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∞

The Perpetuity: Why Cash Forever Is Worth C/r

Why is a claim on a payment every year forever worth only a finite amount, and why exactly C/r?

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Your summary note

1. A claim paying $C$ every year forever
  Define the asset that begins paying $C$ next year and never stops, write out its discounted series $\frac{C}{1+r} + \frac{C}{(1+r)^2} + \cdots$ , and state that the value is finite.
2. Summing the infinite series to $\text{PV} = \frac{C}{r}$
  Multiply the whole series by $(1+r)$ , subtract the original line from it, and carry the cancellation through to $r \times \text{PV} = C$ and then $\text{PV} = \frac{C}{r}$ .
3. Worked values at 10% and at 5%
  Price $100 a year forever at each of the two rates, writing $1,000 and $2,000 on the page, and record the assumption that the interest rate stays constant.
Attempt 1 of 2