Question

Week 7 – Question 1 a. Middleton expects to buy a 9.5% coupon, 15 years bond today, when it is first issued by Alex PLC. If interest rates suddenly rise to 12.5%, what happens to the value of Middleton’s bond? Why? (Word limit 20 - 30 words)

b. A corporate bond has a face value of $1 000, a coupon rate of interest of 10.5% per annum, payable semi-annually, and 20 years remaining to maturity. The market interest rate for bonds of similar risk and maturity is currently 8.5% per annum. Required: i. What is the coupon payment of the bond? (1 mark) ii. What is the present value of the bond? iii. If the coupon payment is payable annual (based on the same information), what is the value of the bond?

Answer 1

Q1 :

If the interest rate rises to 12.5% the value of the bond will fall. As the interest rate risk specifies that interst rate and bond value are inversely proportional. ie if the interst rate rises the bond value falls and vice versa. This is measured by duration for bonds. so a higher interest rate means all the cash flows including the coupon and principal value will discounted at higher interest rate and the present values will be lower. Hence a lower bond value .

Q2 :

Coupon on the bond = Coupon rate * face value * 0.5 = 0.105 * 1000 *0.5 = $52.50

Value of the bond = Coupon * PVIFA( R,N) + PVIF (R,N)

PVIFA (R,N ) = { 1 - ( 1+R)^-N }/ R

= { 1 - ( 1+ 0.085/2)^-20*2 } / 0.085/2

= { 1 - ( 1.0425)^-40 } / 0.0425

= 19.07727

PVIF(R,N) = 1 / 1.0425^40 = 0.189216

Value of bond = 52.50 * 19.07727 + 1000 * 0.189216

=1001.557 + 189.2158

=$1190.77

Value of bond if coupon is paid annually = 105* PVIFA ( 8.5%, 20) + 1000* PVIF ( 8.5% ,20)

= 105 * { [ 1 - ( 1.085^-20 ) ] / 0.085 } + 1000 * ( 1 / 1.085 ^20)

= 105* 9.463337 + 1000 * 0.195616

= 993.65 + 195.616

= $1189.27