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∞

Building the Annuity from Two Perpetuities

How does buying a perpetuity and selling it at date T leave you holding exactly an annuity?

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Your summary note

1. The $T$ -period payment stream and its closed form
  Define an annuity as $C$ each period for $T$ periods, multiply the present-value sum by $(1+r)$ , subtract, and record the resulting $\text{PV} = \frac{C}{r} - \frac{C}{r}\frac{1}{(1+r)^T}$ .
2. Replication with a perpetuity sold at date $T$
  Draw the two perpetuities on one timeline, the second starting at date $T+1$ , show the difference leaves $C$ at dates $1$ through $T$ , and net purchase against resale.
3. The date- $T$ timing convention for the resale
  State that the perpetuity handed over is worth $C/r$ at date $T$ , record that this value discounts over $T$ periods rather than $T+1$ , and write $\frac{C}{r}\frac{1}{(1+r)^T}$ .
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