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∞

Dates as Currencies: Building Net Present Value

Why can't you add yen to pounds, and how does treating each date as its own currency produce net present value?

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Your summary note

1. Adding yen to pounds, and choosing a numeraire
  Record that ¥150 plus £300 is not 450 of anything, convert both ways at the given rates to reach ¥46,050.00 and £300.98, and define a numeraire, noting that either currency can serve.
2. Every date as its own currency
  With date 0 as numeraire, count the currencies and exchange rates $\left(\frac{\text{\textdollar}_t}{\text{\textdollar}_0}\right)$ needed over dates 1 to $T$ , and write $V_0$ as the sum of converted cashflows.
3. The NPV operator and its date-0 cashflow $\text{CF}_0$
  Write the full $V_0$ with $\text{CF}_0$ first, record what “present” and what “net” each capture, and note how $\text{CF}_0$ is converted and signed for an initial investment.
Attempt 1 of 2