1. A firm plan to borrow $900 via issuing debt instruments. The firm can issue a simple loan, a fixed-payment loan or a coupon bond.
(1) If the interest rate is fixed at 8%, the face value of the coupon bond is $1000 and the fixed-payment loan has 5 payments. Carefully specify the cash flow schedule of the three potential instruments with the maturity of 5 years.
(2) With the same settings as that in (1), carefully specify the cash flow schedule of the three potential instruments with the maturity of 10 years.
(3) From the lenders' view, among all six instruments from both (1) and (2), which one is more attractive?
2. The Apple company issues a coupon bond with the face value $1000, the coupon rate 7% and the maturity 10 years.
(1) If the interest rate is assumed to be fixed at 8%, what is the present value of the bond?
(2) Instead, people expect that the interest rate will be fixed at 8% until the end of the 5th year (immediately after the 5th coupon payment) and will either jump to 10% or fall to 5% afterwards with equal chances. Calculate the present value of the bond. Hint: Find the value at the end of the 5th year and then the present value.
3. The U.S. government issues a coupon bond with the coupon rate 5% and the maturity 20 years. The bond with a face value of $1000 is sold at a present value of $900. Meanwhile, the Microsoft company issues a coupon bond with the coupon rate 7% and the maturity 20 years. The bond with a face value of $1000 is also sold at a present value of $900.
(1) Calculate the yield to maturity of the two bonds. Are the two bonds sharing the same yield to maturity? Why?
(2) Immediately after the 3rd coupon is paid, the Greece Debt Crisis occurs. Draw a graph to show the influence of the shock. What will happen to the required interest rates of the two bonds? Hint: Apply the theory of portfolio choice.
(3) Assuming the new present value of the U.S. government bond is $1050, calculate the new yield to maturity.
(4) Assuming the new required interest rate for the Microsoft bond is 7%, calculate the new present value.