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6- Intertemporal Choice

# 6- Intertemporal Choice - Agenda Course Overview Valuing...

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9/14/2010 1 Agenda Course Overview Valuing Payoff Streams Intertemporal consumption: Saving and Borrowing What To Take Away Microeconomics The Structure of the Course Consumers and Producers Market Interaction Today’s lecture Uncertainty Perfect competition Monopoly and Pricing strategies Competitive Strategy Auctions Information in Markets and Agency Game Theory Introduction to Markets Consumer Theory and Demand Technology and Production

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9/14/2010 2 Agenda Course Overview Valuing Payoff Streams Intertemporal consumption: Saving and Borrowing What To Take Away Would you rather get \$5 dollars every year for the next 5 years or \$10 dollars today? How does one compare streams of future payoffs? Let’s start by comparing two periods. What is the equivalent of \$1 tomorrow? If the interest rate is R I could invest \$1 and receive \$(1+R) tomorrow. Conversely, I can borrow \$1 today under the promise of paying back \$(1+R) tomorrow. We will determine the value of a future payment by discounting them at the interest rate that could be earned. The interest rate R often is given on a yearly basis. How to discount a payment of \$1 in 5 years time? By compounding we get that the Present Discounted Value (PDV) of \$1 in 5 years is How to value different streams of future payoffs? 5 1 (1 ) R
9/14/2010 3 So would you rather get \$5 dollars every year for the next 5 years or \$10 dollars today? It will depend on the interest rate. If the interest rate is R then the present discounted value of the stream of \$5 dollars for the next 5 years is: We can draw this value as a function of the interest rate Example 2 5 5 5 5 ... (1 ) (1 ) (1 ) R R R Interest Rate PDV 0 25 10 0.4 In our case, if the interest rate is below 40% you would rather take the streams of payoffs, while if it is above 40% you would take the \$10 today. As the interest rate increases, \$1 in the future is worth less today A bond is a contract in which a borrower agrees to pay the bondholder (lender) a stream of money. How much would you pay for a bond? Suppose that a bond makes “coupon” payments of \$100 per year for the next 5 years. If the interest rate is R then the present discounted value of the coupon payments is : Since the “coupon” payment is constant we can actually develop a simple formula to compute this. If we multiply the PDV by 1/(1+R) we have Subtracting these two quantities we get

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