Question

There is an inverse relationship between bond prices and yields. This inverse relationship will be demonstrated by calculating bond prices to show that interest rates move inversely: if yields rise, then bond prices fall. Bonds will be sold either at a premium or a discount. With this in mind respond to the following question.

You currently own a 30 year Treasury Bond paying a 4% annual coupon rate. The market interest rates for like securities rose to 5%. Would your bond sell for a premium or a discount? Why?

What would the market value of your bond be? Prove your answer by showing your work, the appropriate factors, or the factors that would be used for the fx calculator.

Answer 1

Tenure of the T-Bond = 30 years, Annual Coupon Rate = 4 % and let the bond face value be $ 1000

Annual Coupon Rate = 0.04 x 1000 = $ 40

Applicable Interest Rate = 5 %

The market interest rate is the applicable interest rate and can be considered to be fair required rate of return for investors. However, the coupon rate or the rate of return actually provided by the bond is 4% and is lower than the fair required rate of return. Hence, investors will pay lesser than the bond's face value to buy a bond that provides returns below the fair required rate of return. Therefore, the bond will sell at a discount (to its face value)

Bond Price = Total Present Value of Bond Coupons and Bond Face Value (redeemed at maturity) discounted at the applicable interest rate (prevalent market interest rate)

Bond Price = 40 x (1/0.05) x [1-{1/(1.05)^(30)}] + 1000 /(1.05)^(30) = $ 846.275