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

Coupon Rate is pegged at 4%

Market Interest rates rose to 5%

So the bond will be sold for a discount. The reason is if the market interest rate rises then the value of the bond will decline as the market rates and the price of the bonds are inversely proportional to one another.

Let us suppose that the Par value or the face value of the bond is $1000

Term to Maturity is 30 years

Coupon Rate = 4%

Market Interest Rate = 5%

Value of the bond = Coupon Interest * pvifa (market rates%, no. of years) + Face Value of the bond * pvif (market rates%, no. of years)

Value of the bond = $1000*4%* pvifa (5%, 30yrs) + $1000* pvif (5%, 30yrs)

Value of the bond = $40* pvifa (15.3725) + $1000* (0.2314) = $846.30

As can be clearly seen, the value of the bond is currently selling at $846.30 much lesser than the par value or the face value of the bond. This proves the fact that with the rise in the interest rates value of the bond will be traded at discount.