Q1: A level-coupon bond and British government consols
Q1 (This question is not cumulative)
a) A level-coupon bond carries a coupon rate of 6 percent, payable semi- annually, has 10 years until maturity, and the yield to maturity is 8 per- cent.
(i) What interest payments do bondholders receive each year? (ii) At what price does the bond sell?
(iii) What will happen to the bond price if the yield to maturity falls to 5 percent?
b) TheBritishgovernment’soutstandingperpetualbondshaveannualcoupon payments of $25, payable annually. The market interest rate today is 3.5 percent, at what price are you willing to buy these consols?
c) A pure discount bond has 10 years until maturity and will pay $1,000 at maturity. If the YTM is 8.5%, what is the current price of this pure discount bond?
Q2 (This question is not cumulative)
a) Suppose a five-year, $1,000 bond with semiannual coupons has a price of $957.35 and yield to maturity of 6%. What is the bond’s coupon rate?
b) Hacker Software has 6.2 percent coupon bonds on the market with nine years to maturity. The bonds make semiannual payments and currently sell for 105 percent of par. What is the yield to maturity on this bond? (Write down the expression for YTM and then use a financial calculator or a spreadsheet program to find the answer. Please write down your answer in the form of x.xx%.)
c) Considerafive-yearbondwith7.5percentannualcoupon,currentlyselling at par. Your estimate of its yield to maturity a year from today is 7.5%. Suppose you plan to sell your bond at the end of one year, right after receiving your coupon payment. What is your expected return on bond investment? Note: You don’t need a calculator to answer this question, if you have sufficient knowledge on bond. Explain how you reach your answer.
Q3 (Textbook Question 6.9) The Faulk Corp. has a 6 percent coupon bond out- standing. The Gonas Company has a 14 percent bond outstanding. Both bonds have 12 years to maturity, make semi-annual payments, and have YTM of 10 percent. If interest rates suddenly rise by 2 percent, what is the percent- age change in the price of these bonds? What is interest rates suddenly fall 2 by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bond?
Q4 Suppose you purchase a ten-year bond with 6 percent annual coupons. You hold the bond for four years, and sell it immediately after receiving the fourth coupon. If the bond’s yield to maturity was 4.5% when you purchased and 7% when you sold the bond. What is your annual rate of return on the bond in each of the following situations:
a) All coupons were immediately spent when received.
b) All coupons were reinvested in a bank account, which pays 2 percent interest until the bond is sold.
a) Ayden Inc.’s common stock has paid a dividend of $3.5 per share per year for the last 12 years. Stock analysts expect it to continue to pay at that amount for the foreseeable future. The current required rate of return for the stock is 11%. What is the current price of the stock?
b) Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5 percent per year indefinitely.
i) What price should the stock sell at? The discount rate is 15 percent.
ii) How would your answer change if the discount rate were only 12 percent? Why does the answer change?
c) (Textbook Question 6.28) Metallica Bearings Inc. is a young start-up company. No dividends will be paid on the stock over the next nine years, because the firm needs to plow back its earnings to fuel growth. The company will pay a $9 per share dividend in 10 years and will increase the dividend by 5.5 percent per year thereafter. If the required return on this stock is 13 percent, what is the current share price?
Q6 Janny Corp. is experiencing rapid growth. Dividends are expected to grow at 30 percent per year during the next three years and then slow down to 8 percent per year, indefinitely. The required rate of return on this stock is 13 percent and the company just paid a $2.40 dividend.
a) What are the expected values of DIV1, DIV2, DIV3, and DIV4? b) What is the expected stock price three years from now?
c) What is the stock price today?
d) Find the dividend yield, DIV1/P0.
e) What will next year’s stock price, P1, be?