Foundations of Finance

01Defining Finance and the Financial System 02Valuation and Management: The Two Challenges 03Stocks, Flows, and the Five Cash-Flow Decisions 04Time, Risk, and the Six Principles of Finance 05How to Learn Finance: Practice and Study Habits Problem set0/10 Problem set 20/10 Practice∞

Present Value

01Information and Price: An Auction and Fannie Mae 02Who Pays for the Fannie and Freddie Guarantee?03What Counts as an Asset: Patents, Secrets, Brands 04An Asset as a Sequence of Dated Cashflows 05The Value Operator and the Cashflow Timeline 06Dates as Currencies: Building Net Present Value 07Discount Factors: Market Prices for Future Dollars 08A Worked Net Present Value and Its Assumptions 09The Opportunity Cost of Capital and Present Value Problem set0/10 Problem set 20/10 MIT problem set0/5 Practice∞

01Does the Currency Change an NPV's Sign?02Moral Hazard and Contagion: Where Bailouts Stop 03The NPV Rule at Work, and Choosing the Rate 04The Perpetuity: Why Cash Forever Is Worth C/r 05Reading the Rate Off a Perpetuity's Price 06The Growing Perpetuity, and When Growth Outruns r 07Building the Annuity from Two Perpetuities 08The Annuity Discount Factor and Mortgage Payments 09APR, the Effective Annual Rate, and Compounding Problem set0/10 Problem set 20/10 MIT problem set0/13 Practice∞

01Leverage: How a 10% Fall Becomes a 200% Loss 02Who Absorbs the Loss: Walking Away, Rate Cuts, Bailouts 03Last in Line: Chapter 11 and How Lehman's Equity Hit Zero 04Inflation vs. Time Value: Wealth and the Price Index 05Real Returns: Match the Discount Rate to the Cashflow Problem set0/10 Problem set 20/10 MIT problem set0/7 Practice∞

Real Returns: Match the Discount Rate to the Cashflow

How can a portfolio gain 10% over the year and leave you exactly as well off as when you started?

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←Previous Inflation vs. Time Value: Wealth and the Price Index

Your summary note

1. Nominal return and deflated real wealth
  Write the nominal return as wealth at $t+k$ over wealth at $t$ minus one, give the real wealth definition $W_{t+k}/(1+\pi)^k$ , and deflate $1,100 at 10% inflation back to $1,000.
2. Exact real return $r_{\text{real}} = \frac{1+r_{\text{nominal}}}{1+\pi}-1$
  Derive it from $(1+r_{\text{real}})^k = \widetilde{W}_{t+k}/W_t$ , record the approximation $r_{\text{real}} \approx r_{\text{nominal}} - \pi$ as a subtraction rather than a division, and work the 15% nominal with 10% inflation case.
3. The NPV matching rule
  State the two-line rule pairing nominal cashflows with nominal rates and real cashflows with real rates, define both kinds of cashflow, and note which kind practice usually hands you.
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