Once purchased, bonds can be sold in the secondary market....

Once purchased, bonds can be sold in the secondary market. The value of a bond depends on the prevailing interest rates, which vary over time. Suppose that, in January, 1982 , you bought a 30 -year zero coupon U.S. Treasury bond with a maturity value of $$\$ 100,000$$ and a yield of $15 \%$ annually. a. How much did you pay for the bond? b. In January 1999, your bond had 13 years remaining until maturity. Rates on U.S. Treasury bonds of comparable length were about $4.75 \%$. If you sold your bond to an investor looking for a return of $4.75 \%$ annually, how much money would you have received? c. Using your answers to parts (a) and (b), what was the annual yield on your 17 -year investment?

Once purchased, bonds can be sold in the secondary market. The value of a bond depends on the prevailing interest rates, which vary over time. Suppose that, in January, 1982 , you bought a 30 -year zero coupon U.S. Treasury bond with a maturity value of $$\$ 100,000$$ and a yield of $15 \%$ annually.
a. How much did you pay for the bond?
b. In January 1999, your bond had 13 years remaining until maturity. Rates on U.S. Treasury bonds of comparable length were about $4.75 \%$. If you sold your bond to an investor looking for a return of $4.75 \%$ annually, how much money would you have received?
c. Using your answers to parts (a) and (b), what was the annual yield on your 17 -year investment?

Key Concepts

Zero Coupon Bonds

Zero coupon bonds are debt securities that do not pay periodic interest. Instead, they are issued at a discount to their face (maturity) value and mature at par, with the difference between the purchase price and the maturity value representing the investor’s return. This structure simplifies calculations because the overall return is determined by the appreciation from the discounted price to the full face value at maturity.

Discounting and Present Value

Discounting refers to the process of determining the present value of a future sum of money by applying a specific rate of return. This concept is central in finance as it reflects the time value of money—the idea that a dollar received today is worth more than a dollar received in the future. In bond valuation, discounting future cash flows, such as the maturity value, allows investors to calculate the price they are willing to pay today for the bond.

Yield to Maturity

Yield to maturity (YTM) is the internal rate of return earned by an investor who buys a bond at its current market price, holds it until maturity, and receives all scheduled payments. YTM is critical because it accounts for the total returns over the life of the bond, including any capital gains or losses that result from purchasing the bond at a discount or premium relative to its face value.

Secondary Market Pricing

Secondary market pricing involves the valuation of bonds when they are traded after their initial issuance. This price is influenced by changes in prevailing interest rates and the remaining time until maturity. When interest rates fluctuate, the bond’s price adjusts so that its yield aligns with the current market rates, ensuring that the bond remains competitive relative to similar available instruments.

Interest Rate Risk

Interest rate risk is the potential for loss due to changes in the prevailing interest rates that affect the price of fixed-income securities such as bonds. As interest rates rise, the present value of future cash flows such as a bond's maturity value decreases, leading to a decline in the bond's market price; conversely, when interest rates fall, bond prices typically increase. This sensitivity to rate fluctuations is a fundamental risk consideration for bondholders.

Time Value of Money

Time value of money is a foundational principle in finance that postulates money available now is worth more than the same amount in the future due to its potential earning capacity. This principle underpins the discounting process used when calculating present values of future cash flows from bonds, making it integral to the pricing and investment decision-making process in fixed-income markets.

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