Question

1. Omega Enterprises has an 8% coupon bond with exactly 16 years to maturity. Interest is paid semi-annually. The bond is priced at $1,125 per $1,000 of face value. a.) What is the yield to maturity on this bond? b.)An investor purchased the bond at $1,125 and sold it 5 years later at a price of $1,023. What was the investor’s return. (Hint: calculate the YTM as in a) above but use the sale price as the future value.

2. Alpha Corporation has a bond outstanding with the following characteristics:

Par Value                                 $1,000

Years to maturity                9

Yield to maturity                6.2%

Coupon payments             Semi-annual

Coupon rate                          6%

What is the bond’s price?     

3. A zero coupon bond has a maturity date exactly 16 years away. It currently sells at a price to yield 4.5%. The yield to maturity on the bond suddenly increases to 5.1%. Calculate a.) its price before the rate increase, b.) its price after the rate increase, and c.) the percentage change?  

4. Delta Corporation has a 15 year 5% coupon bond with par value of $1,000 and a price of $1,088.37. The company wants to issue a new 15 year coupon bond at par. What coupon rate does the company need to offer? (Interest is payable semiannually on both bonds. Assume that for both bonds, the next coupon payment is exactly 6 months away.)         

5. A 30 year 6% coupon bond has annual payments and a yield to maturity of 4.55. The bond has a par value of $1,000. a.)What is the value of the bond? b.) What is the present value of the 30 coupon payments? c.) What is the present value of the principal payment? (a is equal to b +c)

6. A convertible bond with a par value of $1,000 has a conversion ratio of 40. The bond is currently approaching maturity and the company’s stock price is $29.50. a.) Would you convert? b.) Why?

Answer 1

1) a. Bond Price can be calculated using I/Y function on a calculator

N = 16 x 2 = 32, PMT = 8% x 1000 / 2 = 40, PV = -1125, FV = 1000

=> Compute I/Y = 3.36% (semi-annual)

YTM = 3.36% x 2 = 6.71%

b. N = 5 x 2 = 10, PMT = 40, PV = -1125, FV = 1023

=> Compute I/Y = 2.76%

Annualized returns = 2.76% x 2 = 5.51%

2) Bond Price can be calculated using PV function

N = 9 x 2 = 18, I/Y = 6.2%/2, PMT = 6% x 1000 / 2 = 30, FV = 1000

=> Compute PV = $986.36

3) a. Current Price, PV = FV / (1 + r)^n = 1,000 / (1 + 4.5%)^16 = $494.47

b. New Price PV = FV / (1 + r)^n = 1,000 / (1 + 5.1%)^16 = $451.19

c. % Change = 451.19 / 494.47 - 1 = -8.75%