Finance, Financial Markets, and NPVFinanceExampleExample cont…Example ConcludedMaintained AssumptionsMoney & TimePresent ValuePresent Value ExamplesThe First PrincipleNet Present ValueNet Present Value ExampleThe Two-Period CaseA Two-period ExampleMulti-period ExamplesSimple vs. Compound InterestThe Present Value of a Series of Future Cash FlowsPresent Value of a Series of Future Cash FlowsMulti-Period NPV ExampleSlide 20Slide 21Slide 22Slide 23Slide 24Valuing Streams of Structured Future Cash FlowsPerpetuityGrowing PerpetuitySlide 28Slide 29AnnuitiesValuing AnnuitiesAnnuity ExampleAnnuity Due ExampleSlide 34Slide 35Growing AnnuitiesSlide 37Slide 38Application: Retirement PlanningRetirement Planning cont…A College Planning Example – Outside ClassCollege Planning cont…Present Value Homework ProblemLeasing vs. Buying a Car – Outside ClassSlide 45Lease vs. Buy cont…Finance, Financial Markets, and NPVFirst PrinciplesFinance•Most business decisions can be looked at as a choice between money now versus money later.•Finance is all about how special markets, the financial markets, help people make themselves better off by moving money across time.•As simple as this sounds, the related concepts seem complex and the markets appear complicated enough to require some introduction.•We will develop the important concept that helps us “keep score” in an honest way while we think about moving money across time.Example•Suppose right now I have $100 but I am not planning to use it until dinner tomorrow.•You on the other hand have the good fortune of having a dinner date tonight but the misfortune of not getting paid until tomorrow. Oh the humiliation. •You offer a solution to the terrible problem.•You suggest I give you the $100 today and tomorrow night you give me $100 back.•This makes you better off by avoiding the humiliation and allowing you to engage in a desired activity, but what about me?Example cont…•One thought is of course that idiot professors don’t really matter in the face of your humiliation. But let’s put that aside for now.•How can we make it so we are both better off and what do we call such an arrangement?•What if you can’t find me or someone as kind and generous?•How can we make the process easier?–Can we keep lots of people from wasting lots of time looking for partners?–Can we balance those who want to borrow and those who want to lend?Example Concluded•Simple as it was our example enabled us to introduce the following fundamental ideas.–Financial market.–Time value of money.–Interest rate (the price in this market).–Financial Intermediaries.–Market clearing.–Equilibrium interest rates.Maintained Assumptions•For the moment, in order to simplify the analysis, we will assume:–Perfect certainty–Perfect capital markets•Information freely available to all participants.•Equal access.•All participants are price takers.•No transactions costs or taxes.–Investors are rational.–We are in a one-period world.•The last assumption will be dropped quickly with the first to follow soon.Money & Time•An important message of the example is that money must be thought of as having two “units.”•Currency ($, £, ¥) is of course the commonly identified unit but time (date received) must also be established before we can determine value.•Example: Your employer offers you a bonus for excellent performance. You may choose between $10,000 today or $12,500 in one year (after the firm does its IPO and has more liquidity).–Compare future values.Present Value•Compare $100 today versus $107 in one year if you can earn 6% interest.•Compare them today instead of in one year.•Rearrange this to find:$ 1 0 0 ( ) $ 1 0 0 ( . ) $ 1 0 61 1 0 6  r i n o n e y e a r$ ( ) $ 1 0 0 ( . ) $ $ 1 0 6t o d a y r t o m o r r o w1 1 0 6   $$( )$ 1 0 6( . )$ 1 0 0$ 1 0 7( . )$ 1 0 0 .t o d a yt o m o r r o wra n d s o t o d a y  1 1 0 6 1 0 69 4Present Value Examples•You just won the new Colorado lottery scratch game. The lottery office offers you $50,000 today or $55,000 if you wait a year. The current interest rate is 7%, what do you do? How much money (present value) will a poor choice cost you?•Your rather odd uncle Ralph has set up a trust in your name that will pay you $1,300,000 in one year. How much can you borrow against this trust if the current interest rate is 9%?The First Principle•The financial markets provide information that enables us to evaluate choices (investment opportunities) both as individuals and as corporations.–An investment opportunity is a way that individuals or firms adjust their consumption (spending) across time.–Since financial markets also represent a way to accomplish this important task we know that:–An investment project can be worth undertaking only if it represents a better option than is available in the financial markets.•Close substitutes provide the basis for comparison.•Lottery example and opportunity costs.Net Present Value•In order to determine whether you are better off making an investment or not we can use the idea of discounting future cash flows and comparing the present value of the future cash in-flows to the current cost. •This is net present value. It is a powerful decision making tool. If NPV is positive what does that tell us? If it is negative?–The interest rate that sets the NPV equal to zero is called the internal rate of return or the yield of the investment. (More on this later.))1(10rCCNPVNet Present Value Example•Do you take a riskless investment that requires $217 to undertake and will payout $230 in one year if the bank is offering you a 5% CD?•NPV: -$217 + $230/1.05 = $2.05 ($, time 0) > 0.•What if you put the $217 in the CD: $217(1.05) = $227.85 so the comparable alternative has a lower future payout.•Comparing directly: $230 - $227.85 = $2.15 ($, time 1).•Note: $2.05(1.05) = $2.15, i.e., the approaches are making exactly the same comparison, NPV does it at time zero. Comparing future values just compares value at time one.The Two-Period Case•One payment two years from now:–We talked about getting cash next year, what if it doesn’t come till two years from now?–One illustration: if is the time 0 value of a cash flow at time 1, is the time 1 value of a time 2 cash payment. We already know how to change a time 1 value to a time 0