The Alaska Purchase On March 29, 1867, William Henry Seward, secretary of state under President Andrew Johnson and Baron Eduard de Stoeckl, Russian minister to the United States, completed the draft of a treaty ceding Russian North America to the United States, and the treaty was signed early the following day. The price-- $7,200,000--amounted to about two cents per acre. Few Americans, however, viewed the purchase as a bargain, and Seward was vilified in the press. "Seward's Icebox" and "Seward's Folly" were the two most popular names for the Alaska Purchase, and ratification by the the Senate and funding by the House of Representatives seemed in jeopardy as a result of the public outrage. Extensive propaganda campaigns and judicious use of bribes by Stoeckl secured the required votes in each house of Congress. Was this a good or a bad deal for the U.S.? To answer this question, we need to figure out the value of $7, 200,000 today. The answer depends on the time value of money, the subject of this class.

Time Value of Money In the most general sense, time value of money refers to the idea that a dollar in hand today is worth more that a dollar promised sometimes in the future. Why? If I offered you a $100 bill, would you take it? Most people would say “ yes. ” What if I offered you your choice of a $100 bill today or the same $100 bill three years from now? Most people would say “ thanks, I'll take it today. ” What if I offered you your choice of a $100 bill today or $200 three years from now?

Time Value of Money What if I offered you your choice of a $100 bill today or $200 three years from now? Most of us would have to stop and think on this one.

Time Value of Money Somewhere around there is your cost of money, the extra amount you demand if you're going to have to wait to get money. Why do you demand a premium? You don't know what $100 will be worth three years from now. You don't know if I'll make the payment three years from now. You don't know if I'll be here three years from now. You don't know if I'll be alive three years from now. You'd like to take that $100 today, so you can spend it, or invest it, and begin enjoying it. Our usual way of comparing one stream of payments with another is to discount both streams of payments back to their "net present value," using a discount rate that everybody agrees is fair.

4-5 Present Value Value today of a future cash flow. Discount Rate Interest rate used to compute present values of future cash flows. Discount Factor Present value of a $1 future payment.

4-6 Present Value Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of any cash flow.

4-7 Valuing an Office Building Step 1: Forecast cash flows Cost of building = C 0 = 350 Sale price in Year 1 = C 1 = 400 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 7%, then Cost of capital = r = 7%

4-8 Valuing an Office Building Step 3: Discount future cash flows Step 4: Go ahead if PV of payoff exceeds investment

4-9 Rate of Return Rule Accept investments that offer rates of return in excess of their opportunity cost of capital

4-10 Rate of Return Rule Accept investments that offer rates of return in excess of their opportunity cost of capital Example In the project listed below, the foregone investment opportunity is 12%. Should we do the project?

4-11 Net Present Value Rule Accept investments that have positive net present value

4-12 Net Present Value Rule Accept investments that have positive net present value Example Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return?

4-13 Constructing a Timeline

4-14 Constructing a Timeline

4-15 The Three Rules of Time Travel Comparing and Combining Values Moving Cash Flows Forward in Time Moving Cash Flows Back in Time Applying the Rules of Time Travel

4-16 Future Value of a Cash Flow

4-17 Present Value of a Cash Flow

4-18 Present Value of a Single Future Cash Flow

4-19 Present Value of a Single Future Cash Flow

4-20 The Three Rules of Time Travel

In 1934, the first edition of a book described by many as the “bible” of financial statement analysis was published. Security Analysis has proven so popular among financial analysts that it has never been out of print. According to an article in The Wall Street Journal, a copy of the first edition was sold by a rare book dealer in 1996 for $7,500. The original price of the first edition was $3.37. What is the annually compounded rate of increase in the value of the book? Present and Future Values

Set this up as a future value (FV) problem. Future value = $7,500 Present value = $3.37 t = = 62 years FV = PV x (1 + r) t so, $7,500 = $3.37 x (1 + r) 62 (1 + r) 62 = $7,500/3.37 = 2, Solve for r: r = (2,225.52) 1/ =.1324 = 13.24%

Future Value of $1000 at 10 Percent Year Beginning Amount Interest Earned Ending Amount 1 $1,000.00$100.00$1, , , , , , , , , Total interest $610.50

4-24 Compound Interest

4-25 The Power of Compounding This graph illustrates the future value of $1000 invested at a 10% interest rate. Because interest is paid on past interest, the future value grows exponentially—after 50 years, the money grows 117-fold and in 75 years (only 25 years later), it is 1272 times larger than the value today.