Question

Victorian Treasury has issued 20-year bonds that pay semiannual coupons at a rate of 2.135%. The current market rate for similar securities is 3.5%. Assume the bond has a face value of $1000.

a. What is the bond’s current market value?

b. What will be the bond’s price if rates in the market decrease to 1.98%.

c. Refer to your answers in part b. How do the interest rate changes affect premium bonds and discount bonds?

d. Suppose the bonds were to mature in 10 years. How do the interest rate changes in part b affect the bond prices?

Answer 1

A-

Value of abond = sum of present values of all coupon payments and face value repayable at maturity

Value of bond = C *(1- (1/(1+r)^n) / r + FV / (1+r)^n

C = coupon = 1000*2.135% = 21,35 ever 6 months

n = 20*2 = 40

r = market rate =3.5%

FV = face value = 1000

Value of bond = 21.35 *(1- (1/(1+0.035)^40) / 0.035 + 1000 / (1+0.035)^40

= 455.93 + 252.57 = 711.5

B -

If market rate decreases to 1.98% than

Value of bond = 21.35 *(1- (1/(1+0.0198)^40) / 0.0198 + 1000 / (1+0.0198)^40

= 586.09 + 456.46 = 1042.55

C -

• A premium bond is one which is issued when the coupon rate is higher than the market rate of interest (as in part B) 2.135 > 1.98 , Investor pays higher price for such bonds that is ,1042.55
• Adiscount bond is one which is issued when the market rate of interest is higher than the coupon rate ( as in part A ) 3.5 > 2.135. Investor pays lower price for such bonds that is , 711.5

D-

If bond was going to mature in 10 years

n = 10 * 2= 20

Value of bond = 21.35 *(1- (1/(1+0.0198)^20) / 0.0198 + 1000 / (1+0.0198)^20

= 349.77 + 675.62 = 1025.39

As a result of reduced period of bond to half ,the price of the bond has reduced from 1042.55 to 1025.39

Note - Due to no mention of Per annum for both coupon and market rate ,they are assumed to be semi annual rates.