Question

You are considering issuing two types of bonds. The current yield to maturity on similar bonds is 4% annually. Both bonds have a face value of $1000 and will pay annual coupons. Bond A has a maturity of 10 years and bond B has a maturity of 20 years. You want to compute the price of both bonds at the prevailing interest rate and see what happens to the price of the bonds as the interest rate changes. You should consider a range of interest rates starting in 2 % and ending in 7%, with increments of 0.1%. Calculate the price of both bonds at each interest rate and plot the bond prices against the interest rate. What do your results indicate about the interest rate risk of bonds with longer time to maturity?

Answer 1

As the current YTM on similar bonds is 4%, the coupon rate will be 4% for both bonds. This is because the bonds will be issued at par initially, and the coupon rate will equal the current market interest rate (YTM).

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = YTM of bonds = market interest rate

nper = Years remaining until maturity

pmt = -1000 * 4% (annual coupon payment = face value * coupon rate)

fv = -1000 (face value receivable on maturity)

The bond prices at different interest rates (YTM) are calculated below ;

The bond prices vs interest rate are plotted below :

From the table and plot, it is observed that :

• Bond B (longer maturity) has a higher price change than Bond A for an equal change in YTM
• Therefore, it is concluded that bonds with longer maturity have higher interest rate risk