Question

In 2003, Molly bought a 10 -year Treasury note for 1,000 dollars. The market interest rate was 3.5 percent. In 2005, Molly wanted to sell the note to pay for college expenses. Interest rates had risen to 4.5 percent. How would the change in interest rates affect the price that Molly was likely to receive for her note? Give reasons for your answer.

Short answer

The bond's price decreases due to higher interest rates in 2005.

Step-by-step solution

Understanding Present Value of Bonds

The price of a bond is the present value of future cash flows, including annual interest payments and the face value upon maturity. This value is influenced by market interest rates.

Initial Interest Rate Impact

Initially, the market interest rate when the bond was purchased was 3.5%. The bond's coupon payments were likely calculated based on this rate, making the bond attractive at the time of purchase.

Effect of Rising Interest Rates

When interest rates rise, like in 2005 when they increased to 4.5%, new bonds are issued at this higher rate. Molly's bond, with a fixed lower rate of 3.5%, becomes less attractive compared to these new bonds.

Calculation of Price Change

To determine the new price, calculate the present value of the remaining bond payments using the new market interest rate of 4.5%. The calculated price will be lower than the original purchase price, reflecting the bond's decreased attractiveness.

Calculation Example

For simplicity, assume the bond pays annual interest. If the note paid $35 annually (3.5% of $1000), calculate the present value of the remaining interest payments and face value using the new rate of 4.5% discount factor. This reduction in price is due to Molly's bond being less competitive than new ones.

Key concepts

Bond Pricing

Bond pricing is essential to understanding how different bonds compare in the market. The price of a bond is determined by the present value of its future cash flows. These typically include regular interest payments, known as coupon payments, and the face value, or principal, which is paid back at maturity.
When evaluating bond pricing:

• The coupon payments remain constant over the life of the bond.
• Bonds are priced based on the current market interest rates.
• If the market interest rates rise, the price of the bond usually falls because the future fixed payments are less attractive compared to new bonds offering higher rates.

This fluctuation in bond pricing is due to the inverse relationship between bond prices and market interest rates.

Present Value

The concept of present value is central to bond pricing and investment decisions. Present value is the current value of a future amount of money or stream of cash flows given a specified rate of return. It allows investors to assess the value today of cash flows they expect to receive in the future.
In the context of Molly's Treasury note:

• The price she could sell it for is based on the present value of remaining future cash flows, which includes future coupon payments and the bond's face value at maturity.
• Changes in market interest rates alter the discount rate used in present value calculations, affecting the bond's market price.
• A rise in interest rates increases the discount rate, reducing the bond's present value and thus its price.

Understanding present value helps in making informed decisions about when to buy or sell bonds based on expected market interest rate movements.

Treasury Notes

Treasury notes (T-notes) are government debt securities with fixed interest payments and maturity periods typically ranging from two to ten years. T-notes are considered almost risk-free as they are backed by the U.S. government.
Some important aspects of Treasury notes include:

• They pay interest every six months and return the face value upon maturity.
• T-notes are sensitive to changes in market interest rates, as seen in Molly's case, where a rise in rates decreases the attractiveness of older bonds issued at lower rates.
• The security and relative predictability of treasury notes make them appealing to conservative investors.

Even though T-notes are stable, they can still be affected by market conditions, a crucial consideration for investors needing liquidity or preparing for future financial needs.