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# CH1-4 - CHAPTER 1 3 Assume that the inflation-free rate of...

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CHAPTER 1 3. Assume that the inflation-free rate of interest is 3 percent and that the inflation rate is 10 percent with complete certainty and no taxes. Determine the nominal interest rate. i = nominal rate r = inflation-free rate i = r + p + rp p = inflation rate r = 3%; p = 10%; i = ? i = 0.03 + 0.1 + (0.03)(0.1) i = 0.133 = 13.3% 4. In a world of certainty with no taxes, the nominal interest rate is 10 percent and the inflation-free interest rate is 5 percent. What is the inflation rate? i = 10%; r = 5%; p = ? i = r + p + rp 0.1= 0.05 + p + 0.05p 0.05= 1.05p p = 0.0476 = 4.76% 5. Assume no taxes. Suppose the inflation-free interest rate is 5 percent. The market forecasts a deflation rate of 15 percent. What is the nominal interest rate? r = 5%; p = -15%; i = ? i = r + p + rp i = 0.05 + (-0.15) + 0.05(-0.15) i = -0.1075 = -10.75% *The nominal interest rate cannot be negative; no one will invest at a negative rate.

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CHAPTER 2 4. The Treasury announces an auction of \$10 billion par value of 52-week Treasury bills. \$2 billion of noncompetitive bids are received. The competitive bids are as follows: Price per \$1 of par Par value 0.9200 \$3 billion 0.9194 \$3 billion 0.9188 \$4 billion 0.9180 \$2 billion 0.9180 \$2 billion 0.9178 \$6 billion Compute the price per dollar of par paid by noncompetitive bidders with a one-price auction. How would this price compared to the price paid by noncompetitive bidders with a discriminatory auction? \$10 billion auction \$2 billion on non competitive bids \$8 billion of competitive bids In a one-price auction, everyone would pay .9188. In a discriminatory auction, the noncompetitive bidders would pay 5 .919 = 8 .9188(2) + .9194(3) + .9200(3) 5. The Treasury auctions \$12 billion of 52-week Treasury bills. Three billion dollars of noncompetitive bids are received. The competitive bids are: Price per \$1 of par Par value 0.9200 \$5 billion 0.9180 \$4 billion 0.9170 \$3 billion 0.9160 \$2 billion What is the price paid per dollar of par (to 4 decimals) by noncompetitive bidders with a single-price (Dutch) auction? \$12 billion auction \$3 billion noncompetitive bids \$9 billion competitive bids Everyone would pay .9180.
6. Suppose that the interest rate on taxable Treasury securities is 5 percent and that the tax rate for all investors is 20 percent. What should the interest rate be on a tax-free municipal bond assuming no default risk and no difference in liquidity? y m = y t (1 – t) = 0.05(1 – 0.20) = 0.04 = 4% 7. The interest rate on fully taxable Treasury securities is 4 percent and the interest rate on tax-free municipal bonds is 2.75 percent. What is the tax rate of investors assuming all investors have the same tax rate, no default risk, and no difference in liquidity risk?

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CH1-4 - CHAPTER 1 3 Assume that the inflation-free rate of...

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