Soluciones De Finanzas

Principles of Managerial Finance Solution

Lawrence J. Gitman

CHAPTER 6

Interest Rates and Bond Valuation

INSTRUCTOR’S RESOURCES

Overview

This chapter begins with a thorough discussion of interest rates, yield curves, and their relationship to required returns. Features of the major types of bond issues are presented along with their legal issues, risk characteristics, and indenture convents. The chapter then introduces students to the important concept of valuation and demonstrates the impact of cash flows, timing, and risk on value. It explains models for valuing bonds and the calculation of yield-to-maturity using either the trial-and-error approach or the approximate yield formula.

PMF DISK

PMF Tutor: Bond and Stock Valuation

This module provides problems for the valuation of conventional bonds and for the constant growth and variable growth models for common stock valuation.

PMF Problem-Solver: Bond and Stock Valuation

This module's routines are Bond Valuation and Common Stock Valuation.

PMF Templates

Spreadsheet templates are provided for the following problems: Problem Topic

Self-Test 6-1 Bond valuation

Self-Test 6-2 Yield to maturity

Problem 6-2 Real rate of interest

Problem 6-24 Bond valuation–Semiannual interest Problem 6-26 Bond valuation–Quarterly interest

Study Guide

Suggested Study Guide examples for classroom presentation: Example Topic

1 Valuation of any asset

4 Bond valuation

9 Yield to call

ANSWERS TO REVIEW QUESTIONS

6-1 The real rate of interest is the rate which creates an equilibrium between the supply of savings and demand for investment funds. The nominal rate of interest is the actual rate of interest charged by the supplier and paid by the demander. The nominal rate of interest differs from the real rate of interest due to two factors:

(1) a premium due to inflationary expectations (IP) and (2) a premium due to issuer and issue characteristic risks (RP). The nominal rate of interest for a security can be defined as k1 = k* + IP + RP. For a three- month U.S. Treasury bill, the nominal rate of interest can be stated as k1 = k* + IP. The default risk premium, RP, is assumed to be zero since the security is backed by the U.S. government; this security is commonly considered the risk-free asset.

6-2 The term structure of interest rates is the relationship of the rate of return to the time to maturity for any class of similar-risk securities. The graphic presentation of this relationship is the yield curve.

6-3 For a given class of securities, the slope of the curve reflects an expectation about the movement of interest rates over time. The most commonly used class of securities is U.S. Treasury securities.

a. Downward sloping: long-term borrowing costs are lower than short-term borrowing costs.

b. Upward sloping: Short-term borrowing costs are lower than long-term borrowing costs.

c. Flat: Borrowing costs are relatively similar for short- and long-term loans. The upward-sloping yield curve has been the most prevalent historically.

6-4 a. According to the expectations theory, the yield curve reflects investor expectations about future interest rates, with the differences based on inflation expectations. The curve can take any of the three forms. An upward-sloping curve is the result of increasing inflationary expectations, and vice versa.

b. The liquidity preference theory is an explanation for the upward-sloping yield curve. This theory states that long-term rates are generally higher than short-term rates due to the desire of investors for greater liquidity, and thus a premium must be offered to attract adequate long-term investment.

c. The market segmentation theory is another theory which can explain any of the three curve shapes. Since the market for loans can be segmented based on maturity, sources of supply and demand for loans within each segment determine the prevailing interest rate. If supply is greater than demand for short- term funds at a time when demand for long-term loans is higher than the supply of funding, the yield curve would be upward-sloping. Obviously, the reverse also holds true.

6-5 In the Fisher Equation, k = k* + IP + RP, the risk premium, RP, consists of the following issuer- and issue- related components:

 Default risk. The possibility that the issuer will not pay the contractual interest or principal as scheduled.

 Maturity (interest rate) risk: The possibility that changes in the interest rates on similar securities will cause the value of the security to change by a greater amount the longer its maturity, and vice versa.

 Liquidity risk: The ease with which securities can be converted to cash without a loss in value.

 Contractual provisions: Covenants included in a debt agreement or stock issue defining the rights and restrictions of the issuer and the purchaser. These can increase or reduce the risk of a security.

 Tax risk: Certain securities issued by agencies of state and local governments are exempt from federal, and in some cases state and local, taxes, thereby reducing the nominal rate of interest by an amount which brings the return into line with the after-tax return on a taxable issue of similar risk.

The risks that are debt-specific are default, maturity, and contractual provisions.

6-6 Most corporate bonds are issued in denominations of $1,000 with maturities of 10 to 30 years. The stated interest rate on a bond represents the percentage of the bond's par value that will be paid out annually, although the actual payments may be divided up and made quarterly or semi-annually.

Both bond indentures and trustees are means of protecting the bondholders. The bond indenture is a complex and lengthy legal document stating the conditions under which a bond is issued. The trustee may be a paid individual, corporation, or commercial bank trust department that acts as a third-party "watch dog" on behalf of the bondholders to ensure that the issuer does not default on its contractual commitment to the bondholders.

6-7 Long-term lenders include restrictive covenants in loan agreements in order to place certain operating and/or financial constraints on the borrower. These constraints are intended to assure the lender that the borrowing firm will

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