Bui Thu HienLecturer of Financial Management Department - …



LECTURE 4 PROBLEMS

4.1 Bond value. A Microgates Industries bond has a 10% coupon rate and a &1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12% yield, what is the bond’s value? What is the effective annual yield on the bond?

4.2 Bond Yields. A Macrohard Corp. Bond carries an 8% coupon, paid semi- annually. The par value is $1,000 and the bond matures in six years. If the bond currently sells for $911.37, what is its yield to maturity (YTM)? What is the effective annual yield?

4.3 Coupon rates. Mustaine Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $1,045. At this price, the bonds yield 7.5%. What must the coupon rate be on Mustaine’s bonds?

4.4 Bond Prices. Lifehouse Software issued 11- year bonds one year ago at a coupon rate of 8.6%. The bond makes semiannual payments. If the YTM on these bonds is 7.5%, what is the current bond price?

4.5 Bond Yields. Clapper Corp. Issued 12- year bonds 2 years ago at a coupon rate of 7.8%. The bonds make semiannual payments. If these bonds currently sell for 108% of par value, what is the YTM?

4.6 Bond price movements. Bond X is a premium bond making annual payments. The bond pays a 8% coupon, has a YTM of 6%, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6% coupon, has a YTM of 8% and also has 13 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices vs. time to maturity.

4.7 Interest rate risk. Bond J is a 5% coupon bond. Bond K is an 11% coupon bond. Both bonds have 8 years to maturity, make semiannual payments, and have a YTM of 9%. If interest rates suddenly rise by 2%, what is the percentage price change of these bonds? What if rates suddenly fall by 2% instead? What does this problem tell you about the interest rate risk of lower- coupon bonds?

4.8 Finding the Bond maturity. Massey corp.has 12% coupon bonds making annual payments with a YTM of 9%. The current yield on these bonds is 9.8%. How many years do these bonds have left until they mature?

4.9 Valuing Bonds. The M corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pay $1,000 every six months over the subsequent eight years, and finally pays $1,750 every six months over the last six years. Bond N also has a face value of $ 20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 12% compounded semiannually, what is the current price of Bond M? Of Bond N?

4.10 Holding Period Yield. The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, you realized return is known as the holding period yield (HPY)

a. Suppose that today you buy a 9% coupon bond making annual payments for $1,150. The bond has 10 years to maturity. What rate of return do you expect to earn on your investment?

b. Two years from now, the YTM on your bond has declined by 1%, and you decide to sell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?

4.11 Dividend growth and Stock valuation. The Marko Corporation has just paid a cash dividend of $2 per share. Investors require a 16% return from investment such as this. If the dividend is expected to grow at a steady 8% per year, what is the current value of the stock? What will the stock be worth in five years?

4.12 More dividend growth and stock valuation. If the problem 3.11, what would the stock sell for today if the dividend was expected to grow at 20% per year for the next 3 years and then settle down to 8% per year indefinitely.

4.13 Nonconstant growth. Metallica Inc. is a start- up company. No dividends will be paid on the stock over the next 9 years, because the firm needs to plow back its earnings to fuel growth. The company will pay a $7 per share dividend in 10 years and will increase the dividend by 6% per year thereafter. If the required return on this stock is 14%, what is the current share price?

4.14 Finding the dividend. Ferradi Corp. stock currently sells for $45 per share. The market requires a 12% return in the firm’s stock. If the company maintains a constant 8% growth rate in dividends, what was the most recent dividend per share paid on the stock?

4.15 Valuing preferred stock. RBS bank just issued some new preferred stock. The issue will pay an $8 annual dividend in perpetuity, beginning6 years from now. If the market requires a 6% return on this investment, how much does a share of preferred stock cost today?

4.16 Negative Growth. Toys Co. is a manufacturing company. The firm just paid a $9 dividend, but management expects to reduce the payout by 8% per year. If you require a 14% return on this stock, what will you pay for a share today?

4.17 Supernormal Growth. Supper Growth Corp. is growing quickly. Dividends are expected to grow at a 32% rate for the next 3 years, with the growth rate falling off to a constant 7% thereafter. If the required return is 15% and the company just paid a $2.25 dividend, what is the current share price?

4.18 Capital Gains vs. Income. Consider four different stocks, all of which have a required return of 20% and a most recent dividend of $4.50 per share. Stock W, X and Yare expected to maintain constant growth rates in dividends for the foreseeable future of 10%, 0% and -5% per year respectively. Stock Z is a growth stock that will increase its dividend by 20% for the next 2 years ansd then maintain a constant 12% growth rate thereafter. What is the dividend yield for each of these four stocks? What is the expected capital gains yield? Discuss the relationship among the various returns that you find for each of these stocks?

4.19 Using Stock Quotes. You have found the following stock quote for RJW Enterprises, Inc. in the financial pages of today’s newspaper. What was the closing price for this stock that appeared in yesterday’s paper? If the company currently has two million shares of stock outstanding, what was net income for the most recent four quarters?

YTD% | 52 weeks |Yld | |Vol | |Net | |Chg |Hi |Lo |Stock |Sym |Div. |% |PE |100s |Last |Chg | |34.2 |38.12 |19.92 |RJW |RJW |0.48 |1.3 |51 |10918 |?? |0.95 | |4.20 Stock Valuation. Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in equal quarterly installments to its shareholders.

a. Suppose a company currently pays a $2.50 annual dividend on its common stock in a single annual installment, and management plans on raising this dividend by 8% per year, indefinitely. If the required return on this stock is 14%, what is the current share price?

b. Now suppose that the company in (a) actually pays it annual dividend in equal quarterly installments, thus, this company has just paid a $.625 dividend per share, as it has for the previous three quarters. What is your value for the current share price now?(Hint: Find the equivalent annual end- of- year dividend for each year)

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