The Impact of Interest Rate Changes on Bond Prices

Investment Analysis and Management Find the duration of a 3-year bond with annual coupon payments of $80 and a par value of $1,000. The current market price of the bond is $950.25. If the YTM of the bond dropped by 1%, what would happen to the bond price? Answer: First, solve for YTM. PV = -950.25, PMT = 80, FV = 1,000, N = 3, solve for i/y = 10%, which means that YTM= 10% Next, solve for duration: D = 2.78 years; modified duration = D* = 2.53 years Bond price will increase by 2.53%, or the new price is $974.27 Which of the following statements is correct? Answer: a a. You hold two bonds, a 10-year, zero-coupon bond and 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 its current level, the zero coupon bond will experience the larger percentage decline. b. The time to maturity does not affect the change in the value of a bond in response to a given change in interest rates. c. 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. d. 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, other things held constant. e. 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. Which of the following events would make it more likely that a company would call its outstanding callable bonds? Answer: c a. b. c. d. e. The company’s bonds are downgraded. Market interest rates rise sharply. Market interest rates decline sharply. The company's financial situation deteriorates significantly. Inflation increases significantly. Three $1,000 face value, 10-year to maturity, non-callable bonds have the same amount of risk, hence their YTMs are equal. Bond 8 has an 8% annual coupon, Bond 10 has a 10% annual coupon, and Bond 12 has a 12% annual coupon. Bond 10 sells at par. Assuming that interest rates remain constant for the next 10 years, which of the following statements is correct? Answer: d 1 a. Bond 8’s current yield will increase each year. b. Since the bonds have the same YTM, they should all have the same price, and since interest rates are not expected to change, their prices should all remain at their current levels until maturity. c. Bond 12 sells at a premium (its price is greater than par), and its price is expected to increase over the next year. d. Bond 8 sells at a discount (its price is less than par), and its price is expected to increase over the next year. e. Over the next year, Bond 8’s price is expected to decrease, Bond 10’s price is expected to stay the same, and Bond 12’s price is expected to increase. A 12-year bond has an annual coupon of 9%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 7%. Which of the following statements is correct? Answer: c a. If market interest rates decline, the price of the bond will also decline. b. The bond is currently selling at a price below its par value. c. If market interest rates remain unchanged, the bond’s price one year from now will be lower than it is today. d. The bond should currently be selling at its par value. e. If market interest rates remain unchanged, the bond’s price one year from now will be higher than it is today. Which of the following bonds would have the greatest percentage increase in value if all interest rates in the economy fall by 1%? Answer: e a. b. c. d. e. 10-year, zero coupon bond. 20-year, 10% coupon bond. 20-year, 5% coupon bond. 1-year, 10% coupon bond. 20-year, zero coupon bond. 2 Sample Problems for Chapters 12&13 1. Multi-stage growth model If N = 3 years, gs = 30%, gn = 8%, D0 = $1.15, RRR = 13.4%, what should be the value of stock today? What are the expected dividend yield and capital gains yield today? How about in 5 years? Answer: D1 = $1.495 D2 = $1.9435 D3 = $2.52655 D4 = $2.728674 V3 = $50.53 (value of the stock in 3 years, using the constant growth model) V0 = $39.21 (by discounting all the cash flows to the present) Expected dividend yield = D1/V0 = 3.81% Expected capital gains yield = 9.59% In 5 years Dividend yield = 5.4% Capital gains yield = 8% 3 2. A share of XYZ stock is now selling at $40.00. XYZ will pay a cash dividend of $2.00 at the end of the year (D1). The stock has a beta of 0.8. The expected return on the market is 10% and the risk-free rate is 5%. What should be the expected stock price in one year? Answer: expected rate of return = 9% (CAPM) Expected dividend yield = D1/ P0 = 2.00/40 = 5% Expected growth rate = g = 4%, Expected stock price in one year = P1 = $41.60 = 40*(1 + g) 3. Intermediate 12-12, 12-13, and 12-14. 4. A top-down analysis of a firm's prospects starts with an analysis of the _______. Answer: b a. firm's position in its industry b. U.S. economy or even the global economy c. industry d. specific firm under consideration 4. An increase in the value of the yen against the U.S. dollar can cause the Japanese automaker, Toyota, to either _____________ on its U.S. sales. Answer: a a. b. c. d. 5. Which one of the following stocks represents industries with below-average sensitivity to the state of the economy? Answer: c a. b. c. d. 6. lose market share or reduce its profit margin gain market share or reduce its profit margin lose market share or increase its profit margin gain market share or increase its profit margin Financials Technology Food and beverage Cyclicals Which of the following is not an example of fiscal policy? a. b. c. d. Social Security spending Medicare spending Fed purchases of Treasury securities Changes in the tax rate 4 Answer: c 7. In macroeconomic terms an increase in the price of imported oil or a decrease in the availability of oil is an example of a _________. Answer: b a. b. c. d. demand shock supply shock monetary shock refinery shock 8. Intermediate 13-15 and 13-16 9. CFA 13-5 10. An underpriced stock provides an expected return which is ________ the required return based on the capital asset pricing model (CAPM). Answer: c a. b. c. d. 11. The constant growth dividend discount model (DDM) can be used only when the _________. Answer: c a. b. c. d. 12. less than equal to greater than greater than or equal to growth rate is less than or equal to the required return growth rate is greater than or equal to the required return growth rate is less than the required return growth rate is greater than the required return You wish to earn a return of 10% on each of two stocks, A and B. Each of the stocks is expected to pay a dividend of $4 in the upcoming year. The expected growth rate of dividends is 6% for stock A and 5% for stock B. Using the constant growth DDM, the intrinsic value of stock A _______. Answer: a a. b. c. d. will be higher than the intrinsic value of stock B will be the same as the intrinsic value of stock B will be less than the intrinsic value of stock B more information is necessary to answer this question 5 13. The market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. Its expected ROE is 12% and its expected EPS is $5.00. If the firm's plowback ratio is 50%, its P/E ratio will be _________. Answer: b a. b. c. d. 8.33 12.50 19.23 24.15 14. Grott and Perrin, Inc. has expected earnings of $3 per share for next year. The firm's ROE is 20% and its earnings retention ratio is 70%. If the firm's market capitalization rate is 15%, what is the present value of its growth opportunities? Answer: b a. $20 b. $70 c. $90 d. $115 15. Todd Mountain Development Corporation is expected to pay a dividend of $3.00 in the upcoming year. Dividends are expected to grow at the rate of 8% per year. The risk-free rate of return is 5% and the expected return on the market portfolio is 17%. The stock of Todd Mountain Development Corporation has a beta of 0.75. Using the constant growth DDM, the intrinsic value of the stock is _________. Answer: d a. b. c. d. 16. 4.00 17.65 37.50 50.00 Ace Frisbee Corporation produces a good that is very mature in their product life cycles. Ace Frisbee Corporation is expected to pay a dividend in year 1 of $3.00, dividend in year 2 of $2.00, and a dividend in year 3 of $1.00. After year 3, dividends are expected to decline at the rate of 2% per year. An appropriate required return for the stock is 8%. Using the multistage DDM, the stock should be worth __________ today. Answer: a a. b. c. d. $13.07 $13.58 $18.25 $18.78 6 Sample Problems 1. The M2 measure is a variant of ________________. a. b. c. d. Answer: a the Sharpe measure the Treynor measure Jensen's alpha the appraisal ratio The information below applies to the next four questions (2-5) The risk free rate, average returns, standard deviations and betas for three funds and the S&P500 are given below. 2. What is the T2 measure for portfolio A? a. b. c. d. 12.4% 2.38% 0.91% 3.64% 7 Answer: b 3. What is the M2 measure for portfolio B? a. b. c. d. Answer: d 0.43% 1.25% 1.77% 1.43% 4. If those portfolios are subcomponents which make up part of a well diversified portfolio then portfolio ______ is preferred. (Check for T2 measure) Answer: b a. A b. B c. C d. S&P500 5. Based on the M2 measure, portfolio C has a superior return of _____ as compared to the S&P500. Answer: c a. -1.33% b. 1.43% c. 2.00% d. 0.00% The information below applies to the next three questions (6-8) The average returns, standard deviations and betas for three funds are given below along with data for the S&P 500 index. The risk free return during the sample period is 6%. 6. You wish to evaluate the three mutual funds using the Sharpe measure for performance evaluation. The fund with the highest Sharpe measure of performance is __________. Answer: b a. b. c. d. Fund A Fund B Fund C indeterminable 8 7. You wish to evaluate the three mutual funds using the Treynor measure for performance evaluation. The fund with the highest Treynor measure of performance is __________. Answer: b a. b. c. d. 8. You wish to evaluate the three mutual funds using the Jensen measure for performance evaluation. The fund with the highest Jensen measure of performance is __________. Answer: b a. b. c. d. 9. Fund A Fund B Fund C S&P500 Which one of the following is largely based on forecasts of macroeconomic factors? Answer: d a. b. c. d. 10. Fund A Fund B Fund C indeterminable Security selection Passive investing Market efficiency Market timing In creating the T2 measure one mixes portfolio P and T-bills to match the _____ of the market and in creating the M2 measure one mixes portfolio P and T-bills to match the _____ of the market. Answer: c a. b. c. d. alpha; beta beta; alpha beta; standard deviation standard deviation; beta 11. Intermediate 18-6 12. CFA 18-1 and 18-4 9 13. Intermediate 19-5 and 19-13 14. The proper formula for interest rate parity is given by _______. a. b. c. d. 15. (1 + rf(UK))/(1 + rf(US)) = F1/E0 (1 + rf(US))/(1 + rf(UK)) = E0/F1 (1 + rf(US))/(1 + rf(UK)) = F0/E0 (1 + rf(US))/(1 + rf(UK)) = F0/E1 Investor portfolios are notoriously over weighted in home country stocks. This is commonly called ________. Answer: c a. b. c. d. 16. Answer: c local fat patriotism home country bias misleading representation A U.S. insurance firm must pay €75,000 in 6 months. The spot exchange rate is $1.32 per euro and in 6 months the exchange rate is expected to be $1.35. The 6 month forward rate is currently $1.36 per euro. If the insurer's goal is to limit its risk should the insurer hedge this transaction? If so how? Answer: b a. The insurer need not hedge because the expected exchange rate move will be favorable. b. The insurer should hedge by buying euro forward even though this will cost more than the expected cost of not hedging. c. The insurer should hedge by selling euro forward because this will cost less than the expected cost of not hedging. d. The insurer should hedge by buying euro forward even though this will cost less than the expected cost of not hedging. 17. The risk-free interest rate in the US is 8% while the risk-free interest rate in the UK is 15%. If the 1-year futures price on the British pound is $2.40, the spot market value of the British pound today should be __________. Answer: c a. b. c. d. $1.93 $2.22 $2.56 $2.76 10 The information below applies to the next three questions (18-20) Suppose a U.S. investor wishes to invest in a British firm currently selling for ₤50 per share. The investor has $7,000 to invest and the current exchange rate is $1.40/₤. 18. How many shares can the investor purchase? a. b. c. d. 19. 14% 10% 9.3% 7.1% After one year, the exchange rate is $1.60/₤ and the share price is ₤55. What is the dollar-denominated return? Answer: a a. b. c. d. 21. 140 100 71.43 none of the above After one year, the exchange rate is unchanged and the share price is ₤55. What is the dollar-denominated return? Answer: b a. b. c. d. 20. Answer: b 25.7% 16% 14.3% 9.3% The dollar per euro spot rate is 1.2 when an importer of French wines places an order. 6 months later, when she takes delivery, the spot rate is 1.3 dollars per euro. If her original invoice was for 30,000 euro, what is her gain or loss due to exchange rate risk? Answer: b a. b. c. d. $3,000 gain $3,000 loss $6,000 loss no gain or loss 11