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ECO 550 Assignment 1: Demand Estimation

A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?Answer   The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity.  The periodic interest rate is greater than 3%.  The periodic rate is less than 3%.  The present value would be greater if the lump sum were discounted back for more periods.  The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually.Which of the following statements regarding a 20-year (240-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)Answer   The outstanding balance declines at a slower rate in the later years of the loan’s life.  The remaining balance after three years will be $225,000 less one third of the interest paid during the first three years.  Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.  Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.  The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.Your bank offers a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. If you invest $2,000 in the CD, how much will you have when it matures?Answer   $3,754.27  $3,941.99  $4,139.09  $4,346.04  $4,563.34Of the following investments, which would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.Answer   Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).  Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).  Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).  Investment D pays $2,500 at the end of 10 years (just one payment).  Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 8% is CORRECT?Answer   Exactly 8% of the first monthly payment represents interest.  The monthly payments will decline over time.  A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.  The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.  The amount representing interest in the first payment would be higher if the nominal interest rate were 6% rather than 8%.A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?Answer   The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.  The periodic interest rate is greater than 3%.  The periodic rate is less than 3%.  The present value would be greater if the lump sum were discounted back for more periods.  The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually.Which of the following statements is CORRECT?Answer   The time to maturity does not affect the change in the value of a bond in response to a given change in interest rates.  You hold two bonds. One is a 10-year, zero coupon, bond and the other is a 10-year bond that pays a 6% annual coupon. The same market rate, 6%, applies to both bonds. If the market rate rises from the current level, the zero coupon bond will experience the smaller percentage decline.  The shorter the time to maturity, the greater the change in the value of a bond in response to a given change in interest rates.  The longer the time to maturity, the smaller the change in the value of a bond in response to a given change in interest rates.  You hold two bonds. One is a 10-year, zero coupon, issue and the other is a 10-year bond that pays a 6% annual coupon. The same market rate, 6%, applies to both bonds. If the market rate rises from the current level, the zero coupon bond will experience the larger percentage decline.Which of the following statements is CORRECT?Answer   An indenture is a bond that is less risky than a mortgage bond.  The expected return on a corporate bond will generally exceed the bond’s yield to maturity.  If a bond’s coupon rate exceeds its yield to maturity, then its expected return to investors exceeds the yield to maturity.  Under our bankruptcy laws, any firm that is in financial distress will be forced to declare bankruptcy and then be liquidated.  All else equal, senior debt generally has a lower yield to maturity than subordinated debtWhich of the following statements is CORRECT?Answer   Most sinking funds require the issuer to provide funds to a trustee, who saves the money so that it will be available to pay off bondholders when the bonds mature.  A sinking fund provision makes a bond more risky to investors at the time of issuance.  Sinking fund provisions never require companies to retire their debt; they only establish ‘targets’ for the company to reduce its debt over time.  If interest rates have increased since a company issued bonds with a sinking fund, the company is less likely to retire the bonds by buying them back in the open market, as opposed to calling them in at the sinking fund call price.  Sinking fund provisions sometimes turn out to adversely affect bondholders, and this is most likely to occur if interest rates decline after the bond has been issued.Which of the following statements is CORRECT?Answer   On an expected yield basis, the expected capital gains yield will always be positive because an investor would not purchase a bond with an expected capital loss.  On an expected yield basis, the expected current yield will always be positive because an investor would not purchase a bond that is not expected to pay any cash coupon interest.  If a coupon bond is selling at par, its current yield equals its yield to maturity.  The current yield on Bond A exceeds the current yield on Bond B; therefore, Bond A must have a higher yield to maturity than Bond B.  If a bond is selling at a discount, the yield to call is a better measure of return than the yield to maturity.If its yield to maturity declined by 1%, which of the following bonds would have the largest percentage increase in value?Answer   A 1-year bond with an 8% coupon.  A 10-year bond with an 8% coupon.  A 10-year bond with a 12% coupon.  A 10-year zero coupon bond.  A 1-year zero coupon bond.Which of the following statements is CORRECT?Answer   If a coupon bond is selling at a discount, its price will continue to decline until it reaches its par value at maturity.  If interest rates increase, the price of a 10-year coupon bond will decline by a greater percentage than the price of a 10-year zero coupon bond.  If a bond’s yield to maturity exceeds its annual coupon, then the bond will trade at a premium.  If a coupon bond is selling at a premium, its current yield equals its yield to maturity.  If a coupon bond is selling at par, its current yield equals its yield to maturity.Assume that interest rates on 15-year noncallable Treasury and corporate bonds with different ratings are as follows: T-bond = 7.72% A = 9.64%AAA = 8.72% BBB = 10.18% The differences in rates among these issues were most probably caused primarily by:Answer   Tax effects.  Default risk differences.  Maturity risk differences.  Inflation differences.  Real risk-free rate differencesWhich of the following statements is CORRECT?Answer   If the risk-free rate rises, then the market risk premium must also rise.  If a company’s beta is halved, then its required return will also be halved.  If a company’s beta doubles, then its required return will also double.  The slope of the security market line is equal to the market risk premium, (rM – rRF).  Beta is measured by the slope of the security market line.If you randomly select stocks and add them to your portfolio, which of the following statements best describes what you should expect?Answer   Adding more such stocks will increase the portfolio’s expected rate of return.  Adding more such stocks will reduce the portfolio’s beta coefficient and thus its systematic risk.  Adding more such stocks will have no effect on the portfolio’s risk.  Adding more such stocks will reduce the portfolio’s market risk but not its unsystematic risk.  Adding more such stocks will reduce the portfolio’s unsystematic, or diversifiable, risk.Assume that the risk-free rate is 6% and the market risk premium is 5%. Given this information, which of the following statements is CORRECT?Answer   If a stock has a negative beta, its required return must also be negative.  An index fund with beta = 1.0 should have a required return less than 11%.  If a stock’s beta doubles, its required return must also double.  An index fund with beta = 1.0 should have a required return greater than 11%.  An index fund with beta = 1.0 should have a required return of 11%.Assume that the risk-free rate is 5%. Which of the following statements is CORRECT?Answer   If a stock’s beta doubled, its required return under the CAPM would also double.  If a stock’s beta doubled, its required return under the CAPM would more than double.  If a stock’s beta were 1.0, its required return under the CAPM would be 5%.  If a stock’s beta were less than 1.0, its required return under the CAPM would be less than 5%.  If a stock has a negative beta, its required return under the CAPM would be less than 5%.Which of the following statements is CORRECT?Answer   Diversifiable risk can be reduced by forming a large portfolio, but normally even highly-diversified portfolios are subject to market (or systematic) risk.  A large portfolio of randomly selected stocks will have a standard deviation of returns that is greater than the standard deviation of a 1-stock portfolio if that one stock has a beta less than 1.0.  A large portfolio of stocks whose betas are greater than 1.0 will have less market risk than a single stock with a beta = 0.8.  If you add enough randomly selected stocks to a portfolio, you can completely eliminate all of the market risk from the portfolio.  A large portfolio of randomly selected stocks will always have a standard deviation of returns that is less than the standard deviation of a portfolio with fewer stocks, regardless of how the stocks in the smaller portfolio are selected.Which of the following statements is CORRECT?Answer   The higher the correlation between the stocks in a portfolio, the lower the risk inherent in the portfolio.  An investor can eliminate almost all risk if he or she holds a very large and well diversified portfolio of stocks.  Once a portfolio has about 40 stocks, adding additional stocks will not reduce its risk by even a small amount.  An investor can eliminate almost all diversifiable risk if he or she holds a very large, well-diversified portfolio of stocks.  An investor can eliminate almost all market risk if he or she holds a very large and well diversified portfolio of stocks.Which of the following statements is CORRECT?Answer   The preferred stock of a given firm is generally less risky to investors than the same firm’s common stock.  Corporations cannot buy the preferred stocks of other corporations.  Preferred dividends are not generally cumulative.  A big advantage of preferred stock is that dividends on preferred stocks are tax deductible by the issuing corporation.  Preferred stockholders have a priority over bondholders in the event of bankruptcy to the income, but not to the proceeds in a liquidation.Stocks X and Y have the following data. Assuming the stock market is efficient and the stocks are in equilibrium, which of the following statements is CORRECT?  XYPrice$30$30Expected growth (constant)6%4%Required return12%10%Answer   Stock Y has a higher dividend yield than Stock X.  One year from now, Stock X’s price is expected to be higher than Stock Y’s price.  Stock X has the higher expected year-end dividend.  Stock Y has a higher capital gains yield.  Stock X has a higher dividend yield than Stock Y.A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 10.1%, and the constant growth rate is g = 4.0%. What is the current stock price?Answer   $23.11  $23.70  $24.31  $24.93  $25.57Stocks A and B have the same price and are in equilibrium, but Stock A has the higher required rate of return. Which of the following statements is CORRECT?Answer   Stock B must have a higher dividend yield than Stock A.  Stock A must have a higher dividend yield than Stock B.  If Stock A has a higher dividend yield than Stock B, its expected capital gains yield must be lower than Stock B’s.  Stock A must have both a higher dividend yield and a higher capital gains yield than Stock B.  If Stock A has a lower dividend yield than Stock B, its expected capital gains yield must be higher than Stock B’s.A share of Lash Inc.’s common stock just paid a dividend of $1.00. If the expected long-run growth rate for this stock is 5.4%, and if investors’ required rate of return is 11.4%, what is the stock price?Answer   $16.28  $16.70  $17.13  $17.57  $18.01The required returns of Stocks X and Y are rX = 10% and rY = 12%. Which of the following statements is CORRECT?Answer   If Stock Y and Stock X have the same dividend yield, then Stock Y must have a lower expected capital gains yield than Stock X.  If Stock X and Stock Y have the same current dividend and the same expected dividend growth rate, then Stock Y must sell for a higher price.  The stocks must sell for the same price.  Stock Y must have a higher dividend yield than Stock X.  If the market is in equilibrium, and if Stock Y has the lower expected dividend yield, then it must have the higher expected growth rate.

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