and 500 million shares, is worth $44.62 a share. The instructive part is where that value comes from: 59% of it sits in the terminal value, the years after the projection ends. Move the discount rate one point either way and the answer swings between $37.67 and $54.15. The DCF calculator makes that sensitivity visible before you rely on a single number.

Stock profit is the calculation people most often get slightly wrong, by leaving out fees and dividends or by quoting a total return without the time it took. One hundred shares bought at $50 and sold at $65 two years later, with $5 of fees each way and $1.20 a share in dividends, made $1,610. That is 32.2% in total and 15.0% a year, and the break-even sale price was $48.90, below the purchase price, because the dividends more than covered the fees. The stock profit calculator shows all four figures.

What all ten assume

None of them model tax. None of them model a market that moves in anything other than a straight line, and that is the main reason to read every answer as arithmetic rather than a forecast. A retirement plan meets its real returns in a particular order, and a bad first few years does more damage than the same years later on.

Most of them want a real return, after inflation, and a target in today's money. Five to seven percent is the range most people use for a globally diversified equity portfolio, based on long-run history. It is an assumption rather than a promise, and the honest way to use any of these is to run your preferred figure, then run it again two points lower and plan around the second answer.

Each tool states its own assumptions and limitations on the page, above the results rather than in a footnote. If a figure here disagrees with one you have seen elsewhere, the assumptions are almost always why, and ours are written down.