How does information about a firm’s prospects get reflected in its share price?

I.              Summary of Key Equations

Equation	Description	Formula
8.1	Price of a bond
8.2	Price of a bond semiannual compounding
8.3	Price of zero coupon bond	PB = Fmn /(1 + i/m)mn

II.           Before You Go On Questions and Answers

Section 8.1

1.               How does information about a firm’s prospects get reflected in its share price?

Investors act upon the expectations of a firm’s prospects through trading of the securities. The buying and selling then causes the price of the security to reflect their assessment of its value.

2.               What is strong-form market efficiency? semistrong-form market efficiency? weak-form market efficiency?

Strong-form market efficiency is a market in which all information, private and public, is reflected in the price of the security. The semistrong-form of market efficiency suggests that only public information is reflected in a security’s price, while the weak-form market efficiency holds that both public and private information is reflected in the current price of a security, but also both public and private information has not been taken into account.

Section 8.2

1.               What are the main differences between the bond markets and stock markets?

A corporate bond market is much larger than the stock market. The biggest investors in corporate bonds are mutual funds, life insurance companies, and pension funds, and given the size of these investors, the trades are conducted in much larger blocks than in the stock market. Also, while most stocks are traded in organized securities markets, most bonds transactions take place through dealers in the OTC market.

2.               A bond has a 7 percent coupon rate, a face value of $1,000, and a maturity of four years. On a time line, lay out the cash flows for the bond.

The annual payments for the bond will be $70 ($1,000 x 7%); thus the time line for cash inflows would be as follows:

            0                      1                         _2        _______3           _____4

                                    $70                     $70                   $70              $1,070 ($1,000 + $70)

3.               Explain what a convertible bond is.

Convertible bonds are bonds that can be converted into shares of common stock at some predetermined ratio at the discretion of the bondholder. The convertible feature allows the bondholder to take advantage of the firm’s prosperity if the share prices rises above a certain value.

Section 8.3

1.         Explain conceptually how bonds are priced.

The current price of a bond is equal to the present value of all the cash flows that will be received from the investment. There are two sets of cash flows from a bond investment. First, there are the coupon payments to be received either annually or semiannually throughout the life of the bond. Second, there is the principal or face value of $1,000 that will be received when the bond matures. In order to find the price of the bond, we must find the present value of the coupons and the present value of the face value. We do this by discounting the entire cash flow stream at the current market rate and adding them up. This gives us the current price of the bond. Recognize that the coupons represent an annuity and that we can use the equation for the present value of an annuity from Chapter 7 to calculate the present value of this cash flow stream.

2.         What is the compounding period for most bonds sold in the United States?

Most bonds sold in the United States pay interest semiannually, whereas European bonds typically only pay interest once a year.

3.         What are zero coupon bonds, and how are they priced?

Zero coupon bonds are debt instruments that do not pay coupon interest but promise a single payment (interest earned plus principal) paid at maturity. The price of a zero coupon bond can be calculated using the same equation as used for coupon bonds, but setting the coupon payments to zero. The resulting formula is as follows:

                              PB = F_mn/(1 + i/m)^mn

Because zero coupon bonds offer the entire payment at maturity, for a given change in interest rates, their price fluctuates more than coupon bonds with a similar maturity.

Section 8.4

1.         Explain how bond yields are calculated.

A bond’s yield can be defined as the interest rate that equates a bond’s price to the present value of its interest payments and principal amount. The calculation of a bond’s yield, or its yield to maturity, takes into account the bond’s time to maturity, the coupon rate, and par

Section 8.5

1.               What is interest rate risk?

Bond prices are negatively related to interest rate movements. As interest rates rise, bond prices fall, and vice versa. Interest rate risk simply recognizes the fact that bond prices fluctuate as interest rates change, and, if you sell a bond before maturity, you may sell the bond for a price other than what you paid for it. The greater the fluctuation in bond prices due to changes in interest rates, the greater the interest rate risk.

2.               Explain why long-term bonds with zero coupons are riskier than short-term bonds that pay coupon interest.

According to bond theorems number two and three, for a given change in interest rates, longer-term bonds with low coupon rates have greater price changes than shorter-term bonds with higher coupon rates. Thus, long-term zero coupon bonds have greater interest rate risk—greater price swings—than short-term bonds that pay coupon payments.