Question

PLEASE SHOW ALL WORKING

For dollar amounts, give your answer to the nearest cent. For interest rates, give our answer as a percentage rounded to 2 decimal places. If any parts of the question use values from earlier parts, use the EXACT values from earlier parts.

QUESTION START

a) Describe the key feature of a zero-coupon bond. (1 mark)

b) “The price of a zero coupon bond should be equal to its face value.” True or false? Explain.

c) “The yield to maturity of a discount bond is greater than its coupon rate.” True or false? Explain.

d) You just purchased a 12-year semi-annual coupon bond with a par value of $1,000 and a coupon rate of 7%. The nominal yield to maturity is 6% per annum. Calculate the market price of the bond.

e) Three years later, immediately after receiving the sixth coupon payment, you sell the bond to your best friend. Your best friend’s nominal yield to maturity is 8% per annum. Calculate the price paid by your best friend.

Answer 1

1.
The bond does not pay any cash flows before maturity i.e, no coupons/interest payments only face value is paid that too at the time of maturity

2.
False, as present value of face value will be less than face value

Present value=Future Value/(1+rate)^t

3.
True, as a bond trades at discount when coupon rate is less than yield or yield is greater than coupon rate

4.

Present value of coupons=Coupon rate*Par value/yield*(1-1/(1+yield/2)^(2*n))=1000*7%/6%*(1-1/1.03^24)=592.7439743

Present value of face value=Par value/(1+yield/2)^(2*n)=1000/1.03^24=491.9337363
Price=Present Value of coupons+Present value of face value=592.7439743+491.9337363
=1084.677711

5.

Present value of coupons=Coupon rate*Par value/yield*(1-1/(1+yield/2)^(2*n))=1000*7%/8%*(1-1/1.04^18)=443.0753941

Present value of face value=Par value/(1+yield/2)^(2*n)=1000/1.04^18=493.628121
Price=Present Value of coupons+Present value of face value=443.0753941+493.628121
=936.7035151