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Chapter 7: Problem 14

EXPECTED INTEREST RATE Lloyd Corporation's \(14 \%\) coupon rate, semiannual payment, \(\$ 1,000\) par value bonds, which mature in 30 years, are callable 5 years from today at \(\$ 1,050\) They sell at a price of \(\$ 1,353.54\), and the yield curve is flat. Assume that interest rates are expected to remain at their current level. a. What is the best estimate of these bonds' remaining life? b. If Lloyd plans to raise additional capital and wants to use debt financing, what coupon rate would it have to set in order to issue new bonds at par?

Short Answer

Expert verified
a. Bonds are likely expected to be called in 5 years. b. Lloyd should set the coupon rate at around 10%.

Step by step solution

01

Determine Current Yield to Maturity (YTM)

To find the YTM, solve for the interest rate "r" in the bond pricing formula:\[ P = \sum_{t=1}^{60} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^{60}} \]where:- \(P\) is the current price of the bond, \(\\(1,353.54\)- \(C\) is the coupon payment, \(\\)70 = \\(1,000 \times 0.14 / 2\)- \(F\) is the face value, \(\\)1,000\)- 60 is the number of periods (30 years \(\times 2\) for semiannual)Use a financial calculator or a software to numerically solve for "r". The YTM is found to be around 10% annually.
02

Evaluate Expected Call Time or Maturity

Since the bonds are callable in 5 years at \(\$1,050\), we need to compare the yield to call (YTC) and YTM. Calculate the YTC:\[ P = \sum_{t=1}^{10} \frac{C}{(1+YTC)^t} + \frac{1050}{(1+YTC)^{10}} \]Solve numerically to find YTC. If YTC is lower than YTM, it's expected the company will call the bonds. Otherwise, the bond will continue to maturity.
03

Assess Bond Life Expectancy

Given interest rates remain the same, compare YTC to YTM. In general, if YTC < YTM, the bonds are likely expected to be called. Assuming this case and typical rate-wise strategies, they may be called in 5 years if such a lower rate exists.
04

Determine Coupon Rate for New Debt at Par

The coupon rate must equal the current YTM (or market interest rate) for the new bonds to be at par. In this scenario, the closest yield found is around 10%. Thus, Lloyd should set a coupon rate close to 10% to issue new bonds at par.

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Key Concepts

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

Yield to Maturity
The Yield to Maturity (YTM) of a bond is essentially the internal rate of return (IRR) an investor can expect if they hold the bond until it matures. It's a comprehensive measure because it incorporates all future coupon payments and the difference between the bond's purchase price and its face value.

For instance, in the given exercise, to find the YTM, you use the bond pricing formula, which ties the present value of these future cash flows to the bond's current market price. Solving this formula gives you the rate "r" which is around 10% annually for Lloyd Corporation's bond. This rate suggests how this particular bond's value changes with time and is indicative of the interest investors make each year.

YTM is crucial for investors who need to compare bonds of different maturities against each other and against other investment vehicles.
Coupon Rate
The coupon rate of a bond is the amount of interest that the bond issuer will pay to the bondholder every year, based on the bond's face value. It is typically expressed as a percentage.

In the exercise, Lloyd Corporation鈥檚 bonds have a coupon rate of 14%, meaning every year, for a $1,000 bond, holders receive $140. Specifically, since these payments are semiannual, the payments actually occur as $70 every six months.

The coupon rate does not change over the life of the bond, which makes it different from YTM - the coupon rate is based on the bond's initial price, whereas YTM considers the current market price. When issuing new debt, if the company wants to set the bonds at par (i.e., the trading price equals the face value), the new bonds' coupon rate should ideally equal the YTM.
Yield to Call
Callable bonds provide the issuer the right to repurchase the bond at a specified call price before the maturity date. Yield to Call (YTC) is calculated under the assumption that the bond will be called, or redeemed, before reaching maturity. It reflects the total yield including the interest yield if the bond is called early.

In the context of the provided exercise, Lloyd Corporation's bonds are callable in five years at $1,050. To determine the YTC, one would solve for the annualized interest rate that equals the present value of future cash flows to the bond's current market price, considering only a five-year period to call.

If the YTC is lower than the YTM, it makes financial sense for the issuer to call the bond to benefit from lower financing costs. Thus, understanding YTC helps investors evaluate the likeliness and financial implication of an early call.
Callable Bonds
Callable bonds are types of bonds that allow the issuer to repay the principal before the bond's maturity date. This feature is advantageous to issuers when interest rates drop because they can refinance the debt at a lower cost, but it presents reinvestment risk to bondholders.

In the exercise given, Lloyd Corporation's bonds are callable after five years, giving the company flexibility to reduce financing costs if market interest rates decrease. This element might result in higher coupon rates to compensate investors for the additional risk.

Investors in callable bonds must be vigilant. If a bond is called, they might have to reinvest their returns at a lower rate, losing out on planned income. Therefore, understanding the terms and potential outcomes related to callable bonds is essential for both issuers and investors alike.

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Most popular questions from this chapter

BOND VALUATION \(\quad\) You are considering a 10 -year, \(\$ 1,000\) par value bond. Its coupon rate is \(9 \%\), and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of \(8.16 \%\), how much should you be willing to pay for the bond?

BOND VALUATION An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of \(\$ 1,000\), and has a yield to maturity of \(9.6 \%\) Bond C pays a \(10 \%\) annual coupon, while Bond \(Z\) is a zero coupon bond. a. Assuming that the yield to maturity of each bond remains at \(9.6 \%\) over the next 4 years, calculate the price of the bonds at each of the following years to maturity: $$\begin{array}{ccc} \text { Years to Maturity } & \text { Price of Bond } \mathbf{C} & \text { Price of Bond } \mathbf{Z} \\ \hline 4 & & \\ 3 & & \\ 2 & & \\ 1 & & \\ 0 & & \\ \hline \end{array}$$ b. Plot the time path of prices for each bond.

YIELD TO MATURITY AND YIELD TO CALL Kaufman Enterprises has bonds outstanding with a \(\$ 1,000\) face value and 10 years left until maturity. They have an \(11 \%\) annual coupon payment, and their current price is \(\$ 1,175 .\) The bonds may be called in 5 years at \(109 \%\) of face value (Call price \(=\$ 1,090\) ). a. What is the yield to maturity? b. What is the yield to call if they are called in 5 years? c. Which yield might investors expect to earn on these bonds? Why? d. The bond's indenture indicates that the call provision gives the firm the right to call the bonds at the end of each year beginning in Year \(5 .\) In Year \(5,\) the bonds may be called at \(109 \%\) of face value; but in each of the next 4 years, the call percentage will decline by \(1 \% .\) Thus, in Year \(6,\) they may be called at \(108 \%\) of face value; in Year \(7,\) they may be called at \(107 \%\) of face value; and so forth. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?

YIELD TO MATURITY Heymann Company bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a \(\$ 1,000\) par value and a coupon rate of \(9 \%.\) a. What is the yield to maturity at a current market price of (1) \(\$ 829\) and (2) \(\$ 1,104 ?\) b. Would you pay \(\$ 829\) for each bond if you thought that a "fair" market interest rate for such bonds was \(12 \%-\) that is, if \(\mathrm{r}_{\mathrm{d}}=12 \% ?\) Explain your answer.

YIELD TO CALL Six years ago the singleton Company issued 20-year bonds with a \(14 \%\) annual coupon rate at their \(\$ 1,000\) par value. The bonds had a \(9 \%\) 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.
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