The Alaska Purchase On March 29, 1867, William Henry Seward, secretary of state under President...

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.

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Present Value

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.

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Present Value

Discount Factor = DF = PV of $1

Discount Factors can be used to compute the present value of any cash flow.

DFr t

1

1( )

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Valuing an Office Building

Step 1: Forecast cash flows

Cost of building = C0 = 350

Sale price in Year 1 = C1 = 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%

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Valuing an Office Building

Step 3: Discount future cash flows

Step 4: Go ahead if PV of payoff exceeds investment

374)07.1(400

)1(1 r

CPV

24374350 NPV

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Rate of Return Rule

• Accept investments that offer rates of return in excess of their opportunity cost of capital

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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?

14.3%or .143350,000

350,000400,000

investment

profitReturn

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Net Present Value Rule

• Accept investments that have positive net present value

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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?

55.4$1.10

60+-50=NPV

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Constructing a Timeline

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Constructing a Timeline

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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

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Future Value of a Cash Flow

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Present Value of a Cash Flow

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Present Value of a Single Future Cash Flow

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Present Value of a Single Future Cash Flow

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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 = $7,500Present value = $3.37t = 1996 - 1934 = 62 years

• FV = PV x (1 + r)t so,$7,500 = $3.37 x (1 + r)62

(1 + r)62 = $7,500/3.37 = 2,225.52• Solve for r:

r = (2,225.52)1/62 - 1 = .1324 = 13.24%

Future Value of $1000 at 10 Percent

Year Beginning Amount Interest Earned Ending Amount

1 $1,000.00 $100.00 $1,100.00

2 1,100.00 110.00 1,210.00

3 1,210.00 121.00 1,331.00

4 1,331.00 133.10 1,464.10

5 1,464.10 146.40 1,610.50

Total interest $610.50

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Compound Interest

0

5

10

15

20

0 5 10 15 20 25 30

Number of Years

FV

of

$1

10% Simple

10% Compound

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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.