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Chapter 8: Problem 9

Six years ago, The singleton Company sold a 20 -year bond issue with a 14 percent annual coupon rate and a 9 percent call premium. Today, singleton called the bonds. The bonds originally were sold at their face value of \(\$ 1,000\). Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.

Short Answer

Expert verified
The realized rate of return is the calculated IRR value from the cash flows.

Step by step solution

01

Identify Initial Details and Facts

The bonds have a coupon rate of 14% annually and they were originally sold at a face value of $1,000. The call premium is 9%, meaning the call price is 109% of the face value. The bonds are called today, six years after they were issued.
02

Calculate the Annual Coupon Payment

The annual coupon payment, which is the interest paid to the bondholders each year, is calculated as 14% of the bond's face value. Therefore, the annual coupon payment is \( 0.14 \times 1,000 = 140 \).
03

Determine the Call Price

The bond is called with a 9% premium on the face value. Therefore, the call price is \( 1,000 + 0.09 \times 1,000 = 1,090 \).
04

Calculate Total Cash Flow Received by Investor

Investors receive six coupon payments of $140 each over six years and the call price when the bond is called. Total cash flow is calculated as: \( 6 \times 140 + 1,090 = 1,930 \).
05

Calculate Realized Rate of Return

The realized rate of return can be calculated by considering the total cash flow received and the initial investment. Using the formula for the internal rate of return (IRR), set up the IRR equation where the cash flow from year 0 (initial investment) is \(-1,000\), and cash flows from years 1 to 6 are \(140\), with the final year's cash flow being \(1,090\). The equation is \(-1,000 = \frac{140}{(1 + r)^1} + \frac{140}{(1 + r)^2} + ... + \frac{140 + 1,090}{(1 + r)^6}\) and solve for \(r\).
06

Solve the IRR Equation for Realized Rate

Solving the above IRR equation yields the realized rate of return (IRR). For the given cash flows, the IRR will be approximately found using a financial calculator or spreadsheet software's IRR function.

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Key Concepts

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

Bond Valuation
Bond valuation is the process used to determine the fair value of a bond. It plays a crucial role in deciding if an investment in bonds is worthwhile.

To value a bond, one needs to calculate the present value of its expected future cash flows. These cash flows usually consist of regular coupon payments and the principal, or face value, which is returned at maturity.

In the case of the Singleton Company bond, its valuation at issue was straightforward since it was sold at face value of $1,000. However, investors must consider different aspects like coupon rate, maturity date, and potential call features.
  • **Coupon Rate:** The interest rate that the bond issuer pays to the bondholders. For Singleton, this was 14% annually.
  • **Face Value:** The amount paid back to the bondholder at maturity. Singleton's bonds had a face value of $1,000.
  • **Call Features:** Bonds may be called before maturity. Investors should assess how a call affects the bond's pricing and yield.
Bond valuation helps investors understand the return on investment considering these elements.
Internal Rate of Return
The Internal Rate of Return (IRR) is a critical concept for assessing investment performance.

It represents the discount rate at which the net present value (NPV) of an investment's cash flows equals zero. In simpler terms, IRR is the single rate of return expected from an investment over its lifespan. For Singleton Company bondholders, calculating the IRR involved analyzing serveral key factors:
  • **Initial Investment:** The amount of money initially spent. Here, that was $1,000.
  • **Cash Flows:** Recurring coupon payments and the call price. Singleton's bondholders received $140 annually and $1,090 when the bond was called.
  • **Time Period:** Over six years until the bond was called.
Determining IRR can be complex, as it involves solving an equation with either mathematical tools like financial calculators or software, which estimate the bond's realized rate of return. Here, the IRR helped investors understand the gain or loss achieved upon calling the bond.
Call Premium
The call premium is an important feature for bondholders. It is the additional amount a bond issuer pays to the bondholder when the bond is called before its maturity date.

In this context, Singleton Company included a 9% call premium on its bonds, meaning bondholders would receive 109% of the face value if the bond were called. The call premium can affect the overall yield and the investor's decision. Here's why it is critical:
  • **Compensation:** Provides compensation to bondholders for the loss of future coupon payments due to early redemption.
  • **Pricing Impact:** Bonds with high call premiums can be priced differently compared to those without, affecting perceived market value and investor attraction.
  • **Yield Consideration:** A higher call premium can increase the yield to call, an important metric when evaluating a callable bond's return.
For Singleton bondholders, the call premium increased the call price to $1,090, impacting the realized rate of return when the bond was called in year six. Understanding the implications of a call premium aids investors in making well-informed bond investment choices.

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Most popular questions from this chapter

A 10 -year, 12 percent semiannual coupon bond, with a par value of \(\$ 1,000,\) may be called in 4 years at a call price of \(\$ 1,060 .\) The bond sells for \(\$ 1,100\). (Assume that the bond has just been issued. a. What is the bond's yield to maturity? b. What is the bond's current yield? c. What is the bond's capital gain or loss yield? d. What is the bond's yield to call?

The Garraty Company has two bond issues outstanding. Both bonds pay \(\$ 100\) annual interest plus \(\$ 1,000\) at maturity. Bond \(L\) has a maturity of 15 years, and Bond \(S\) a maturity of 1 year a. What will be the value of each of these bonds when the going rate of interest is (1) 5 percent, (2) 8 percent, and (3) 12 percent? Assume that there is only one more in terest payment to be made on Bond S. b. Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1-year)?

Nungesser Corporation has issued bonds that have a 9 percent coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of \(\$ 1,000\), and a yield to maturity of 8.5 percent. What is the price of the bonds?

Assume that in February 1970 the Los Angeles Airport Authority issued a series of 3.4 percent, 30 -year bonds. Interest rates rose substantially in the years following the issue, and as they did, the price of the bonds declined. Also, assume in February 1983,13 years later, the price of the bonds had dropped from \(\$ 1,000\) to \(\$ 650 .\) In answering the following questions, assume that the bond requires annual interest payments. a. Each bond originally sold at its \(\$ 1,000\) par value. What was the yield to maturity of these bonds when they were issued? b. Calculate the yield to maturity in February 1983 c. Assume that interest rates stabilized at the 1983 level and stayed there for the remainder of the life of the bonds. What would have been the bonds' price in February \(1998,\) when they had 2 years remaining to maturity? d. What was the price of the bonds the day before they matured in 2000 ? (Disregard the last interest payment. e. In \(1983,\) the Los Angeles Airport bonds were classified as "discount bonds." What happens to the price of a discount bond as it approaches maturity? Is there a "builtin capital gain" on such bonds? f. The coupon interest payment divided by the market price of a bond is called the bond's current yield. Assuming the conditions in part c, what would have been the current yield of a Los Angeles Airport bond (1) in February 1983 and (2) in February 1998? What would have been its capital gains yields and total yields (total yield equals yield to maturity) on those same two dates?

The Heymann Company's bonds have 4 years remaining to maturity. Interest is paid annually; the bonds have a \(\$ 1,000\) par value; and the coupon interest rate is 9 percent. a. What is the yield to maturity at a current market price of (1)\(\$ 829\) or \((2) \$ 1,104 ?\) b. Would you pay \(\$ 829\) for one of these bonds if you thought that the appropriate rate of interest was 12 percent \(-\) that is, if \(\mathrm{k}_{\mathrm{d}}=12 \%\) ? Explain your answer.
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