FIN 3403 Bliss practice problems ch6-8

Moredyk Corporation's bonds have a 15-year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (rd) is 5.30%, based on semiannual compounding. What is the bond's price?

$1,200.05 Explanation: FV=1000 Coupon rate=7.25% Periods=2 Yrs to maturity=15 Periods=15*2=30 Going annual rate=YTM(rd)=5.30% Periodic rate=rd/2=pmt=36.25 PV=1,200.05

Morin Company's bonds mature in 8 years, have a par value of $1,000, and make an annual coupon interest payment of $65. The market requires an interest rate of 6.7% on these bonds. What is the bond's price?

$987.92 Explanation: N=8 I/YR=6.7% PMT=65 FV=1,000 PV=987.92

Kern Corporation's 5-year bonds yield 6.60% and 5-year T-bonds yield 3.40%. The real risk-free rate is r* = 2.5%, the default risk premium for Kern's bonds is DRP = 1.90% versus zero for T-bonds, the liquidity premium on Kern's bonds is LP = 1.3%, and the maturity risk premium for all bonds is found with the formula MRP = (t - 1) 0.1%, where t = number of years to maturity. What is the inflation premium (IP) on all 5-year bonds?

0.50% Explanation: IP=6.60%-2.50%-0.40%=0.50% 0.40% gotten by doing (t-1)*0.1%

Kelly Inc's 5-year bonds yield 7.50% and 5-year T-bonds yield 4.70%. The real risk-free rate is r* = 2.5%, the default risk premium for Kelly's bonds is DRP = 0.40%, the liquidity premium on Kelly's bonds is LP = 2.4% versus zero on T-bonds, and the inflation premium (IP) is 1.5%. What is the maturity risk premium (MRP) on all 5-year bonds?

0.70% Explanation: MRP=4.70%-2.50%-1.50%=0.70%

Bill Dukes has $100,000 invested in a 2-stock portfolio. $32,500 is invested in Stock X and the remainder is invested in Stock Y. X's beta is 1.50 and Y's beta is 0.70. What is the portfolio's beta? Cannot around your intermediate calculations. Round the final answer to 2 decimal places.

0.96 Explanation: 32,500/100,000=0.325=weight of stock x 67,500/100,000=0.675=weight of stock y X beta=1.50 Y beta=0.70 0.325*1.50=0.4875 0.675*0.70=0.4725 0.4875+0.4725=0.96

Suppose the yield on a 10-year T-bond is currently 5.05% and that on a 10-year Treasury Inflation Protected Security (TIPS) is 3.00%. Suppose further that the MRP on a 10-year T-bond is 0.90%, that no MRP is required on a TIPS, and that no liquidity premium is required on any T-bond. Given this information, what is the expected rate of inflation over the next 10 years? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

1.15% Explanation: Expected inflation=r(T10)-r*-MRP 5.05%-3%-0.90%=1.15%

Jim Angel holds a $200,000 portfolio consisting of the following stocks: Stock Investment Beta A $ 50,000 1.70 B 50,000 0.80 C 50,000 1.00 D 50,000 1.20 Total $200,000

1.175 Explanation: 50,000/200,000=0.25 0.25*1.70=0.425 0.25*0.80=0.20 0.25*1=0.25 0.25*1.20=0.30 0.425+0.20+0.25+0.3=1.175

Cheng Inc. is considering a capital budgeting project that has an expected return of 23% and a standard deviation of 30%. What is the project's coefficient of variation? Do not round your intermediate calculations. Round is the final answer to 2 decimal places.

1.30 Explanation: 30%/23%=1.30

Kay Corporation's 5-year bonds yield 7.50% and 5-year T-bonds yield 4.40%. The real risk-free rate is r* = 2.5%, the inflation premium for 5-year bonds is IP = 1.50%, the default risk premium for Kay's bonds is DRP = 1.30% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t - 1) 0.1%, where t = number of years to maturity. What is the liquidity premium (LP) on Kay's bonds?

1.80%

Suppose the real risk-free rate is 3.25%, the average future inflation rate is 4.35%, and a maturity risk premium of 0.07% per year to maturity applies, i.e., MRP = 0.007%(t), where t is the number of years to maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of 1.20% apply to A-rated corporate bonds but not to T-bonds. How much higher would the rate oof return be on a 10-year A-rated corporate bond than on a 5-year Treasury bond? Here we assume that the pure expectations theory is NOT valid. Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

2.05% Explanation: T-bond yield:r(t-bond)=r*+IP+MRP A bond yield:r(Corp)=r*+IP+MRP+DRP+LP T-bond yield=3.25+4.35+0.35=7.95 A bond yield=3.25+4.35+0.70+1.20+0.50=10 Difference=10-7.95=2.05%

McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.)

2.62% Explanation: If held to maturity: N=25 PV=1,250 PMT=90 FV=1,000 I/YR=YTM=6.88% If called in 5 years: N=5 PV=1,250 PMT=90 FV=1,050 I/YR=YTC=4.26 Difference: 6.88-4.26=2.62%

Taggart Inc.'s stock has a 50% chance of producing a 46% return, a 30% chance of producing a 10% return, and a 20% chance of producing a −28% return. What is the firm's expected rate of return?

20.40% Explanation: (50%?*0.46)+(30%*0.10)+(20%*-28%)=0.23+0.03+(-0.056%) =0.204 or 20.40%

5-year Treasury bonds yield 6.1%. The inflation premium (IP) is 1.9%, and the maturity risk premium (MRP) on 5-year T-bonds is 0.4%. There is no liquidity premium on these bonds. What is the real risk-free rate, r*?

3.80% Explanation: r (t-bond)=6.10% IP=1.90% MRP+0.40% LP and DRP=0% r*=6.10%-1.90%-0.40%=3.80%

Adams Enterprises' noncallable bonds currently sell for $1,480. They have a 15-year maturity, an annual coupon of $85, and a par value of $1,000. What is their yield to maturity?

4.14% Explanation: N=15 PV=1,480 PMT=85 FV=1000 I/YR=4.14

If 10-year T-bonds have a yield of 6.2%, 10-year corporate bonds yield 11.9%, the maturity risk premium on all 10-year bonds is 1.3%, and corporate bonds have a 0.4% liquidity premium versus a zero liquidity premium for T-bonds, what is the default risk premium on the corporate bond?

5.30%

Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 2.80%. What rate of return would you expect on a 5-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

5.30% Explanation: r*=2.50% Inlation=2.80% Yield on 5-year T-bond:2.50+2.80=5.30%

Koy Corporation's 5-year bonds yield 11.75%, and 5-year T-bonds yield 5.15%. The real risk-free rate is r* = 3.0%, the inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for Koy's bonds is LP = 0.75% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t - 1) 0.1%, where t = number of years to maturity. What is the default risk premium (DRP) on Koy's bonds?

5.85% Explanation: r=r*+IP+MRP+DP+LP DRP=11.75%-5.15%-0.75%=5.85%

Keenan Industries has a bond outstanding with 15 years to maturity, an 8.25% nominal coupon, semiannual payments, and a $1,000 par value. The bond has a 6.50% nominal yield to maturity, but it can be called in 6 years at a price of $1,085. What is the bond's nominal yield to call?

6.10%

Sadik Inc.'s bonds currently sell for $1,250 and have a par value of $1,000. They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)?

6.28% Explanation: N=5 PV=1,250 PMT=105 FV=1100 I/YR=YTC=6.28% Use "rate" formula in excel.

Suppose the real risk-free rate is 3.50%, the future rate of inflation is expected to be constant at 4.60%. What rate of return would you expect on a 1-year Treasury security? assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

8.10% Explanation: r*=3.50% Inflation=4.60% Yield on a 1-year T-bond=8.10%

Suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 4.20%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years to maturity, hence the pure expectations theory is NOT valid. What rate of return would you expect on a 4-year Treasury security? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

8.80% Explanation: Yield on a t-year T-bond=r*+IPt+MRPt=4.20+4.20+0.80=8.80%

Assume that all interest rates in the economy decline from 10% to 9%. Which of the following bonds would have the largest percentage increase in price?

A 10-year zero coupon bond.

A bond trader observes the following information: -The Treasury yield curve is downward sloping. -Empirical data indicate that a positive maturity risk premium applies to both Treasury and corporate bonds. -Empirical data also indicate that there is no liquidity premium for Treasury securities but that a positive liquidity premium is built into corporate bond yields. On the basis of this information, which of the following statements is most CORRECT?

A 5-year corporate bond must have a higher yield than a 10-year Treasury bond.

Which of the following statements is correct?

All else equal, bonds with larger coupons have less price risk than bonds with smaller coupons.

You have the following data on three stocks: Stock Standard deviation Beta A 20% 0.59 B 10% 0.61 C 12% 1.29 If you are a strict risk minimizer, you would choose Stock________ if it is to be held in isolation and Stock _______ if it is to be held as part of a well-diversified portfolio.

B; A

Which of the following would be most likely to lead to a higher level of interest rates in the economy?

Corporations step up their expansion plans and thus increase their demand for capital.

The CAPM is built on historic conditions, although in most cases we use expected future data and applying it. Because beta is used in the CAPM are calculated using the expected future data, they are not subject to changes in future volatility. This is one of the strengths of the CAPM.

False

The realized return on a stock portfolio is the weighted average of the expected returns on the stocks in the portfolio.

False

The standard deviation is a better measure of risk that the coefficient of variation if the expected returns of the securities being compared differ significantly.

False

The tighter the probability distribution of its expected future returns, the greater the risk of a given investment as measured by its standard deviation.

False

The risk-free rate is 6%; Stock A has a beta of 1.0; Stock B has a beta of 2.0; and the market risk premium, rm-rrf, is positive. Which of the following statements is CORRECT?

If Stock A's required return is 11%, then the market risk premium is 5%.

Assume that a noncallable 10-year T-bond has a 12% annual coupon, while a 15-year noncallable T-bond has an 8% annual coupon. Assume also that the yield curve is flat, and all Treasury securities have a 10% yield to maturity. Which of the following statements is CORRECT?

If interest rates decline, the prices of both bonds would increase, but the 15-year bond would have a larger percentage increase in price.

Short Corp just issued bonds that will mature in 10 years, and Long Corp issued bonds that will mature in 20 years. Both bonds promise to pay a semiannual coupon, they are not callable or corvertible, and they are equally liquid. Further assume that the Treasury yield curve is based only on the pure expectations theory. Under these conditions, which of the following statements is CORRECT?

If the Treasury yield curve is upward sloping and Short has less default risk than Long, then Short's bonds must under all conditions have a lower yield than Long's bonds.

Assume that inflation is expected to decline steadily in the future, but that the real risk-free rate, r*, will remain constant. Which of the following statements is CORRECT, other things held constant?

If the pure expectations theory holds, the Treasury yield curve must be downward sloping.

A 10-year bond pays an annual coupon, its YTM is 8% and it currently trades at a premium. Which of the following statements is CORRECT?

If the yield to maturity remains at 8%, then the bond's price will decline over the next year.

Stock A's beta is 1.5 and Stock B's beta is 0.5. Which of the following statements must be true, assuming the CAPM is correct.

In equilibrium, the expected return on stock A will be greater than that on B.

Which of the following events would make it more likely that a company would call its outstanding callable bonds?

Market interest rates decline sharply.

Assume that the current corporate bond yield curve is upward sloping. Under this condition, then we could be sure that

Maturity risk premiums could help to explain the yield curve's upward slope.

For a portfolio of 40 randomly selected stocks, which of the following is most likely to be true?

The Beta of the portfolio is equal to the weighted average of the betas of the individual stocks.

Tucker Corporation is planning to issue new 20-year bonds. The current plan is to make the bonds non-callable, but this may be changed. If the bonds are made callable after 5 years at a 5% call premium, how would this affect their required rate of return?

The required rate of return would increase because the bond would then be more risky to a bondholder.

If the Treasury yield curve is downward sloping, how should the yield to maturity on a 10-year Treasury coupon bond compare to that on a 1-year T-bill?

The yield on a 10-year bond would be less than that on a 1-year bill.

A bond has a $1,000 par value, makes annual interest payments of $100, has 5 years to maturity, cannot be called, and is not expected to default. The bond should sell at a premium if market interest rates are below 10% and at a discount if interest rates are greater than 10%.

True

Bad managerial judgments or unforeseen negative events that happen to a firm are defined as "company-specific," or "unsystematic," events, and their effects on investment risk can in theory be diversified away.

True

If investors are risk averse and hold only one stock, we can conclude that the required Break of return on a stock whose standard deviation is 0.21 Will be greater than the required return on a stock whose standard deviation is 0.10. However, if stocks are held in portfolios, it is possible that the required return could be higher on the stock with the lower standard deviation.

True

If the pure expectations theory is correct, a downward-sloping yield curve indicates that interest rates are expected to decline in the future.

True

Junk bonds are high-risk, high-yield debt instruments. They are often used to finance leveraged buyouts and mergers, and to provide financing to companies of questionable financial strength.

True

Restrictive covenants are designed primarily to protect bondholders by constraining the actions of managers. Such covenants are spelled out in bond indentures.

True

The four most fundamental factors that affect the cost of money are (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) inflation.

True

The prices of high-coupon bonds tend to be less sensitive to a given change in interest rates than low-coupon bonds, other things held constant.

True

The risk that interest rates will increase, and that increase will lead to a decline in the prices of outstanding bonds, is called "interest rate risk", or "price risk".

True

Which oof the following statements is correct?

You hold two bonds, a 10-year, zero coupon, issue 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.

You have the following data on (1) the average annual returns of the market for the past 5 years and (2) similar information on stocks A and B. Which of the possible answers best describes the historical betas for A and B? Years Market Stock A Stock B 1 0.03 0.16 0.05 2 -0.05 0.20 0.05 3 0.01 0.18 0.05 4 -0.10 0.25 0.05 5 0.06 0.14 0.05

bA<0; bB = 0

Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 9.5% nominal yield to maturity on this investment, what is the price you should be willing to pay for the bond?

$1,000 Explanation: Because the coupon rate and nominal yield are the same, (9.5%), the maximum price will equal the face value.