lecture 12 - Economics 310 Money and Banking Lecture11...

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Economics 310 Money and Banking Lecture 11 University of  Michigan Fall 2010  
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2 Lecture 1 Reading Bond Market and Interest Rates Chapters 4 and 5 Results and Answer Keys will be posted later today Exam
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3 Lecture 1 The coupon bond The coupon bond is just the same as the deposit account specified above, where P = price of the bond V = face value of the bond W = regular coupon payment = c V c = “coupon rate” n = term to maturity
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4 Lecture 1 The coupon bond V = P(1+i) n – W(1+i) (n-1) – W(1+i) (n-2) – ... – W(1+i) – W = P(1+i) n – cV(1+i) (n-1) – cV(1+i) (n-2) – ... – cV(1+i) – cV Divide both sides by (1+i) n and rearrange: P = cV/(1+i) + cV/(1+i) 2 + … + cV/(1+i) n + V/(1+i) n The price of the bond is the discounted value of all payments made to the bond holder
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5 Lecture 1 Example:  The Coupon Bond Suppose Face value: V = $1000 Term to maturity: n = 2 Coupon rate: c = 0.1 Yearly coupon payments: cV = $100 Price: P = $1000 P = cV/(1+i) + cV/(1+i) 2 + V/(1+i) 2 1000 = 100/(1+i) + 100/(1+i) 2 + 1000/(1+i) 2 i = 0.1 (10%) Observe: If you deposit P = $1000 into the bank at 10% interest, you can withdraw $100 at the end of the first and the second years, and still have $1000 in the bank.
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6 Lecture 1 A Special Case  On a coupon bond: If P = V, then i = c Intuition: Think of the bank account that is equivalent to this bond. If P = V, then the amount of money in the account does not grow. That means all interest earned is withdrawn each period. Since the price of the bond and the interest rate are inversely related If P > V, then i < c If P < V, then i > c
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7 Lecture 1 Pricing bonds Given: Relationship between bond price and interest rate Information about the interest rate the bond must deliver E.g. an equilibrium condition implied by interest rates on substitute assets we can price a given bond P = cV/(1+i) + cV/(1+i) 2 + … + cV/(1+i) n + V/(1+i) n
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8 Lecture 1 Pricing bonds Consider the following coupon bond: Face value: V = $2000 Term to maturity: n = three years Coupon rate: 0.06 i.e. coupon payments are $120 each year A perfectly substitutable asset offers an interest rate of 5% i.e. in equilibrium, the coupon bond must also offer i =0.05 P = cV/(1+i) + cV/(1+i) 2 + cV/(1+i) 3 + V/(1+i) 3 = $120/(1.05) + $120/(1.05) 2 + $120/(1.05) 3 +$2000/(1.05) 3 = $2054.46 Note: P > V is implied since i < c
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