Core Concepts

A shortcut for how long money takes to double: divide 72 by the annual return in percent. At 9% that is 8 years, at 6% it is 12. It works because compounding is exponential and the natural log of 2 is about 0.69, so the exact answer is roughly 69 divided by the rate. 72 is used instead because it divides cleanly by more numbers.

• Years to double is roughly 72 divided by the percentage return
• 9% doubles in about 8 years, 6% in about 12
• The exact constant is about 69, from the natural log of 2
• 72 is chosen for arithmetic convenience, it divides more cleanly
• It is accurate for mid single digit rates, less so at extremes

Whether you know why the constant is roughly 70 rather than treating 72 as magic.

Nominal is the headline number, real is what is left after inflation, so real is what your purchasing power actually did. If you earn 8% while inflation runs at 3%, the quick answer is 5%, and the precise one is 1.08 divided by 1.03 minus one, about 4.85%. The rule that matters in modeling is consistency: discount nominal cash flows at a nominal rate and real at a real rate.

• Nominal is before inflation, real is after
• Rough answer is the difference, 8% less 3% is 5%
• Precise answer is 1.08 over 1.03 minus one, about 4.85%
• Real return is what purchasing power actually did
• Match nominal cash flows to nominal rates, real to real

Whether you know the subtraction is an approximation and can give the exact form.

It is the value of the next best alternative you gave up. In valuation it is the discount rate: the return an investor could earn elsewhere at the same risk, which is why WACC is a required return rather than an accounting cost. It also shows up in deals. Cash used to fund an acquisition was earning interest, and forgoing that interest is a real cost in accretion analysis.

• The value of the next best alternative forgone
• The discount rate is an opportunity cost, not a fee
• That is why WACC is a required return, not an expense
• Cash used in a deal forgoes the interest it was earning
• Applies to time and management attention as well as money

Whether you can point to where it appears in a model rather than defining it in the abstract.

Because you can invest a dollar today and have more than a dollar next year. That opportunity cost is the core of it. Inflation and risk add to the effect, but even with zero inflation and zero risk, the ability to earn a return means money today is worth more.

• Lead with opportunity cost, not inflation
• Inflation erodes future purchasing power
• Future cash is uncertain, so it carries risk
• Time value holds even at zero inflation
• This is the entire reason we discount cash flows

Most candidates say 'inflation' first. The real answer is opportunity cost, and inflation is only one component.

Because investors have alternatives and they are risk averse. If a risky investment offered the same expected return as a government bond, nobody would hold the risky one, so its price falls until the expected return is high enough to attract a buyer. The extra return is not a reward that risk creates, it is the discount investors demand before they will accept uncertainty.

• Investors are risk averse and have safer alternatives
• Price adjusts until the expected return compensates for uncertainty
• The premium is demanded by buyers, not generated by the asset
• This is why the discount rate rises with risk in a DCF
• Only risk that cannot be diversified away earns a premium

Whether you frame it as a price adjustment rather than as a rule. The mechanism matters for the diversification follow-up.

Profit is an accounting opinion about a period, cash is a fact. Revenue is recognized when earned, not when collected, so a sale on credit is profit with no cash. Depreciation is a cost with no cash. Capex is cash with no cost. Inventory bought is cash out but not an expense until sold. Profit tells you whether the business model works, cash tells you whether you survive the quarter.

• Accrual accounting recognizes revenue and cost when earned or incurred
• Credit sales are profit today and cash later, or never
• Depreciation is expense without cash, capex is cash without expense
• Inventory ties up cash before it becomes an expense
• Profit shows the model works, cash determines survival

Whether you can give concrete examples in both directions rather than stating the principle abstractly.

It is the blended annual return the company must generate to keep everyone who funded it satisfied. Debt holders want their contracted interest, equity holders want compensation for taking the riskiest position. WACC weights those two required returns by how much of the company each provides. Any project earning more than WACC creates value, anything below it destroys value.

• The blended required return of all capital providers
• Weighted by the market value share of each
• It is a hurdle rate, not a cost the company literally pays
• Equity is more expensive because equity holders are paid last
• Returns above WACC create value, below it destroy value

Whether you can explain it as a hurdle rate. Candidates who can only recite the formula usually cannot say what it is for.

Two reasons. Equity holders are paid last in a liquidation, after every creditor, so they carry more risk and demand a higher return for it. And interest on debt is tax deductible while dividends are not, so the government subsidizes debt but not equity. The combination means the required return on equity is always above the after-tax cost of debt for the same company.

• Equity is the residual claim, paid after all creditors
• Higher risk requires higher expected return
• Interest is tax deductible, dividends are not
• The tax shield lowers the effective cost of debt further
• This holds for the same company at the same point in time

Whether you give both the risk reason and the tax reason. Most candidates give only one.

Money multiple is total cash out over cash in and ignores time entirely. IRR is the annualized rate and is extremely sensitive to time. A 3x over five years is about a 25% IRR, but the same 3x over three years is about 44%. So multiple alone ignores how long capital was tied up, and IRR alone rewards a fast small win over a large slow one. Funds are judged on both.

• Money multiple is cash out over cash in, time blind
• IRR is the annualized return and is highly time sensitive
• 3x in five years is roughly 25% IRR
• The same 3x in three years is roughly 44%
• Each hides what the other reveals, so sponsors quote both

Whether you can put rough numbers on the time sensitivity. Saying they differ is not the same as showing it.

It depends entirely on what is consuming the cash. If growth is funding working capital and capacity that will produce returns above the cost of capital, negative free cash flow is an investment and it is fine, provided the company can fund it. If the core business loses money on every unit sold, growth makes things worse. The questions are whether unit economics work and whether funding is secured.

• Ask what is consuming the cash: investment or losses
• Investment ahead of returns above WACC is value-creating
• Negative unit economics mean growth destroys value faster
• Funding access determines whether it is survivable
• Check contribution margin before judging the headline number

Whether you refuse the binary and ask what the cash is being spent on. That is the actual analytical answer.