Debt valuation problems

DEBT VALUATION PROBLEMS

Problem 1. What is the intrinsic value for a 2 year 5% riskless coupon bond given the following data:

· par value of bond £1,000

· 1 year zero coupon Treasury bill is traded at £90,9

· 2 year zero coupon Treasury bill is traded at £79,7

Determine intrinsic value for a 2 year 5% coupon bond. Demonstrate your strategy (construct an arbitrage portfolio), if current market price for the bond from the first question is 105% of par.

Problem 2.

You are given the following information about bonds:

Bond	Face value	Coupon	Maturity	Price
A	$100	N/A	1 year	$94,34
B	$100	10%	2 years	$103,74
C	$100	9%	3 years	$93,8

Required:

a. Assume that all these bonds make only annual payments. Find the spot rates for all three years.

b. Suppose that the government has decided to issue a three year coupon bond with annual payments and face value of $100. What should the coupon rate be for it to sell at par?

c. One of you clients is interested in a three year zero coupon bond with a face value of $100. Since there is no such a bond on the market, your job is to make a copy of it. Carefully explain your approach and results.

Problem 3. You have been asked to estimate the value of a 3-year bond with a coupon that will be low initially but it is expected to grow later in the bond’s life. The coupon is expected to be 5% of the face value of the bond (which is $ 1000) for the first year, and will increase by 1% each year for the second and third year.

Unfortunately such bonds are not traded on the market, but you could observe four other bonds traded:

Bond	Maturity, years	Coupon, %	Face value, $	Price, $
A				70.84
B				1082.17
C				1018.96
D				95.24

Required:

a. State all assumptions needed to value the bond using given information.

b. Estimate intrinsic value of the bond.

Problem 4.

You observe two 6 year coupon bonds trading on the market. The first bond has a 6% coupon and is currently trading with a 5% discount, while the second 10% coupon bond is trading with a 5% premium. Determine 6 year spot rate.

Problem 5. Suppose that 1 year zero - coupon bonds are now selling for £877.19, and 2 year zero – coupon bonds are now selling at £797.19. Both bonds have face value of £1,000. You are able to trade both types. Suppose that a new project, which will begin in 1 year time, will require capital in the amount of £ 23,000. After discussion, your bank offers to lend you the required money for the project in 12 months with repayment in 24 months at an interest rate of 15%. Carefully explain whether you should accept the bank’s offer. If you don’t accept it, explain how you are going to finance the project.

Problem 6. A T-bill with six-month maturity and $10000 face value sells for $9700. A one-year maturity T-bond paying semiannual coupons of $40 sells for $1000. Find the current six-month spot rate and the forward rate for the following six-month period.

Problem 7. Suppose you bought a 10 year, $1,000 par bond with an 8% coupon at par today. Immediately after buying it, market spot rates (assume, yield curve is flat) rise to 10% and stay permanently. Find your return, if you sell the bond after 3 years. Assume annual coupons.

Problem 8. It is 1996 and you notice that the yields to maturity of your company’s two bond, 5s of 2000 and 9s of 2000, are selling at 87.44 and 100.71 respectively, which results in yields to maturity of 8.87 and 8.78 percent. Your financial manager is puzzled as to why two bonds of the same quality and same maturity do not have the same yield to maturity. You are shocked and thinking about firing him/her. What kind of explanation should he/she give in order to save his/her job? (Assume spot rate for period four periods are 6, 7, 8 and 9 percent).

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