Question

1. Bond X is a premium bond making annual payments. The bond pays an 8 percent coupon, has a YTM of 6 percent, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 13 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13

years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity.

2. Both Bond Twain and Bond Brooks have 6 percent coupons, make semiannual payments, and are priced at par value. Bond Twain has 2 years to maturity, whereas Bond Brooks has 15 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Twain? Of Bond Brooks? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Twain be then? Of Bond Brooks? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

Answer 1

Part a.

We can calculate the prices at different times to maturity using the PV function of Excel or any financial calculator as shown:

If we plot the graph of these values, we get the following plot:

Here we see that the price of bond X which was selling at premium due to YTM higher than coupon rate, starts coming down to par value as it moves towards maturity. On the contrary, the bond Y starts moving up to the par value as it approaches maturity. The reason of this is that, as we move towards maturity, the remaining number of coupon payments decreases. As they are the only source of differential in price, the price starts approaching par value as that becomes more & more significant part of the expected future cash flows from the bond.

Part b.

Here also, we can calculate the different values of prices using the PV function as shown below:

On plotting, we get the following graph (from insert menu -> Line chart in Excel)

Here we can see that the price of Bond brooks (which is a longer term bond) is more sensitive to changes in the Yield to maturity rate as compared to bond Twain which is a short term bond. This phenomena is true in general as short term bond prices are less sensitive to interest rate risks as compared to long term bonds.