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A firm's bonds have a maturity of 10 years with a \(\$ 1,000\) face value, an 8 percent semiannual coupon, are callable in 5 years at \(\$ 1,050,\) and currently sell at a price of \(\$ 1,100 .\) What are their yield to maturity and their yield to call? What return should investors expect to earn on this bond?

Short Answer

Expert verified
Expect a return based on YTC, approximately 5.75% annually.

Step by step solution

01

Understand Bond Characteristics

This bond has a maturity of 10 years with a face value of $1,000 and offers an 8% annual coupon, paid semiannually. It is callable in 5 years at a price of $1,050.
02

Calculate Semiannual Coupon Payment

The bond pays an 8% annual coupon rate. Since payments are semiannual, divide the rate by 2: \[ 0.08 \times 1000 = 80 \text{ annual coupon} \] \[ \text{Semiannual coupon} = \frac{80}{2} = 40 \]
03

Yield to Maturity (YTM) Calculation

To find the YTM, use the bond price formula, solving for YTM with a financial calculator or trial approach. The bond's price of $1,100 is equal to the present value of future cash flows, discounted by the YTM. Use:\[ 1100 = \sum_{t=1}^{20} \frac{40}{(1+YTM/2)^t}+ \frac{1000}{(1+YTM/2)^{20}} \] Solving gives approximately 6.34% annually.
04

Calculate Yield to Call (YTC)

Compute YTC using the bond's callable feature in 5 years. Assume the bond will be redeemed at the call price of $1,050:\[ 1100 = \sum_{t=1}^{10} \frac{40}{(1+YTC/2)^t}+ \frac{1050}{(1+YTC/2)^{10}} \] Solving provides a YTC of approximately 5.75% annually.
05

Compare YTM and YTC

Since the bond sells above face value, it is more likely to be called at the lower rate, the YTC of 5.75%, compared to the YTM of 6.34%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Yield to Call
When discussing bonds, it's essential to understand the concept of yield to call (YTC). Yield to call refers to the return an investor can expect if a bond is called before it matures at its call date. This often applies to callable bonds, which give the issuer the option to repay the bond before the maturity date. The YTC is calculated similarly to the yield to maturity but stops at the bond's call date instead of its maturity date.
This calculation assumes the bond will be redeemed at its call price, which is typically higher than the face value to compensate for exiting the investment early.

In our example, we computed the YTC using the bond's callable feature in 5 years with a call price of $1,050. The expectation is that if the interest rates drop, the issuer may choose to call the bond to reissue at a lower rate. This makes understanding YTC crucial for investors, particularly those holding premium bonds, as these are more likely to be called.
  • YTC provides insight into potential returns if a bond is called early.
  • Important for callable bonds, which offer issuers flexibility to repay early.
  • Often compared with YTM to assess potential returns.
Bond Valuation
Bond valuation is the technique used to determine the fair value of a bond. A bond's value arises from its future cash flows, which include periodic coupon payments and the repayment of face value at maturity. Investors use bond valuation to decide whether a bond is priced appropriately or if it offers a good return relative to its cost.
The fundamental formula for bond valuation attributes the bond's price to the present value of these future cash flows, discounted by the required rate of return (or yield).

To determine the bond's value, you need to calculate the present value of all future cash inflows, considering the bond's coupon payments and its face value at maturity. This makes understanding bond valuation fundamental for any investor looking to manage risk and optimize returns.
  • Bond valuation involves calculating present value of future cash flows.
  • Helps investors assess if the bond is overpriced or underpriced.
  • Essential for investment strategies and decision-making.
Coupon Rate
The coupon rate of a bond is the annual interest rate paid by the bond's issuer relative to its face value. This rate determines the periodic interest payments that investors will receive, typically fixed and expressed as a percentage.
For example, a bond with a face value of $1,000 and an 8% coupon rate pays $80 annually as interest. If the payments are semiannual, as in our example, each payment is $40.

Understanding the coupon rate is important for estimating consistent income from bond investments. It affects the bond's current yield and aids investors in comparing different bonds with varying rates and payment frequencies.
  • The coupon rate indicates the bond's annual interest payment.
  • Helps estimate expected income from the bond.
  • Useful for comparing efficiency and profitability of various bonds.
Callable Bonds
Callable bonds are a type of bond that allows the issuer to repurchase and retire the bond before its maturity date. This flexibility benefits companies when interest rates decrease, enabling refinancing at lower costs.
A callable bond generally offers a higher yield or coupon rate to compensate investors for the potential short lifespan due to the call option.

Investors must be cautious with callable bonds as they carry reinvestment risk if called early. This means having to reinvest funds at potentially lower rates. Understanding the implications and features of callable bonds is vital for proactive bond management.
  • Callable bonds give issuers the right to repay bonds early.
  • Their appeal is a typically higher yield to offset reinvestment risk.
  • A key consideration is the issuer's intention and interest rate trends.

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Most popular questions from this chapter

Bond \(X\) is non-callable, has 20 years to maturity, a 9 percent annual coupon, and a \(\$ 1,000\) par value. Your required return on Bond \(X\) is 10 percent, and if you buy it you plan to hold it for 5 years. You, and the market, have expectations that in 5 years the yield to maturity on a 15-year bond with similar risk will be 8.5 percent. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.)

Last year Clark Company issued a 10 -year, 12 percent semiannual coupon bond at its par value of \(\$ 1,000\). The bond can be called in 4 years at a price of \(\$ 1,060,\) and it now sells for \(\$ 1,100\). a. What are the bond's yield to maturity and its yield to call? Would an investor be more likely to actually earn the YTM or the YTC? b. What is the current yield? Is this yield affected by whether or not the bond is likely to be called? c. What is the expected capital gains (or loss) yield for the coming year? Is this yield dependent on whether or not the bond is expected to be called?

Six years ago, the singleton Company issued 20 -year bonds with a 14 percent annual coupon rate at their \(\$ 1,000\) par value. The bonds had a 9 percent call premium, with 5 years of call protection. Today, singleton called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Explain why the investor should or should not be happy that singleton called them.

Nungesser Corporation's outstanding bonds have a \(\$ 1,000\) par value, a 9 percent semiannual coupon, 8 years to maturity, and an 8.5 percent YTM. What is the bond's price?

Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8 percent annual coupon rate and were issued 1 year ago at their par value of \(\$ 1,000,\) but due to changes in interest rates, the bond's market price has fallen to \(\$ 901.40 .\) The capital gains yield last year was -9.86 percent. a. What is the yield to maturity? b. For the coming year, what is the expected current yield and the expected capital gains yield? c. Will the actual realized yields be equal to the expected yields if interest rates change? If not, how will they differ?

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