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)

No of periods = 20 years * 2 = 40 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (2.135% / 2) * $1000

Coupon per period = $10.675

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

Bond Price = $10.675/ (1 + 3.5% / 2)¹ + $10.675 / (1 + 3.5% / 2)² + ...+ $10.675 / (1 + 3.5% / 2)⁴⁰ + $1000 / (1 + 3.5% / 2 )⁴⁰

Using PVIFA = (1 - (1 + Interest rate)^{- no of periods} / interest rate to value coupons

Bond Price = $10.675 * (1 - (1 + 3.5% / 2)^-40) / (3.5% / 2) + $1000 / (1 + 3.5% / 2 )⁴⁰

Bond Price = $305.24 + $499.60

Bond Price = $804.84

Current Market price = Bond Price = $804.84

b)

Bond’s price if the market interest rates decrease to 1.98%

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

Bond Price = $10.675/ (1 + 1.98% / 2)¹ + $10.675 / (1 + 1.98% / 2)² + ...+ $10.675 / (1 + 1.98% / 2)⁴⁰ + $1000 / (1 + 1.98% / 2 )⁴⁰

Using PVIFA = (1 - (1 + Interest rate)^{- no of periods} / interest rate to value coupons

Bond Price = $10.675 * (1 - (1 + 1.98% / 2)^-40) / (1.98% / 2) + $1000 / (1 + 1.98% / 2 )⁴⁰

Bond Price = $351.18 + $674.32

Bond Price = $1025.50

c)

If market interest rates decrease, Discount bonds & Premium bonds will increase their Bond price. A large decrease in market interest rates can make the Discount bonds to trade as premium bonds

If market interest rates increase, Discount bonds & Premium bonds will decrease their Bond price. A large increase in market interest rates can make the Premium bonds to trade as discount bonds

d)

Bond’s price if the maturity reduces to 10 years & market interest rates decrease to 1.98%

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

Bond Price = $10.675/ (1 + 1.98% / 2)¹ + $10.675 / (1 + 1.98% / 2)² + ...+ $10.675 / (1 + 1.98% / 2)²⁰ + $1000 / (1 + 1.98% / 2 )²⁰

Using PVIFA = (1 - (1 + Interest rate)^{- no of periods} / interest rate to value coupons

Bond Price = $10.675 * (1 - (1 + 1.98% / 2)^-20) / (1.98% / 2) + $1000 / (1 + 1.98% / 2 )²⁰

Bond Price = $192.83 + $821.17

Bond Price = $1014.00