The science of value. Every financial decision boils down to one question: is this worth more than it costs, once you account for time and risk? Master a single idea β the time value of money β and the rest unfolds from it.
1The big idea
Finance = value across time & risk
Money has a price for waiting (time) and a price for uncertainty (risk). Finance gives you one consistent way to compare cash flows that arrive at different times and carry different risks β by translating them all into value today.
TimeCash sooner is worth more than the same cash later β you could invest it in the meantime.
RiskCash that's uncertain is worth less than cash that's guaranteed. Riskier bets must promise more.
Memory hook π§ The whole subject is one sentence: "a euro today is worth more than a euro tomorrow." Everything else is just doing that idea with arithmetic.
2The cornerstone
The Time Value of Money
Because money can earn a return, the same amount is worth different things at different times. Pushing money forward in time grows it (compounding); pulling it backward shrinks it (discounting).
Same β¬100, two directions: compound it forward to grow, discount it backward to value future money today.
The discount rate (r)The interest/return rate is the engine. It bundles together the reward for waiting and the compensation for risk. A higher r means future money is worth much less today.
3The two core formulas
Present Value & Future Value
These two formulas are mirror images β one multiplies, one divides by the same factor (1+r)n.
Future value β growing money forward
FV = PV Γ (1 + r)n
β¬100 at 10% for 3 years β 100 Γ 1.1Β³ = β¬133.10
Present value β pulling money back to today
PV =
FV(1 + r)n
β¬133.10 in 3 years at 10% β 133.10 Γ· 1.1Β³ = β¬100 today
Memory hook π§ Forward = multiply, backward = divide. Compounding and discounting are the same factor (1+r)n used in opposite directions.
4Why the future shrinks
Discounting Visualized
A stream of equal future payments isn't worth its face value today. Each year further out is discounted harder β so the present value of distant cash melts away.
Each bar is the same β¬100 promised β but the further away it is, the less it's worth today.
Discount factorThe shrink factor for year n is 1 Γ· (1+r)n. At 10%, year 1 = 0.909, year 5 = 0.621, year 30 β 0.057. Distant cash is almost worthless today at high rates.
5β The decision rule
Net Present Value (NPV)
The king of capital budgeting. Take a project's future cash flows, discount each back to today, add them up, and subtract what you paid upfront. If what comes back (in today's money) beats what you put in, the project creates value.
Red = money out now. Green = discounted money back. NPV is the net of the two, in today's euros.
Net present value
NPV =
Ξ£CFt(1 + r)t
β Initial Investment
Sum the present value of every future cash flow, then subtract the upfront cost.
NPV > 0 β ACCEPT. The project earns more than your required return; it adds value.
NPV < 0 β REJECT. It returns less than the discount rate demands; it destroys value.
Memory hook π§ NPV = value created, in today's money. Positive = the project is worth more than it costs. It's the single most trusted rule in finance.
6The break-even rate
Internal Rate of Return (IRR)
The IRR is the discount rate that makes NPV exactly zero β the project's own built-in return. Compare it to your required return (the "hurdle rate"): clear the hurdle and it's worth doing.
As the discount rate rises, NPV falls. Where it hits zero = the IRR. Left of it, the project is profitable.
IRR > required return β ACCEPT.
IRR < required return β REJECT.
IRR's weak spots β οΈIRR can mislead with unusual cash-flow patterns (multiple IRRs) or when comparing differently-sized projects. When NPV and IRR disagree, trust NPV β it measures value directly.
7The simple (flawed) one
Payback Period
The most intuitive method: how long until you get your money back? Quick and popular, but it has two big blind spots.
What it isThe time for cumulative cash inflows to recover the initial investment. Shorter = faster recovery = preferred.
Flaw 1Ignores the time value of money (unless you use "discounted payback").
Flaw 2Ignores all cash flows after payback β a project with huge later profits can look worse than a mediocre quick one.
Memory hook π§ Payback answers "when am I made whole?" β a useful liquidity/risk gut-check, but never the sole basis for a decision. NPV is the real judge.
8No reward without it
Risk & Return
Where does the discount rate come from? Risk. Investors demand higher expected returns to bear higher uncertainty β that's the fundamental trade-off behind every r.
Higher risk demands higher expected return β the line every investor climbs by choice.
Two kinds of riskSystematic (market-wide, can't diversify away β recessions, rates) vs unsystematic (company-specific, can be diversified away by holding many assets). Investors are only rewarded for bearing systematic risk.
Memory hook π§ "No free lunch." Want higher returns? You must accept more risk. The only "free" gain in finance is diversification β spreading bets to kill unsystematic risk.
9The company's hurdle rate
Cost of Capital (WACC)
What discount rate should a company actually use? Its own cost of money. A firm is funded by a mix of debt and equity, each with its own cost β the WACC blends them by weight.
Weight each source by its share of total funding, then add. Debt is cheaper (and tax-deductible) but too much adds risk.
Weighted average cost of capital
WACC = (E/V)Β·Re + (D/V)Β·RdΒ·(1 β Tax)
E = equity value, D = debt value, V = E + D. The (1βTax) reflects that interest is tax-deductible β the "tax shield."
Tie it together π§ WACC is the "r" in your NPV. A project is only worth doing if it returns more than the company's blended cost of capital. Next module: capital structure, valuation (DCF) & CAPM build directly on this.
π― Active recall
Cover the answer, say it aloud, then tap to check. The big ones: re-draw the NPV cash-flow diagram and the IRR curve from memory. Revisit today, +3 days, +1 week.
State the time value of money in one sentence.
A euro today is worth more than a euro tomorrow, because today's euro can be invested to earn a return (and future money carries risk).
β¬100 in 2 years at 10% β what's it worth today?
PV = 100 Γ· 1.1Β² = 100 Γ· 1.21 β β¬82.6.
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β What is NPV and its decision rule?
NPV = sum of discounted future cash flows minus the initial investment. NPV > 0 β accept (creates value); NPV < 0 β reject. It's value created in today's money.
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What is the IRR?
The discount rate that makes NPV = 0 β the project's own rate of return. Accept if IRR > required return (hurdle rate).
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When NPV and IRR disagree, which do you trust, and why?
NPV. It measures value directly in currency; IRR can mislead with non-standard cash flows (multiple IRRs) or projects of different sizes.
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Name the two flaws of the payback period.
(1) It ignores the time value of money; (2) it ignores all cash flows after payback is reached.
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Systematic vs unsystematic risk β which is rewarded?
Systematic (market-wide) risk can't be diversified away, so investors are compensated for it. Unsystematic (company-specific) risk can be diversified away, so it earns no premium.
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What is WACC and what's it used for?
The weighted average cost of equity and debt: (E/V)Β·Re + (D/V)Β·RdΒ·(1βTax). It's the company's hurdle rate β the "r" used to discount cash flows in NPV.
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Module 7 of your MBA Β· Phase 2 Β· Re-draw the NPV diagram & IRR curve from memory before moving on. πΈ