New on FinoLib · Volume II: Capital Markets
I have just published a new article on FinoLib, my free finance education library: Time Value of Money: Formula, Present Value and Valuation. It is part of Volume II: Capital Markets. Below is a summary of the topic in plain, expert language, so you can follow the idea even before you open the full article.
1.1 From Reading Numbers to Valuing Businesses
The idea in plain words
A business is worth the cash it will produce in the future, measured in today’s money. Every valuation method is a different way to estimate that one number. A discounted cash flow, or DCF, builds it from your own forecast. Comparable companies use what the market pays for similar listed firms, like checking the price of similar houses on the street. Precedent deals use what buyers actually paid to take control. Professionals build several, then investigate where they disagree, because the gaps show which assumptions matter.
Key points
■A multiple is a DCF in shorthand: justified P/E = (1 − g ÷ ROE) ÷ (r − g), so 5% growth at a 20% ROE and a 9% cost of equity justifies 18.75x.
■Borrowing a peer’s multiple without its growth and returns can overpay by 50% (18.75x paid versus a justified 12.5x).
■Banks, early-stage, cyclical, distressed and conglomerate businesses each change which method leads and how it is built.
Decision rule
If the business has positive, forecastable cash flows, build the DCF as the anchor and use comps and precedents to test it. If the methods differ by more than about 20%, treat the gap as a question (which input explains it?) rather than averaging it away. If cash flows are negative or unforecastable for more than five years, lead with scenario-weighted DCFs and use multiples as a sanity check; for banks and insurers, switch to equity-level methods. The 20% trigger is a working heuristic, not a standard.
The costliest mistake
Borrowing a multiple without borrowing the economics. Apply the peer’s 18.75x P/E to a target growing 3% with a 12% ROE at the same 9% cost of equity: its justified P/E is (1 − 0.03 ÷ 0.12) ÷ (0.09 − 0.03) = 0.75 ÷ 0.06 = 12.5x. On $100 million of next-year earnings, paying 18.75x means $1,875 million for a business worth $1,250 million on the same formula: a 50% overpayment, hidden because both pay out 75% of earnings. Avoid it by matching growth and returns on capital, not just the industry label builds the peer set).
1.2 The Time Value of Money — The Idea Underneath Everything
The idea in plain words
A dollar today is worth more than a dollar next year, because today’s dollar can be put to work earning a return. To compare cash at different dates, you shrink future money back to today’s value, which is called discounting. The higher the rate and the longer the wait, the more it shrinks. For example, $100,000 due in three years at 10% is worth $75,131 today. Every price in finance, from bonds to businesses, rests on this one idea.
Key points
■An annuity, a perpetuity and a growing perpetuity have one-line formulas: $10,000 a year for 5 years at 8% is worth $39,927; forever, $125,000; growing 2% a year, $166,667.
■The growing-perpetuity formula only works when the discount rate exceeds the growth rate, and it becomes explosive as the two converge.
■Match nominal cash flows with nominal rates: discounting a nominal stream at the real rate turned a $2,000 value into $4,227.
Decision rule
Discount every cash flow at a rate built on the same basis as the cash flow: the same currency, the same inflation treatment (nominal with nominal, real with real), the same compounding period, and a risk premium that matches whose cash it is (the whole firm’s in Section 1.4: The Weighted Average Cost of Capital (WACC), shareholders’ in Section 1.5: CAPM — The Cost of Equity).
The costliest mistake
Mixing nominal cash flows with a real discount rate. A business will pay $100 next year, growing 3% a year in nominal terms; the nominal required return is 8% and expected inflation is 2.5%. The correct value is $100 ÷ (0.08 − 0.03) = $2,000. Discount the same nominal stream at the real rate, 1.08 ÷ 1.025 − 1 = 5.37%, and you get $100 ÷ (0.0537 − 0.03) = $4,227: more than double, from one inconsistency. Avoid it by labeling every forecast and every rate as nominal or real; company forecasts and market yields are almost always nominal.
Recap
Present value discounts a future cash flow by (1 + r)ⁿ; annuities, perpetuities and growing perpetuities extend that to streams, with the growing perpetuity requiring the rate to exceed growth. Rates and cash flows must share the same currency, inflation basis and compounding period, or the answer can more than double.
What the full article covers
In the full article I take you through these sections:
■1.1 From Reading Numbers to Valuing Businesses
■1.2 The Time Value of Money — The Idea Underneath Everything
It includes worked examples, a look under the hood at the mechanics, a clear decision rule, the one mistake that costs people the most, a recap, a reveal-on-click quiz and the official sources behind every figure.
Volume II: Capital Markets
Read the full article on FinoLib
The complete article, Time Value of Money: Formula, Present Value and Valuation, with every worked example, diagram, quiz and source, is free to read in Volume II, Capital Markets on finolib.com.
Explore the Finance Education Series: Vol. II — Capital Markets · Vol. I — Global Economy · Vol. III — Finance Encyclopedia · Vol. IV — Finance Careers · Vol. V — Personal Finance